text:
# mercury

properties
[ Xe ] 4 f 14 5 d 10 6 s 2
80 ed
General
Name , symbol , atomic number Mercury, Hg, 80
Element category Transition metals
Group , period , block 12 , 6 , d
Appearance silvery white
CAS number 7439-97-6
EC number 231-106-7
ECHA InfoCard 100.028.278
ATC code
Mass fraction of the earth's envelope 0.4 ppm
Atomic
Atomic mass 200,592 (3) and
Atomic radius (calculated) 150 (171) pm
Van der Waals radius 155 pm
Electron configuration [ Xe ] 4 f 14 5 d 10 6 s 2
1. Ionization energy 10.437 504 (6) eV 1 007.07 kJ / mol
2. Ionization energy 18th.75687 (4) eV1 809.76 kJ / mol
3. Ionization energy 34.49 (5) eV3 325 kJ / mol
4. Ionization energy 48.55 (15) eV4 684 kJ / mol
5. Ionization energy 61.20 (20) eV5 905 kJ / mol
Physically
Physical state liquid
density 13.5459 g / cm 3 at 293.15K
Mohs hardness not applicable
magnetism diamagnetic ( Χ m = −2.8 10 −5 )
Melting point 234.32 K (−38.83 ° C)
boiling point 630.2 K (357 ° C)
Molar volume (solid) 14.09 · 10 −6 m 3 · mol −1
Heat of evaporation 58.2 kJ / mol
Heat of fusion 2.37 kJ mol −1
Vapor pressure 0.163 Pa at 293 K.
Speed of sound 1407 m s −1 at 293.15 K.
Specific heat capacity 140 J kg −1 K −1
Work function 4.49 eV
Electric conductivity 1.04 · 10 6 A · V −1 · m −1
Thermal conductivity 8.3 W m −1 K −1
Chemically
Oxidation states 1, 2 , 4
Normal potential 0.8535 V (Hg 2+ + 2 e - → Hg)
Electronegativity 2.00 ( Pauling scale )
Isotopes
isotope NH t 1/2 ZA ZE (M eV ) ZP
196 ed 0.15% Stable
197 ed {syn.} 64.14 h ε 0.600 197 Au
198 ed 9.97% Stable
199 ed 16.87% Stable
200 Hg 23.1% Stable
201 ed 13.18% Stable
202 ed 29.86  % Stable
203 ed {syn.} 46.612 d β - 0.462 203 Tl
204 ed 6.87% Stable
205 ed {syn.} 5.167 min β - 1.531 205 Tl
206 ed in traces 8.15 min β - 1.308 206 Tl
For other isotopes see list of isotopes
NMR properties
Spin
quantum
number I
γ in
rad · T −1 · s −1
E r  ( 1 H) f L at
B = 4.7 T
in MHz
199 ed 1/2 4.846 · 10 7 0.001 17.91
201 ed 3/2 -1.789 · 10 7 0.0002 6.61
safety instructions
GHS hazard labeling from  Regulation (EC) No. 1272/2008 (CLP) , expanded if necessary

danger

H and P phrases H: 330-360D-372-410
P: 201-273-304 + 340-308 + 310
MAK

Switzerland: 0.005 ml m −3 or 0.05 mg m −3

Toxicological data
As far as possible and customary, SI units are used.
Unless otherwise noted, the data given apply to standard conditions .

Mercury ( ancient Greek ὑδράργυρος Hydrargyros , liquid silver ', derived from Latin h ydrar g yrum ( Hg ), so named by Dioscurides ; Latin argentum vivum and mercurius ; English mercury and quicksilver ) is a chemical element with the symbol Hg and the ordinal number 80 Although it has a closed d-shell , it is often counted among the transition metals . In the periodic table it is in the 2nd subgroup or the 12th  IUPAC group , which is also called the zinc group . It is the only metal and, besides bromine, the only element that is liquid under standard conditions. Due to its high surface tension, mercury does not wet its inert base, but rather forms lenticular drops because of its strong cohesion . Like any other metal, it is electrically conductive.

## etymology

Ampoule with drops of mercury

Mercury originally means "bold silver", i. H. fast - cf. English quick - or moving or living silver (from ahd. quëcsilabar , quëchsilper , mhd. quëcsilber , këcsilber to Germanic kwikw , [quick] lively ') as a translation of synonymous (middle) Latin argentum vivum , "living silver", z. B. Pliny .

Sulfur alcohols are known as mercaptans (“mercury scavengers”) because they can react with mercury to form mercury sulfides.

## history

Alchemy symbol

Mercury has been known at least since ancient times. It is mentioned in the works of Aristotle , Theophrastus of Eresus , Pliny the Elder, and other writers of antiquity. From ancient times to the 20th century it was used as a medicinal product (due to its toxicity , which was first reported by the doctor and empiricist Herakleides of Taranto , but with corresponding negative consequences).

In ancient times, mercury was obtained by rubbing cinnabar with vinegar or by heating cinnabar using a sublimation process. Vitruvius was already familiar with the alloy of mercury with gold. This was used for fire gilding objects, whereby the mercury evaporated. In the 5th century AD, the sublimate ( mercury (II) chloride ) was known as a mercury compound . Paracelsus was the first doctor who made precipitates and basic mercury salts and used them as remedies. From the 16th century onwards, mercury became economically important because it was needed to extract silver from silver ores through amalgam formation .

Mercury was used medicinally in ancient times and the Middle Ages.

At the end of the 19th century, mercury was considered a suitable drug against gynecological problems , which is why it was sometimes administered in toxic quantities.

From the end of the 15th to the beginning of the 20th century, mercury preparations such as the gray mercury ointment or asurol were widely used to treat syphilis (most recently also in combination with arsenic compounds such as arsphenamine ; see also organic biometallic chemistry ). For a mercury cure , the mercury was usually applied to the skin, injected, or occasionally even inhaled, which in many cases resulted in symptoms of poisoning. Syphilis was considered a popular disease and allusions to the symptoms of syphilis and the associated mercury poisoning can be found in many literary works of the time.

Metallic mercury was used to treat intestinal obstruction during the same period . The patient ingested several kilograms of metallic mercury orally in order to overcome the obstacle in the intestine. If he survived the treatment, the metal would naturally leave his body with no further symptoms of intoxication.

In the past, mercury (I) chloride was used both externally, for example against corneal spots or genital warts, and often internally and until the 1990s as a spermicide in the form of vaginal suppositories for contraception . In the past, almost all Merfen preparations, including lozenges, had the organic mercury compound phenyl mercury borate , which was discovered to be effective around 1951, as an active ingredient , whereas today these are all mercury-free. Also antiseptic worked Merbromin in approved only to 2003 Mercurochrom .

The Dutch physicist Heike Kamerlingh Onnes discovered the phenomenon of superconductivity in mercury for the first time in 1911 . Below 4.183 Kelvin (−268.967 ° C), the electrical resistance disappears completely. The proximity to the boiling point of helium contributed to the discovery, but it is purely coincidental.

In ancient Greece, mercury symbolized both the god Hermes and the associated planet . This was later adopted by the Romans and the alchemists for the equated god Mercurius . Therefore, in Latin mercurius and in English mercury, both the name for mercury and for the planet and god. As an alternative term for the metal, quicksilver is also used in English .

Mercury was used in alchemy to refine metals. For example, the addition of mercury to copper should produce silver. The aim was also to solidify the mercury, the fixatio mercurii , for example (described in the 15th century by Hans Kluge) by physico-chemical treatment of a mixture of mercury with vitriol to which other additives such as tartar, saltpeter and glass powder were added.

For the medieval alchemists, mercury, sulfur and salt were the three basic elements. The unicorn symbolized the mercury.

## Occurrence

Mercury pearl on cinnabarite

Mercury occurs naturally in its pure form and is the only liquid substance that has traditionally been recognized as a mineral by the IMA . Mercury is also a companion mineral in hard coal .

There are mercury deposits in Serbia , Italy , China , Algeria , Russia and Spain, among others . It is mostly found as a mineral in the form of cinnabar (HgS) in areas with former volcanic activity. Mercury is also less common than normal . The largest cinnabar deposits on earth are located near the Spanish town of Almadén . Production ended in 2003 and the Almadén mine was converted into a visitor mine . Far rarer mercury minerals are Montroydit (HgO), Paraschachnerit , Schachnerit , Eugenit , Luanheit and moschellandsbergite (all AGHG). Another mineral is Belendorffit (CuHg).

Large amounts of mercury are also bound in the frozen biomass of the permafrost soils in the northern hemisphere. About twice as much mercury is stored in these as in all other soils, the atmosphere and the oceans combined. If the permafrost is thawed more intensely, as is expected due to man-made global warming , biological degradation processes would start, through which the mercury is possibly released into the environment, where it can be. a. could harm arctic ecosystems, aquatic life in the oceans, and human health.

Mercury is traditionally traded in metal barrels (English " flask ") of 76 pounds (34.473 kg) and quoted on the commodities exchange in the unit "FL" = flask.

Due to the long atmospheric lifespan of elemental mercury of several months to a year, emissions into the air lead to a median air concentration of 1.2 to 1.8 ng / m 3 in the northern hemisphere and around, which is relatively constant over the entire earth's atmosphere 1.0 ng / m 3 in the southern hemisphere .

## Extraction and presentation

Pure mercury is obtained by allowing the mercury ore cinnabar (HgS) to react with oxygen (roasting process) . The reaction products are elemental mercury and sulfur dioxide :

${\ displaystyle \ mathrm {{} HgS \ + O_ {2} \ longrightarrow {} Hg + SO_ {2}}}$

Worldwide, around one million tons of metallic mercury has been extracted from cinnabar and other ores over the past five centuries. About half of this occurred before 1925 (as of 2000).

## properties

Mercury at room temperature

Mercury is a silver-white, liquid heavy metal . It is sometimes still counted among the precious metals , but is much more reactive than the classic precious metals (e.g. platinum , gold ), which are in the same period. It forms alloys with many metals, the so-called amalgams . Mercury is a poor conductor of electricity compared to other metals. Apart from the noble gases, it is the only element that is monatomic in the gas phase at room temperature.

With a density of 13.5 g / cm 3, mercury is around 13.5 times as dense as water , so that, according to Archimedes' principle, its carrying capacity is also 13.5 times as high; thus an iron cube (density 7.9 g / cm 3 ) also floats in mercury. Recently carried out Monte Carlo simulations show that the density of mercury is also subject to relativistic effects. Non-relativistic calculations would suggest a density of 16.1 g / cm 3 .

### conductivity

The metal bond in mercury is created by delocalized electrons. These electrons occupy certain, discrete energy levels in bands that are created by the broadening of atomic states through interaction. There is no periodic structure in liquid metals like mercury . Therefore the quasi-pulse is not a good quantum number and the electronic band configuration cannot be represented in the Brillouin zone , as is usual for solid metals. Due to the Pauli principle , the electrons gradually fill up the energy states, only the conduction band remains incompletely occupied. The electrons in this band are delocalized and form the electron gas . The electrical conductivity can also be explained classically by these electrons.

### Physical state

The answer to the question of why mercury is liquid at room temperature can be found in the consideration of the bond between the mercury atoms. First of all, mercury has a very special electron configuration. As an element of the 12th group of the PSE , mercury atoms have completely filled s and d atom orbitals , which means a very stable and energetically favorable constellation. The conduction band is thereby empty. In the case of the lighter homologues zinc and cadmium , which are in the same group of PSE as mercury, but are solid at room temperature, the energetic difference between the valence band and the conduction band is so small that electrons can easily jump from the valence band to the conduction band, creating a metal bond comes about.

The peculiarity of mercury lies in the 4f orbital, which is completely filled with 14 electrons. Due to the lanthanide contraction and the relativistic effect , there is an increase in mass and a less efficient shielding of the nuclear charge. Only recently it was possible to demonstrate using a Monte Carlo simulation that the melting point anomaly of mercury is actually due to relativistic effects. Without relativistic effects, a melting point would be expected that would be 105 K higher than that observed experimentally.

Occupied orbitals are thereby drawn closer to the nucleus, as is the valence band of mercury. However, unoccupied orbitals such as the conduction band are not shifted towards the core, which leads to a particularly large energy difference between the valence and conduction band, which is significantly lower for zinc and cadmium. Hardly any electrons can leave the valence band and reach the conduction band, which makes the metal bond unusually weak. This also explains the volatility and the poor conductivity of mercury, which is atypical for metals.

### Melting point

Transition temperature from α-mercury to the liquid phase
Melting point
(° C)
Pressure
( MPa )
dT / dp
(K / GPa)
0−38.8344 0000.10 51.78
013.7500 1013.25 49.84
241.8500 6079.50 42.44

### boiling point

Transition temperature from α-mercury or liquid mercury into the gaseous phase
Temperature
(° C)
Vapor pressure Remarks Quel-
le
(Pa) (Torr)
−63.6800 0.000 001 7
−57.7200 0.000 006 5
−56.8400 0.000 006 9
−49.8500 0.000 031 6
−43.4000 0.000 097 5
−42.7700 0.000 100 0
−41.7600 0.000 114 0
−38.8344 0.000 165 0 Triple point
0, 0000 0.046 700 0 0.000350
10, 0000 0.103 000 0 0.000775
20th, 0000 0.242 000 0 0.001820
30th, 0000 0.543 000 0 0.004070
50, 0000 2, 000 000 0
75, 0000 9, 000 000 0
100, 0000 37, 000 000 0
125, 0000 129, 000 000 0
126.2000 130, 000 000 0 1, 000000
150, 0000 383, 000 000 0
164.8000 670, 000 000 0 5, 000000
204.6000 2,660, 000 000 0 20th, 000000
242, 0000 8,000, 000 000 0 60, 000000
260.6750 13,060, 000 000 0
290.7000 26,700, 000 000 0 200, 000000
300.4600 33.293, 000 000 0
323, 0000 53,300, 000 000 0 400, 000000
340.7360 75,568, 000 000 0
357, 0000 101,325, 000 000 0 760, 000000 Boiling temperature under normal conditions
396.9100 200,000, 000 000 0
460.2600 500,000, 000 000 0
517.0500 1,000,000, 000 000 0
583.5500 2,000,000, 000 000 0
691.6500 5,000,000, 000 000 0
794.8500 10,000,000, 000 000 0
923.8500 20,000,000, 000 000 0
1151.8500 50,000,000, 000 000 0
1365.8500 100,000,000, 000 000 0
1476.9000 174,000,000, 000 000 0 Critical point (end of vapor pressure curve)

## Isotopes

A total of 34 isotopes and 9  nuclear isomers with mass numbers from 175 to 208 are known of mercury  . Seven of these isotopes are stable (with mass numbers 196, 198, 199, 200, 201, 202 and 204). Of the radioactive isotopes, only 194 Hg has a relatively long half-life with 444 years (520 years according to more recent data). The other isotopes and core isomers only have half-lives between 1.1 milliseconds and 46.612 days.

## use

### thermometer

Compared to other liquids, the thermal expansion of mercury is just under an order of magnitude lower, but in the range between 0 ° C and 180 ° C it only shows about 2 percent linearity errors:

${\ displaystyle V (\ theta) = V_ {0} \ left (1 + 1 {,} 82 \ cdot 10 ^ {- 4} {\ frac {\ theta} {^ {\ circ} \ mathrm {C}} } +7 {,} 8 \ cdot 10 ^ {- 9} {\ frac {\ theta ^ {2}} {^ {\ circ} \ mathrm {C} ^ {2}}} \ right).}$

In addition, mercury does not wet glass and is easy to detect visually. It is therefore suitable for use in liquid thermometers and contact thermometers . As an outdoor thermometer in very cold regions, however, it can only be used to a limited extent due to its melting point (−38.83 ° C).

Due to its high toxicity , its use is nowadays limited to the scientific field; Depending on the temperature range, mercury can partly be replaced by colored fillings made of alcohol, petroleum, propylene carbonate, pentane, toluene, creosote, isosamyl benzoate, hydrogenated mineral oil or Galinstan as well as by electronic thermometers.

The first usable mercury thermometer was developed by Daniel Gabriel Fahrenheit around 1720 . A thermometer contains an average of 150 mg of mercury. In a clinical thermometer , the amount can be up to 1 g. This corresponds roughly to a bead with a diameter of 5.2 mm.

Since April 3, 2009, the placing on the market of new mercury-containing clinical thermometers, barometers and blood pressure monitors has been prohibited within the EU; This does not apply to measuring devices for scientific or medical use as well as old and used devices.

### Pressure gauge / barometer

Pressure gauge with mercury column

The classic design of a manometer (“differential pressure meter”) is a U-tube, the ends of which are connected to the two pressure atmospheres via lines. To this day, mercury is widely used as a pressure gauge liquid. The advantages of mercury are: high density, the non-wetting of glass and the negligible vapor pressure. Mercury is colorless but opaque.

The simplest and oldest design of the barometer is a stable, one-sided closed glass tube with an inner diameter of about 4–6 mm, which is filled to the brim with mercury with the closed end facing down, then closed with the thumb, turned upside down and with the thumb under the mercury level in a wide, half-full cup is dipped before the thumb releases the opening below.

The mercury column in the pipe only drops until the force of the air pressure outside the pipe and the weight of the mercury in the pipe are in equilibrium . At normal pressure (1 atmosphere) this is 760 mm "column of mercury". The old specification in the Torr unit for air pressure corresponds to the height of the mercury column in millimeters, 1 mm of mercury column corresponds to 133.21  Pascal .

### counter

Mercury switch

Due to its electrical conductivity and the very high surface tension (0.476 N / m at 20 ° C), mercury is ideal for use as a contact material in the mercury switches previously used . Because of the problem with the disposal of electronic scrap, the use of mercury in switches has been prohibited in most areas of application in the EU (" RoHS " directive) since 2005 . In special applications, contacts wetted with mercury are still used today in order to achieve particularly low contact resistances or to prevent the contacts from bouncing (e.g. Hg relays).

Thanks to gravity, mercury tilt switches work similarly to the spirit level on a spirit level; A movable drop of mercury in a curved or straight glass tube opens and closes the electrical contact between two metal pins melted into the glass, depending on the inclination. Such tilt switches are sometimes found in old staircase light timers , in thermostats of hot water storage tanks , in pressure switches of house water pumps and as rumble protection in washing machines . In the previously used turbo inverters , a mercury beam was used as a circling "switch finger".

Early wandering writing systems were based on spring contacts, including perforated tape and a mercury bath.

### Mercury vapor lamps

Visible part of the mercury spectrum. The purple line is barely visible to the eye. Particularly strong lines are in the (left) subsequent invisible UV.
Hg gas discharge tube

Mercury is in discharge vessels ( mercury vapor lamps ) of gas discharge lamps ( fluorescent lamps , " energy saving ", the cold cathode tubes mercury vapor pressure and -höchstdrucklampen, sun lamp , quartz lamp , so-called. " Black light ") are used.

### amalgam

Mercury forms with many other metals spontaneously alloys , the amalgams are mentioned. Amalgams are z. B. used as a dental filler . A mixture of mercury and powder of metals such as silver can be pressed into a drilled opening in the tooth for a period of time and soon hardens to form amalgam. While tooth material shrinks over the years due to bacterial-chemical attack, amalgam has the tendency to expand plastically as a metal due to high chewing pressure and the side effect of inhibiting the growth of bacteria. If a piece of aluminum foil is pressed firmly onto an amalgam filling while chewing - possibly accidentally, as is typical of chocolate packaging - a galvanic element is formed and a corresponding electrical direct current flows, which is perceived as an unpleasant metallic stimulus in the tooth nerve.

In March 2017, a regulation was passed in the European Parliament that significantly restricts the use of amalgam. From July 2018, young people under the age of 15 as well as pregnant and breastfeeding women are no longer allowed to receive dental fillings made of amalgam. Basically, from then on, premixed mixtures must also be used in order to keep the mercury content optimal. Amalgam separators are then also required in the ordination sewage system. A study should clarify by 2020 whether amalgam should be completely banned from dentistry by 2030. Restrictions were also imposed on the industrial use of mercury.

Since mercury destroys the protective oxide skin of the aluminum through aluminum amalgam formation, carrying mercury-containing devices (e.g. clinical thermometers) on aircraft is not prohibited, but limited according to the IATA Dangerous Goods Regulations (1 piece / passenger and must be in a protective cover - DGR 2.3 ). Mercury is assigned to dangerous goods class 8 - corrosive materials . There is a corrosive effect in connection with almost all metals, u. a. Zinc, Magnesium and Aluminum, which are used in aircraft construction. Liquid mercury has an embrittling effect on aluminum and aluminum alloys through liquid metal embrittlement .

### Disinfectants and pickling agents

In the wound disinfectant mercurochrome , the active ingredient was an organic mercury salt. The mercuchrome iodine solution available today is a povidone iodine solution. In Merfen , another disinfectant, formerly phenylmercuric was included. HgCl 2 ( sublimate ) was previously used as a disinfectant in hospitals. Thimerosal is an organic mercury compound that is used in very low concentrations as a bactericide to preserve vaccines.

Conventional agriculture uses mercury compounds as a dressing agent for seeds . This has been banned in Germany since 1984. In Iraq , there was mass poisoning from 1971–1972 as a result of the consumption of seeds.

Mercury (II) chloride was previously used as a disinfectant and pickling agent as well as for wood preservation and corpse preservation.

### electrolysis

In terms of quantity, mercury played a major role in the production of caustic soda and chlorine by chlor-alkali electrolysis using the amalgam process . During the electrolysis , the reduced sodium metal is transferred as an amalgam, a sodium-mercury alloy, into a separate cell, the decomposer, in order to prevent the formation of the explosive chlorine gas and the undesired sodium monooxochlorate (sodium hypochlorite) in the electrolysis cell. A large part of the German and European facilities working with the amalgam process are currently being converted to alternative, mercury-free processes (membrane processes) in order to reduce mercury emissions.

### Gold washing

One process of gold mining uses mercury to loosen the fine gold dust , creating gold amalgam (see amalgamation ). Since mercury becomes liquid at low temperatures, it forms alloys that melt particularly easily. During washing and subsequent annealing to recover pure gold, the mercury is released into the environment. This is the main reason for the high level of environmental pollution from this type of gold mining (see also environmental emissions, below ). Alternatives to the amalgam process should be promoted. The gold for the German river gold ducats minted from the 17th to the 19th centuries was removed or cleaned by amalgamation in order to melt it.

In the past, silver was also extracted in this way in the Harz Mountains .

### art

It is said that there were rivers of mercury in the tomb of the first Chinese emperor Qin Shihuangdi . The soil in the area has been scientifically examined and found an unnaturally high mercury content. But this alone is no proof of the correctness of the legend.

Mexican archaeologists have found liquid mercury below the temple pyramid of Quetzalcoatl in Teotihuacán . The researchers suspect that it is the ritual representation of the Maya underworld river - comparable to the ancient Greek Styx.

The American artist Alexander Calder built a mercury fountain in 1937 to commemorate those who died from mercury mining. Around the year 1000 there were pools filled with mercury in the palaces of the caliphs of Cordoba ( Medina az-Zahra ), Cairo and Baghdad , which were used to play with the effects of light, as well as mercury ponds set in large porphyry shells (for Cairo, 50 cubits are in Square, i.e. approx. 26 m × 26 m).

Fire gilding was used for a long time in handicrafts . As with gold mining, the easy amalgam formation and thermal separation of gold and mercury were used here. This method can also be used to gild copper sheets, which was used, for example, for the cupolas of St. Isaac's Cathedral in St. Petersburg in the 19th century.

### Other uses

• The metal is used in button cells and batteries. However, there is now only one producer in Taiwan; Import into the EU is no longer permitted.
Mercury vapor rectifier emits light during operation
• In astronomy , mercury is used to build relatively inexpensive telescopes with a large mirror surface (see liquid mirror ): Mercury is filled into a plate-shaped, air-bearing mirror carrier, which is then set in rotation. As a result of the rotation, the mercury is distributed over the entire surface of the mirror support in a thin layer and forms an almost perfect parabolic mirror . A disadvantage of these telescopes is that they can only look vertically upwards ( zenith ), since only then is a suitable paraboloid of rotation created by gravity . Without rotating the mirror, mercury mirrors were used in metrology as a flatness standard .
• The property of mercury to behave like a non-wetting liquid (exceptions: amalgam formers such as copper, silver, gold, aluminum) is the basis for mercury porosimetry . Here, mercury is pressed under pressure (0 to 4000 bar) into pores of different sizes. Statements about the nature, shape, distribution and size of pores and cavities can be made about the pressure applied and the amount of mercury required. This method is used, among other things, in mineralogy, pharmacy and the ceramic sciences.
• In the past, mercury salts were used by hat makers, especially to make the castor hats made of beaver fur , which were very fashionable in the 18th century . The English expression " mad as a hatter " ("crazy like a hatter") (see also hat maker syndrome ) probably goes back to the application. He was also popularized by the Mad Hatter character in Lewis Carroll's Alice in Wonderland .
• The first nuclear reactors of the fast breeder type were cooled with mercury (e.g. Clementine reactor in Los Alamos / USA 1946–1952 and similar reactors in the Soviet Union). However, due to major corrosion problems and the difficult handling of the poisonous mercury, they soon switched to liquid sodium. While the Clementine reactor was dismantled by 1970, that is still pending for the Russian mercury-cooled reactors, which were shut down more than 50 years ago.
• It has been known for a number of years that, from around 1955, boiling mercury was used in the military HERMEX project to separate weapons- grade plutonium from spent reactor fuel elements . More than 1000 tons of plutonium-containing mercury from this closed HERMEX project are still stored in the Oak Ridge National Laboratory .
• Also in the Oak Ridge National Laboratory, an extensive project for the extraction of tritium for hydrogen bombs using approx. 11,000 tons of mercury was carried out from 1950 to 1963 . About 3% of the mercury was released into the environment.
• Mercury vapor was used to develop the image in the daguerreotype , the first practicable photography process. The resulting photo consisted of a mercury precipitate on a silver-plated copper plate.
• At the end of the 17th century, the physician Anton Nuck introduced the injection of mercury into anatomical specimens .
• Mercury is used in high-power spallation sources as a target for generating neutrons , e.g. B. SNS / USA or JSNS / Japan. About 20 tons of mercury are bombarded with a proton beam with a particle energy of about 1  GeV . Mercury atomic nuclei are shattered and around 20 neutrons are released for each irradiated proton. The planned European Spallation Source ESS in Lund (Sweden) is not expected to use mercury.

## Pushing back the application and extraction

The heavy metal Aarhus Protocol to the UNECE - 1979 Convention on Long-range Transboundary Air Pollution entered into force in 2003 and aims to reduce emissions of the heavy metals lead , cadmium and mercury.

From 9th (the day of the pharmacy) to 25th October 2007 in a campaign by the Ministry of Life and the Chamber of Pharmacists in Austria, one million mercury thermometers were collected from private households via pharmacies and brought to an underground warehouse in Germany via pharmaceutical wholesalers and the waste disposal company Saubermacher. This amount corresponds to one ton of mercury. As an incentive, there was a digital clinical thermometer for every returned item (worth around € 1). The initiators only expected 50,000 thermometers and had to deliver 200,000 digital thermometers.

In 2009 Sweden decided to generally ban the use of mercury. The ban means that the use of amalgam in dental fillings will cease and that products containing mercury will no longer be allowed to be marketed in Sweden. According to the Swedish Ministry of the Environment, the ban is "a strong signal for other countries and Sweden's contribution to the EU and UN's goals to reduce the use and emissions of mercury." This was preceded by a 2008 ban on the use of mercury in Norway. A UN conference was held in Stockholm in 2010 on this subject. In Switzerland, the quantities of mercury imported fell sharply after 2008 from over 3000 kg to around 600 kg per year in the period 2009–2013 and further to 70 kg in 2016. Mercury intended for dental products makes up the majority of this. The EU's “Community Strategy for Mercury” of January 28, 2005 aims to reduce emissions, supply and demand for mercury. Existing quantities should be managed, people should be protected from exposure , understanding created and measures promoted. According to the EU directive of September 2006, the mercury content of batteries and accumulators was limited to 0.0005 percent by weight (button cells, however, 2%).

The EC regulation on the prohibition of the export of mercury and certain compounds as well as the safe storage of mercury of October 22, 2008 has banned the export of mercury and mercury containing - with exceptions - from the EU since March 15, 2011. On the same date, mercury, which has been put out of action by process changes in the chlor-alkali industry in particular, is to be treated as hazardous waste and to be stored and monitored in high-security areas underground, such as abandoned salt mines. Europe has so far been the main producer of mercury in the world. The inventory of mercury, especially in the chlor-alkali electrolysis concentrated in Germany, is around 1000 t.

The world production of mercury has decreased from its maximum in 1970 with 10,000 t / a until 1992 by 3,000 t / a.

Since 2001, the United Nations has put mercury on the list of regulated substances of global pollution in its United Nations Environmental Program Governing Council .

Ten years after the impetus from Switzerland and Norway, 140 countries signed the Minamata Agreement in Geneva on January 19, 2013 after lengthy negotiations , the first binding agreement to restrict the extraction and containment of mercury emissions. The convention regulates the production, use and storage of mercury and the handling of waste containing mercury; compliance is monitored by an advisory commission. New mines are not allowed to be built, existing ones have to be closed within 15 years so that mercury is then only available for recycling. Humans have doubled the mercury concentration in the top 100 m of the oceans over the past 100 years, according to a UN report.

## disposal

Spilled mercury can be picked up with special mercury tongs or by shoveling two suitably troughed sheets of paper against each other. Small residues can be amalgamated with a zinc plate or zinc powder or converted to sulphide with sulfur and then swept up solidified. Mercury waste must be collected as hazardous waste and specially disposed of.

In laboratory practice, it should be avoided that mercury flows into cracks in the floor, from where it would be released into the environment through evaporation over the years.

Either mercury (I) (also diquecury (I)) or mercury (II) compounds are important here:

## Analytics

### Classic, inorganic detection reactions

#### Amalgam sample

Amalgam sample

Mercury salts can be detected with the help of the amalgam sample . The hydrochloric acid solution is poured onto a copper sheet and a solid, silvery amalgam stain remains. Silver ions can interfere with the detection and are therefore precipitated as AgCl.

${\ displaystyle \ mathrm {Hg ^ {2 \ operatorname {+}} + Cu \ longrightarrow Hg + Cu ^ {2 \ operatorname {+}}}}$

#### Glow tube sample

Another proof of mercury is the glow tube sample. The substance to be analyzed is mixed with approximately the same amount of sodium carbonate (soda) and ignited in the fume cupboard. Elemental mercury is deposited as a metallic mirror on the test tube wall .

#### Qualitative evidence in the separation process

In the qualitative separation process, mercury can be detected both in the HCl group and in the H 2 S group. After adding HCl, calomel, Hg 2 Cl 2 , is formed, which reacts to finely divided mercury and mercury (II) amido chloride after adding ammonia solution. After the introduction of H 2 S, divalent mercury precipitates in the form of black cinnabar, HgS, and can be detected with the help of the amalgam sample.

### Instrumental analysis of mercury

A number of methods are available for trace analysis of mercury and its organic derivatives. However, new and improved methods are constantly being presented in the literature. Sample processing is a problem that should not be underestimated.

#### Atomic Absorption Spectrometry (AAS)

Of the various AAS techniques , the quartz tube and graphite tube techniques provide the best results for inorganic and organometallic mercury compounds. A quartz cuvette is heated electrically to over 900 ° C and the sample is atomized. The absorption is then measured at 253.7 nm. An example is a detection limit for CH 3 HgCl of 100 µg / L. Another popular technique for the detection of elemental mercury or mercury organyls is the generation of cold steam in connection with the AAS. At very low concentrations, the volatile analyte species are first enriched with the formation of amalgams on gold or silver surfaces that have been placed in a graphite cuvette. It is then atomized at 1400 ° C. and the absorption measured. A detection limit of 0.03 ng was achieved in this way.

#### Atomic Emission Spectrometry (AES)

In the AES , the microwave-induced plasma (MIP) and the inductively coupled plasma (ICP) have proven themselves for atomization. With this method, too, detection takes place at 253.65 nm and 247.85 nm. With the help of the MIP-AES, absolute detection limits of 4.4 ng / g sample were found. The ICP-AES has a detection limit of 20 to 50 ng / mL.

#### Mass spectrometry (MS)

Mercury has a total of seven stable isotopes of different abundance. For mass spectrometry, however, often only 201 Hg (13.22%) and 202 Hg (29.80%) are relevant. With the help of ICP-MS, inorganic mercury compounds and mercury organyls such as methyl mercury, CH 3 Hg, can be determined with detection limits of up to 2.6 ng / g.

#### Neutron Activation Analysis (NAA)

The NAA is based on the nuclear reaction A Hg (n, γ) A + 1 Hg (irradiation of mercury with neutrons). This creates radioactive mercury nuclides . The intensity of the resulting characteristic gamma radiation is determined with a high-purity germanium detector . It is proportional to the number of activated cores present and quantitative statements can be made through internal calibration. 197m Hg with a half-life of 2.7 days at 77.3 keV is often detected.

#### Voltammetry

Anodic stripping voltammetry (ASV) is best suited for the electrochemical determination of Hg traces. The voltammetric measurement is preceded by a reductive enrichment period on the gold measuring electrode. The actual determination follows by measuring the oxidation current when scanning a voltage window from 0 V to 600 mV. The height of the oxidation peak at 500 mV correlates with the amount of mercury present. Detection limits of 12 pM (2.4 ng / l) mercury were achieved in seawater after an enrichment time of 2 minutes. In addition, inverse voltammetry on gold, platinum or carbon electrodes can be used.

#### Automated analytics

There are now automated analyzers for the routine analysis of mercury. They are usually based on the principle of thermal decomposition, followed by amalgamation and subsequent measurement of the atomic absorption (see AAS). With such analysis devices, solid and liquid samples can be examined for their mercury content within a few minutes. These commercially available devices are very sensitive and meet the requirements of national quality assurance standards such as US EPA method 7473 and ASTM method D-6722-01.

## Environmental emissions

Percentage of anthropogenic sources of mercury emissions worldwide in 2010
Mercury air emission sources in Germany (Federal Environment Agency)

Mercury is released in large quantities through human activities. It is estimated that around 2500 tonnes are released into the atmosphere as gaseous mercury as a result of anthropogenic emissions every year , as well as considerable amounts in the soil and water. The anthropogenic share of the total emissions is estimated to be around 30%. Total emissions to the environment from the dawn of civilization through 2010 were estimated at 1.1–2.8 million tons.

Significant emission sources are:

• the (small-scale) gold mining (Artisanal Small Scale Mining). According to estimates, 20 to 30 percent of the gold mined worldwide is obtained through non-industrial mining, i.e. by gold prospectors. If all gold miners in the world were to use the environmentally friendly borax process , the emission of around 1,000 tons of mercury, around 30% of global mercury emissions, could be avoided.
• The energy industry , especially coal-fired power plants : The mercury emissions from the energy industry for 2010 are estimated at around 859 tonnes worldwide, of which around 86% come from the burning of coal. The ongoing expansion of coal-fired power plants in China will mean that coal combustion will become the largest emitter in the future. In stone and brown coal , mercury is indeed only in trace amounts, but the high amount of global burnt coal leads to significant release rates. In Germany, the energy industry has been emitting around 7 tons of mercury at a constant rate since 1995.
• Cement works (due to mercury in limestone and when using waste / sewage sludge as fuel),
• Non-ferrous metal smelters (due to mercury in ores, especially gold, copper, zinc and lead extraction),
• Steel production (especially when using scrap),
• Production of chlorine, hydrogen and caustic soda ( chlor-alkali electrolysis with amalgam process).

In the airside mercury emissions from Germany (10257 kg in 2013), the energy industry had a share of 68% (6961 kg) due to coal-fired power plants, metal smelting 11% (1080 kg) and cement and a. Mineral industry 6% (609 kg). With around 10 tonnes of mercury emissions, Germany, together with Poland and Greece, is the front runner in Europe.

In January 2016, a study commissioned by the Greens showed that the mercury limit values that have been in force in the USA for 1,100 coal-fired power plants since April 2015 are not complied with by any coal-fired power plant in Germany, as there are no correspondingly strict legal requirements. If the same limit values for mercury emissions were to apply as in the USA (a monthly mean equivalent to around 1.5 µg / m³ for hard coal power plants and 4.4 µg / m³ for lignite power plants), of the 53 reportable coal power plants in Germany, only the power plant that has since been shut down could be used Dates (block 1–3) stay on the net. For several years now, the Federal Environment Agency has recommended lowering the limit value in the exhaust gas from coal-fired power plants to 3 µg / m³ daily and 1 µg / m³ annual. When implementing the European Industrial Emissions Directive , the Federal Government and the majority of the Bundestag decided at the end of October 2012 for coal-fired power plants to have limit values of 30 µg / m³ as a daily average and (for existing power plants from 2019) 10 µg / m³ as an annual average. At the expert hearing in the Environment Committee of the Bundestag on October 15, 2012, an adjustment to the US limit values was recommended. In June 2015, a working group led by the European Commission with representatives from member states, industrial and environmental associations determined that annual mean mercury emission values below 1 µg / m³ can be achieved in coal-fired power plants with mercury-specific technologies. Low mercury emissions can be achieved by adding activated carbon, using a precipitant in the flue gas scrubber or special filter modules. Catalysts and the addition of bromine salts can improve mercury discharge because they convert elemental mercury into ionic mercury. The increase in electricity generation costs associated with these processes is estimated to be less than 1 percent.

For example, the hard coal power plant in Lünen-Stummhafen , the hard coal power plant in Wilhelmshaven , the hard coal power plant in Werne , the hard coal power plant in Hamm-Uentrop , the hard coal power plant in Hamm-Uentrop , the hard coal power plant in Hamm-Uentrop , reach low mercury concentration values in the range of 1 microgram per standard cubic meter and below. Power plant in Großkrotzenburg near Hanau and the lignite power plant in Oak Grove (Texas / USA ).

The following two tables list companies in Germany that are required to report that in 2010 more than 100 kilograms of mercury per year were released into the air or that more than 5 kilograms of mercury was discharged into water per year. Figures in bold indicate higher emissions than in the previous year.

Companies with more than 100 kg of mercury air emissions in Germany in 2010 compared with 2012 to 2015 ( PRTR )
Plant type Company name operator Mercury (kg)
2010 2012 2013 2014 2015
Brown coal - power plant Lippendorf power plant * Vattenfall 1,160 482 410 489 490
Brown coal - power plant Jänschwalde power plant ** Vattenfall 592 505 330 501 431
Brown coal - power plant Niederaussem power plant RWE 499 497 527 485 486
Brown coal - power plant Weisweiler power plant RWE 271 299 227 232 176
Brown coal - power plant Black Pump power plant Vattenfall 243 228 194 303 339
Steel mill Tormented bearer Salzgitter AG 229 131 67.9 49.7 148
Brown coal - power plant Schkopau power plant E.ON , EP Energy 227 441 430 405 267
Brown coal - power plant Boxberg power plant Vattenfall 226 235 370 392 486
Brown coal - power plant Neurath power plant RWE 181 497 667 672 708
Coal - power plant Bremen-Hafen power plant swb AG 156 150 45.4 <10 16.6
Brown coal - power plant Frimmersdorf power plant RWE 153 119 68.6 79.1 95.9
Coal - power plant Large power plant in Mannheim RWE , EnBW , MVV Energie 146 137 154 139 148
Chemical industry Factory Ludwigshafen BASF 140 97 62.7 70.5 61.2
Incineration Waste incineration in Hagen Hagen waste disposal company 140 *** <10 <10 <10 <10
Steel mill Kehl plant Baden steel works 140 211 211 117 k. A.
Coal - power plant Scholven power plant E.ON 135 144 155 151 79
Chemical industry Factory Frankfurt Akzo Nobel Industrial Chemicals 131 63.9 63.9 63.9 31.9
Chemical industry Lülsdorf plant Evonik Degussa 111 68.5 68.5 8.17 47.2
Coal - power plant Farge power station GDF Suez 106 109 113 17.1 15.5
Chlor-alkali electrolysis Rustersiel plant INEOS Chlor Atlantic 101 77 58.2 ***** - -
total 5,087 4,491 4.223 4.174 4.026
Germany total 10,310 9,985 9,627 9,239 9,095
Share of listed establishments in total **** 49% 45% 44% 45% 44%
* with sewage sludge - waste incineration ** with substitute fuel - waste incineration
*** measurement / reporting error; actually: <10 **** values <10 kg calculated with zero ***** July 2013 closed
Sewage treatment plants with a report of more than 5 kilograms of mercury discharge into a body of water in Germany in 2010 compared with 2012 and 2015 ( PRTR )
River basin Company name operator Mercury (kg)
2010 2012 2015
Isar / Danube Munich I Gut Großlappen Munich city drainage 19.5 7.69 <1
Isar / Danube Munich II - Gut Marienhof Munich city drainage 11.3 2.45 <1
White Elster / Saale / Elbe Rosenthal sewage treatment plant Municipal waterworks Leipzig 10.8 8.1 8.1
Spree / Havel / Elbe Waßmannsdorf sewage treatment plant Berliner Wasserbetriebe 9.8 <1 <1
Rur / Maas Central sewage treatment plant Düren - remember Eifel-Rur water association 8.89 2.12 <1
Elbe Magdeburg / Gerwisch sewage treatment plant Municipal Works Magdeburg 8.1 <1 k. A.
Weser Minden - Leteln sewage treatment plant Municipal companies Minden 7.53 5.9 <1
Wupper / Rhine Buchenhofen sewage treatment plant Wupper Association 7th 2 2
Elbe Köhlbrandhöft / Dradenau sewage treatment plant network Hamburg city drainage 6th <1 3.4
Rhine Huckingen sewage treatment plant Business enterprises Duisburg 6th <1 <1
Spree / Havel / Elbe Ruhleben sewage treatment plant Berliner Wasserbetriebe 5.8 <1 <1
total 101 38 13.5

Products containing mercury have been banned in Norway since 2008 and in Sweden since 2009.

Due to the known dangers of released mercury, the UN Environment Program ( UNEP ) drew up an international agreement (" Minamata Agreement "), which was signed in October 2013 by 140 countries. The aim is to reduce mercury emissions from mining, production processes, products and waste worldwide. The agreement became binding with the ratification of the 50th signatory state on May 18, 2017 and entered into force on August 16, 2017.

The American Blacksmith Institute has determined the top 10 most heavily contaminated places on earth since 2006 . Mercury is often one of the pollutants in the “nominated” locations.

The export of mercury or mercury-containing substances with a mercury concentration of over 95% from the EU to non- EU countries is prohibited.

## Damage to health from mercury

Mercury is a poisonous heavy metal that gives off vapors even at room temperature . Pure metallic mercury is comparatively harmless when absorbed through the digestive tract, but inhaled vapors are highly toxic.

Organic mercury compounds are extremely toxic because, unlike elemental mercury, they are fat-soluble. They can be ingested with food, but also through the skin. They easily penetrate most protective gloves. They are almost completely absorbed and incorporated into fatty tissue. They arise in the food chain through biomethylation of mercury (or mercury salts) to methyl mercury . The main source of human exposure to methylmercury is through consumption of marine fish. Organic mercury compound poisoning became known worldwide in the mid-1950s through reports of Minamata disease . The main sources of exposure to inorganic mercury are ingestion through food and through dental amalgam.

Depending on the intake, both acute and chronic poisoning are possible. The fall of the English ship Triumph in 1810, on which more than 200 people poisoned themselves when a barrel of mercury leaked, can serve as an example . In 2007 and 2015, Ayurvedic remedies with high levels of mercury attracted attention.

## literature

• Günther Tölg, Irmgard Lorenz: Mercury - a problem element for humans? In: Chemistry in Our Time. 11 (5), 1977, pp. 150-156, doi: 10.1002 / ciuz.19770110504 .
• Klaus Brodersen: Mercury - a toxic, useful and unusual precious metal. In: Chemistry in Our Time. 16 (1), 1982, pp. 23-31, doi: 10.1002 / ciuz.19820160105 .
• Fritz Schweinsberg: Significance of mercury in environmental medicine - an overview. In: Environmental medicine in research and practice. 7 (5), 2002, pp. 263-278.
• Ralf Ebinghaus u. a .: Mercury Contaminated Sites - Characterization, Risk Assessment and Remediation . Springer Verlag, Berlin 1999, ISBN 3-540-63731-1 .
• Carl J. Watras, John W. Huckabee: Mercury Pollution - Integration and Synthesis . Lewis Publishers, Ann Arbor 1994, ISBN 1-56670-066-3 .
• Jander Blasius, Joachim Straehle, Eberhard Schweda: Textbook of analytical and preparative inorganic chemistry. 16th edition. S. Hirzel Verlag, 2006, ISBN 3-7776-1388-6 , p. 466.
• Bruno Lange, Zdenek J. Vejdelek: Photometric analysis . Verlag Chemie, Weinheim 1987, ISBN 3-527-25853-1 .
• Rolf Schiller: Recycling of hazardous waste. Waste containing mercury. Dornier-System GmbH May 1977. Study for the Federal Ministry for Research and Technology (BMFT).
• A. Ritscher: Use, disposal and environmental pollution of mercury. Overview of the situation in Switzerland. Federal Office for the Environment, Bern 2018. Environmental status No. 1832: 51 p.

## Historical sources

Commons : Mercury  - album with pictures, videos and audio files
Wiktionary: Mercury  - explanations of meanings, word origins, synonyms, translations
Wikibooks: Inorganic Chemistry / Mercury Internship  - Learning and Teaching Materials
Wikibooks: Wikijunior The Elements / Elements / Mercury  - Learning and teaching materials

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86. Christian Tebert et al .: Mercury reduction strategy for North Rhine-Westphalia ( Memento from March 13, 2017 in the Internet Archive ) (PDF 6.24 MB) Expert opinion on behalf of the State of North Rhine-Westphalia, Ökopol - Institute for Ecology and Politics / Eco -Institute / Lawyer Kremer, Hamburg / Berlin, April 2016.
87. Ralph Ahrens: Less mercury emissions from coal-fired power plants with more technology. on: ingenieur.de , VDI nachrichten , October 24, 2014.
88. Annual mean value 2014: <0.001 mg / m³ Informing the public in accordance with Section 23 of the 17th BImSchV about the operation of the coal-fired power plant in Wilhelmshaven with sewage sludge co-incineration. ( Memento from January 9, 2016 in the Internet Archive ) E.ON Kraftwerke GmbH, Hanover, July 31, 2015.
89. Annual mean value: 1.2 µg / m³, Bernd Kröger: Gersteinwerk emits less mercury than others. wa.de, Westfälischer Anzeiger , January 8, 2016.
90. Annual mean value 2014: 0.6 µg / m³, Alexander Schäfer: Westphalia power plant is well below the limit value. wa.de, Westfälischer Anzeiger , January 5, 2016.
91. Annual mean value 2012: 0.9 µg / m³, Christian Tebert: Mercury emissions from coal-fired power plants in Germany and the USA against the background of the BAT discussion and legal requirements (lecture) VDI Conference on Measurement and Reduction of Mercury Emissions , Düsseldorf, 15. April 2015.
92. Luminant Oak Grove Power Station PROMECON Prozess- und Messtechnik Conrads GmbH, Barleben. Retrieved January 8, 2016.
93. Luminant's Oak Grove Power Plant earns Powers Highest Honor. In: POWER Magazine. Electric Power, January 8, 2010.
94. ^ Emissions development 1990–2014, classic air pollutants, heavy metals National trend tables for the German reporting of atmospheric emissions since 1990, Federal Environment Agency (Excel table), as of February 3, 2015.
95. Telephone information from the operations manager of the Hagen waste incineration plant, April 23, 2014.
96. ^ Bans mercury in products. on: regjeringen.no
97. Chapter XXVII, Environment, 17th Minamata Convention on Mercury at treaties.un.org, status as of January 17, 2018.
98. Top Ten Threats 2013.pdf of the Blacksmith Institute.
99. REGULATION (EC) No. 1102/2008 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of October 22, 2008 on the ban on the export of metallic mercury and certain mercury compounds and mixtures and the safe storage of metallic mercury (PDF; 84 kB). (PDF) Official Journal of the European Union, L 304/75, November 14, 2008.
100. Food supplement: Poison discovered in Ayurveda products. ( Memento from September 30, 2007 in the Internet Archive ) In: Ökotest. March 1, 2007.
101. Ayurvedic medicine: Two German couples poisoned in Sri Lanka. In: Spiegel online. September 26, 2015.


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## anonymous 4 years ago Find the average rate of change for f(x) from -2 to 8 and the equation of the secant line containing (-2, f(-2)) and (8, f(8)). Please show all of your work.

1. anonymous

Find the average rate of change for f(x) = x^3 -6x^2 -5 from -2 to 8 and the equation of the secant line containing (-2, f(-2)) and (8, f(8)). Please show all of your work.

2. anonymous

$\frac{f(8)-f(-2)}{8-(-2)}$ is the slope, aka $\frac{f(8)-f(-2)}{10}$

3. saifoo.khan

That's what i was writing^

4. anonymous

lol now it is an actual function, but the work is the same, just compute the numerator

5. anonymous

look at the question i just posted.. the first one was missing some numbers

format: plain


text:
# Compactly supported cohomology of a connected manifolds of finite type.

Is it possible that the compactly supported cohomology (over rational number filed) of connected manifold (non-oriented) of finite type is zero? In case of ordinary cohomology at least Zero-th cohomology group is non-zero. In case of oriented manifold this zero-th cohomology groups corresponds to the n-th cohomology group of compactly supported cohomology (using Poincare duality). Let us supposed M be a non-compact non-oriented manifold. It is true or not there is at least one cohomology group of compactly supported cohomology of M is non-zero. If yes then what is its degree?

No, for instance if $M$ is the open Mobius band, we have $H^*_c(M;\Bbb Q) = 0$.
The point is that if $M$ is the interior of a compact manifold with boundary $\bar M$, then $H^*_c(M) \cong H^*(\bar M, \partial \bar M)$; and then there is the isomorphism $$H^*(\bar M, \partial \bar M) \cong H^*(\bar M/\partial \bar M, *),$$ where we take on the right side relative cohomology at the basepoint we collapsed $\partial \bar M$ into. Cohomology of a locally contractible space relative to a basepoint is just reduced cohomology.
Now the closed mobius band $\bar M$ has boundary a circle, and collapsing it to a point is homeomorphic to filling it in with a disc, which is the real projective plane $\Bbb{RP}^2$. So $H^*_c(M;\Bbb Q) = \tilde H^*(\Bbb{RP}^2;\Bbb Q) = 0$.


text:
# Acid Base and salts class 10 ncert solutions Science

QUESTION1: You have been provide with three taste tubes. One of them contains distilled water and the other two contains an acidic solution and a basic solution, respectively. If you are given only red litmus paper, how will you identify the contents of each tube?
Answer:
We know from the chapter concept that
 Basic solution Litmus paper change to blue Acid Solution No change Neutral solution No change
Thus, basic solution can be easily identified.
When acid and a base react with each other. They neutralize each other to form salt and water.
So following steps can be taken to distinguish the test tubes with the help of litmus paper
Step 1: Let us mark the three taste tubes as P, Q, and R respectively
Step2: A drop of solution in taste tube P is put on the red litmus paper. Same is repeated with solution Q and R. If either of them change colour to blue, then it is basic. Therefore, out of three, one is eliminated.
Step 3: Out of remaining two, anyone can be acidic or neutral. Now a drop of basic solution is mixed with a drop of each of the remaining two solutions separately and then a drop of each solution is put on the red litmus paper.
If the colour of red litmus turns blue, then that solution is neutral and if there is no change in colour, then that solution is acidic.
This is because acidic and basic solutions neutralize each other. Hence , we can distinguish between the three types of solutions.
QUESTION 2: Why should curd and sour substances not be kept in brass and copper vessels?
Answer: Curd and other sour substances contain acids. Therefore , when they are kept in copper and brass vessels, the metal reacts with the acid to liberate hydrogen gas and harmful products, thereby spoiling the food.
QUESTION 3 which gas is usually liberated when an acid reacts with a metal? Illustrate with an example . How will you test for the presence of this gas?
Answer: Hydrogen gas is usually liberated when an acid reacts with a metal.

Example
Procedure: Step 1: Take few pieces of zinc granules and add 5 ml of dilute H2 SO 4
Step 2: Shake it and pass gas produced into a soap solution. The bubbles are formed in the soap solution. These soap bubbles contain hydrogen gas.
Zn + dil. H2 SO 4 --àZnSO 4 + H 2
Test for hydrogen gas: The evolved hydrogen gas can be tested by bringing a burning candle near the soap bubbles. Hydrogen gas burns with a pop sound.
QUESTION 4: Metal compound A reacts with dilute hydrochloric acid to produce effervescence. The gas evolved extinguishes a burning candle. Write a balanced chemical equation for the reaction if one of the compounds formed is calcium chloride.
Answer:
Metal compound A should be compounds of Ca as a calcium salt is formed in the product.  We know that CO 2 extinguishes a burning candle. Also , since carbon dioxide is liberated, therefore, it must be a carbonate. Hence, it is calcium carbonate.
CaCO 3(S) + 2HCL(aq) --à CaCL 2(S) + CO 2(g) + H 2O(I)
Hence metal compound A is calcium carbonate.
QUESTION 5: Why do HCL, HNO 3, etc., show acidic characters in aqueous solutions while  solution of compounds like alcohol and glucose do not show acidic character?
Answer: HCL and HNO 3 dissociate in the presence of water to form hydrogen or hydronium ions.
Although aqueous solutions of glucose and alcohol contain hydrogen , these cannot dissociate in water to form hydrogen or hydronium ions. Hence they do not show acidic character.
QUESTION 6 : Why does an aqueous solution of acid conduct electricity?
Answer: Acid dissociate in aqueous solutions to form ions. These ions are responsible for conduction of electricity.
QUESTION 7 : Why does dry HCL gas not change the colour of the dry litmus paper?
Answer: Dry HCL gas does not change the colour of the dry litmus paper because it does not contain hydrogen or  hydronium ions.
QUESTION 8:  While diluting an acid , why is it recommended that the acid should be added to water and not water to the acid?
Answer:  As the  reaction between an acid and water is exothermic reaction, It is recommended that acid should be added to water and not water to the acid because the process of dissolving an acid in water is exothermic . If water is added to acid , since large amount of acid is present, a large amount of heat is generated, the mixture splashes out and causes burns.
QUESTION 9: How is the concentration of hydronium ions (H 3O+) affected when a solution of an acid is diluted?
Answer: When an acid is diluted, the concentration of hydronium ions (H 3O +) per unit volume decreases. This means that the strength of the acid decreases.
QUESTION 10: How is the concentration of hydroxide ions (OH -) affected when excess base is dissolved in a solution of sodium hydroxide?
Answer: the concentration of hydroxide ions (OH -) would increase when excess base is dissolved in a solution hydroxide.

QUESTION 11  : You have two solutions A and B . The pH of solution A is 6 and pH of solution B is 8. Which solution has  more hydrogen ion concentration ? Which of this acidic and which one is basic?
Answer:
We know from the chapter concept that
 pH < 7 Acidic Solution pH=7 Neutral solution pH > 7 Basic solution
A pH value of less than 7 indicates an acidic solution, while greater than 7 indicates a basic solution. Therefore, the solution with pH  = 6 is acidic and has more hydrogen ion concentration then the solution pH = 8 which is basic.
QUESTION 12: What effect does the concentration of H +(aq) ions have on the nature of the solution?
Answer:  The concentration of H + ions is directly proportional to the acidic of a solution.
If the concentration of H+ ions is increased, the solution becomes more acidic. If the concentration of H+ ions decreased, the solution becomes less acidic or more basic.
QUESTION 13: Do basic solution also have H + (aq) ions? If yes then why are these basic?
Answer: Yes, a basic solution also has H + (aq) ions. However their concentration is less as compared to the concentration of OH - (aq) ions that makes the solution basic.
QUESTION 14: Under what  soil condition do you think a farmer would treat the soil of his field with quick lime (calcium oxide) or slaked lime (calcium hydroxide) or chalk (calcium carbonate)?
Answer: As  calcium oxide , calcium hydroxide and calcium carbonate are basic in nature. So, when an acid is base react , a neutralization reaction takes place.So If the soil is acidic and improper for cultivation, then to neutralize the acidity of the soil, the farmer would treat the soil with quick lime or slaked lime or chalk.
QUESTION 15: What is common name of compound CaOCL 2?
Answer: Bleaching powder .
QUESTION 16: Name the substance which on treatment with chlorine yields bleaching powder?
Answer: Calcium hydroxide [Ca(OH)2]
QUESTION 17: Name sodium compound which is used for softening hard water?
Answer: Washing soda (Na2 CO 3.10H2O) is used for softening hard water.
QUESTION 18: What will happen if a solution of sodium hydrocarbonate is heated?
Answer: When a solution of sodium hydrocarbon ate is heated, sodium carbonate and water are  formed with the evolution of carbon dioxide gas.
2NaHCO3  ->   Na 2CO 3 +H 2O + CO 2
NaHCO 3    : sodium hydrocarbonate         Na 2CO3 : Sodium Carbonate
QUESTION 19: Write an equation to show the reaction between Plaster of Paris and water?
Answer: The chemical equation for the reaction of Plaster of Paris and water can be represented as:
CaSO 4.(1/2) H 2O   +1 ½ H 2O  ->  CaSO 4.2H 2O
Plaster of pares      -> CaSO 4.(1/2) H 2O                    Gypsum ->CaSO 4.2H 2O
QUESTION 20: A solution turns red litmus blue, its pH is likely to be
(a) 1
(b) 4
(c) 5
(d) 10
Answer: Bases turns red litmus blue and acids turn litmus red . Basic solution has a pH value more than 7. Since the solution turns red litmus blue, its pH is likely to be 10  QUESTION 21 A solution reacts with crushed egg-shells to give a gas that turns lime water milky. The solution contains
(a) NaCL
(b) HCL
(c) LicL
(d) KCl
Answer: HCL
QUESTION 22: 10 mL of a solution of NaOH is found to be completely neutralized by 8 mL of a given solution of HCL. If we take 20mL of the same solution of NaOH, the amount of HCL solution (the same solution as before)  required to neutralize it will be:
(a) 4mL
(b) 8mL
(c) 12mL
(d) 16mL
Answer: (d) 16mL
.
QUESTION 23 Which one of the following types of medicines is used for treating indigestion?
(a) Antibiotic
(b) Analgesic
(c) Antacid
(d) Antiseptic
Answer: Antacid
QUESTION 24: Write word equation and then balanced equations for the reaction taking place when-
(a) Dilute sulphuric acid reacts with zinc granules.
(b) Dilute hydrochloric acid reacts with magnesium ribbon.
(c) Dilute sulphuric acid reacts with aluminum powder.
(d) Dilute hydrochloric acid reacts with iron filings.
Answer:
How to solve these type of question
• First convert the word equation into skeletal equation
• Start by finding out how many atoms of each type are on each side of the equation
• You can make  a little table listing the numbers of each atom for the left hand side and for the right hand side
• Balance the different Atoms on both side of equation by  multiply the chemical species on the side which doesn't have enough atoms of that type by the number required to bring it up to the same as the other side.
(a) Sulphuric acid + Zinc --> Zinc sulphate + Hydrogen
H 2SO 4(aq) + Zn(s) -- > ZnSO 4(aq) + H 2(g)
(b) Hydrochloric acid + Magnesium ---> Magnesium chloride + Hydrogen
2HCL(aq) + Mg(s) --> MgCl  2(aq)  + H 2(g)
(c) Sulphuric acid + Aluminium --> Aluminum sulphate + Hydrogen
3H 2SO 4(aq) + 2Al(s) ---> Al 2(SO 4) 3 (aq) +3H 2(g)
(d) Hydrochloric acid + iron --> Ferric chloride + Hydrogen
6HCl (aq) + 2Fe(s) ---> 2FeCl 3(aq) + 3H 2(g)
QUESTION 25 Compound such as alcohols and glucose also contain hydrogen but are not categorized as acids. Describe an activity to prove it.
Answer:

Procedure:
Step 1: Two nails are fitted in a cork and are kept it in a 100mL beaker.
Step 2: The nails are then connected  to the two terminals of a 6-volt battery through a bulb and switch.
Step 3: Some dilute HCl is poured in the beaker and current is switched on.
Step 4: The same experiment is then performed with glucose solution and alcohol solution.
Observations: It will be observed that the bulb glows in the HCl solution and does not glow in the glucose solution.
HCl dissociate into H + (aq) and Cl -(aq) ions. These ions conduct electricity in the solution which results in the glowing of the bulb. On the other hand, the glucose solution which does dissociate into ions. Therefore, it does not conduct electricity.
Conclusion: From this activity, it can be concluded that all acid contain hydrogen but not all compounds containing hydrogen are acids.
That is why , though alcohol and glucose contain hydrogen , they are not categorized as acids.
QUESTION 26 Why does distilled water not conduct electricity , whereas rain water does?
Answer: Distilled water is a pure form of water and is devoid of any ionic species. Therefore , it does not conduct electricity . Rain water , being an impure form of water , contains many ionic species such as acid and therefore, it conducts electricity.
QUESTION 27 Why do acids not show acidic behavior in the absence of water ?
Answer: Acids do not show acidic behavior in the absence of water because there are no hydrogen ions available for conduction of electricity. Acids  dissociate in the presence of water to give free hydrogen ions. It is the hydrogen ions that are responsible for the acidic behavior.
QUESTION 28: Five solutions A,B,C,D and E when tested with universal indicator showed pH as 4,1,11,7 and 9, respectively. Which solution is
(a) neutral?
(b) strongly alkaline?
(c) strongly acidic?
(d) weakly acidic?
(e) weakly alkaline?
Arrange the pH in increasing order of the concentration of hydrogen ions
Answer
We know from the chapter concept that
 pH < 7 Acidic Solution pH=7 Neutral solution pH > 7 Basic solution
(a) Neutral →Solution D with pH 7
(b) Strongly alkaline →Solution C with pH 11
(c) Strongly acidic →Solution B with pH 1
(d) Weakly acidic →Solution A with pH 4
(e) Weakly alkaline →Solution E with pH 9
Arrangement  in  increasing order of concentration of hydrogen ions 11<9<7<4<1
QUESTION 29: Equal lengths of magnesium ribbons are taken in the test tubes A and B. Hydrochloric acid (HCl) is added to test tube A, while acetic acid (CH 3COOH) is added to test tube B. In which test tube will the fizzing occur more vigorously and why?
Answer: The fizzing will occur strongly on the test tube A, in which hydrochloric acid (HCl) is added. This is because HCl is a stronger acid then CH 3COOH and therefore produces hydrogen gas at a faster speed due to which fizzing occurs.
QUESTION 30 Fresh milk has a pH of 6. How do you think the pH will change as it turns into curd? Explain your answer.
ANSWER:
We know from the chapter concept that
 pH < 7 Acidic Solution pH=7 Neutral solution pH > 7 Basic solution
The pH of milk is 6. As it changes to curd , the pH will reduce because curd is acidic in nature. The acid present in it decrease the pH.
QUESTION 31: A milkman adds a very small amount of baking soda to fresh milk.
(a) Why does he shift the pH of the milk from 6 to slightly alkaline?
(b) Why does this milk take a long time to set as curd?
Answer: (a) The milkman shift the pH of the fresh milk  from 6 to  slightly alkaline because in alkaline condition, milk does not set as curd easily.
(b) Since this milk is slightly basic than usual milk , acids produced to set the curd are neutralized by the base. Therefore , it takes a longer time for the curd to set.
QUESTION 32 Plaster of Paris should be stored in moisture –proof container. Explain why?
Answer: Plaster of Paris should be store in moisture – proof container because Plaster of Paris, a powdery mass , absorbs water (moisture) to form a hard solid known as gypsum.
CaSO 4.1/2 + 1 1/2H 2O -->CaSO 4.2H 2O
QUESTION 33: What is neutralization reaction? Give two examples.
Answer:
Neutralization reaction: A reaction in which an acid and base react with each other to give a salt and water is termed as neutralization reaction. In this reaction, energy is evolved in the form of heat.
For example:
 (1) NaOH + HCl  --à NaCl  + H 2O (2) During indigestion ( Caused due to production of excess of hydrochloric acid in the stomach) , we administer an antacid ( generally milk of magnesia, Mg(OH) 2 which is basic in nature ) The antacid neutralizes the excess of acids and thus give relief from indigestion.        Mg(OH) 2 +2HCl --àMgCl 2 +2H 2O
QUESTION 34: Give two important uses of washing soda and baking soda.
Answer: Two important used of washing soda and baking soda is as follows:
 Washing soda Baking soda It is used in glass, soap, and paper industries. It is used to remove permanent hardness of water. It is used as baking powder. Baking powder is a mixture of baking soda and a mild acid known as tartaric acid. When it is heated or mixed in water, it releases Carbon dioxide gas that makes bread or cake fluffy. It is used in soda –acid fire extinguishers

link to this page by copying the following text
Also Read

### Practice Question

Question 1 Which among the following is not a base?
A) NaOH
B) $NH_4OH$
C) $C_2H_5OH$
D) KOH
Question 2 What is the minimum resistance which can be made using five resistors each of 1/2 Ohm?
A) 1/10 Ohm
B) 1/25 ohm
C) 10 ohm
D) 2 ohm
Question 3 Which of the following statement is incorrect? ?
A) For every hormone there is a gene
B) For production of every enzyme there is a gene
C) For every molecule of fat there is a gene
D) For every protein there is a gene


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# Math Help - Maclaurin Series

1. ## Maclaurin Series

Use an appropriate local quadratic approximation to approximate tan61

http://img212.imageshack.us/img212/1256/52475955jo9.png

this is the answer from the solution mannual

Can anybody explain this more clearly?
Thank you

2. Originally Posted by soleilion
Use an appropriate local quadratic approximation to approximate tan61

http://img212.imageshack.us/img212/1256/52475955jo9.png

this is the answer from the solution mannual

Can anybody explain this more clearly?
Thank you
Work in radians and expand as a Taylor series about $60^{\circ}=\pi/3 {\rm{rad}}$

$
f(x+\varepsilon)=f(x)+\varepsilon~\left. \frac{df}{dx}\right|_{x}+\frac{\varepsilon^2}{2}~\ left. \frac{d^2f}{dx^2}\right|_{x}+..
$

Now:

$\frac{d}{dx}\tan(x)=(\sec(x))^2=1+(\tan(x))^2$,

and

$\frac{d^2}{dx^2}\tan(x)=2 (\sec(x))^2 \tan(x)=2\left[\frac{d}{dx}\tan(x)\right] \tan(x)$.

Now all you need is that $\tan(\pi/3)=\sqrt{3}$, and the $\varepsilon$ corresponding to $1^{\circ}$ is $\varepsilon=\pi/180$

RonL

3. Originally Posted by CaptainBlack
Work in radians and expand as a Taylor series about $60^{\circ}=\pi/3 {\rm{rad}}$

$
f(x+\varepsilon)=f(x)+\varepsilon~\left. \frac{df}{dx}\right|_{x}+\frac{\varepsilon^2}{2}~\ left. \frac{d^2f}{dx^2}\right|_{x}+..
$

Now:

$\frac{d}{dx}\tan(x)=(\sec(x))^2=1+(\tan(x))^2$,

and

$\frac{d^2}{dx^2}\tan(x)=2 (\sec(x))^2 \tan(x)=2\left[\frac{d}{dx}\tan(x)\right] \tan(x)$.

Now all you need is that $\tan(\pi/3)=\sqrt{3}$, and the $\varepsilon$ corresponding to $1^{\circ}$ is $\varepsilon=\pi/180$

RonL
As the answer from my website link, why it just shows f'', second prime? why not third or more or less than second?

4. Originally Posted by soleilion
As the answer from my website link, why it just shows f'', second prime? why not third or more or less than second?
Because it asks for a locally quadratic approximation which means that the highest order term in $\varepsilon$ should be $\varepsilon^2$ which means we only go as far as the second derivative.

RonL