Deformation (engineering)

29 yr old Orthopaedic Surgeon Grippo from Saint-Paul, spends time with interests including model railways, top property developers in singapore developers in singapore and dolls. Finished a cruise ship experience that included passing by Runic Stones and Church. In physics, Henry's law is one of the gas laws formulated by William Henry in 1803. It states:

"At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid."

An equivalent way of stating the law is that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

An everyday example of Henry's law is given by carbonated soft drinks. Before the bottle or can of carbonated drink is opened, the gas above the drink is almost pure carbon dioxide at a pressure slightly higher than atmospheric pressure. The drink itself contains dissolved carbon dioxide. When the bottle or can is opened, some of this gas escapes, giving the characteristic hiss. Because the partial pressure of carbon dioxide above the liquid is now lower, some of the dissolved carbon dioxide comes out of solution as bubbles. If a glass of the drink is left in the open, the concentration of carbon dioxide in solution will come into equilibrium with the carbon dioxide in the air, and the drink will go "flat".

A slightly more exotic example of Henry's law is in the decompression and decompression sickness of underwater divers.

Formula and the Henry's law constant

Henry's law can be put into mathematical terms (at constant temperature) as

$p=k_{\mathrm{H}}c$

where p is the partial pressure of the solute in the gas above the solution, c is the concentration of the solute and k_H is a constant with the dimensions of pressure divided by concentration. The constant, known as the Henry's law constant, depends on the solute, the solvent and the temperature.

Some values for k_H for gases dissolved in water at 298 K include:

oxygen (O₂) : 769.2 L·atm/mol

carbon dioxide (CO₂) : 29.41 L·atm/mol

hydrogen (H₂) : 1282.1 L·atm/mol

There are various other forms of Henry's Law which define the constant k_H differently and require different dimensional units. In particular, the "concentration" of the solute in solution may also be expressed as a mole fraction or as a molarity.

Other forms of Henry's law

The various other forms of Henry's law are discussed in the technical literature.

Table 1: Some forms of Henry's law and constants (gases in water at 298.15 K)

equation:	$k_{\mathrm{H},\mathrm{p}\mathrm{c}}=\frac{p}{c_{\mathrm{a}\mathrm{q}}}$	$k_{\mathrm{H},\mathrm{c}\mathrm{p}}=\frac{c_{\mathrm{a}\mathrm{q}}}{p}$	$k_{\mathrm{H},\mathrm{p}\mathrm{x}}=\frac{p}{x}$	$k_{\mathrm{H},\mathrm{c}\mathrm{c}}=\frac{c_{\mathrm{a}\mathrm{q}}}{c_{\mathrm{g}\mathrm{a}\mathrm{s}}}$
units:	$\frac{\mathrm{L}\cdot \mathrm{a}\mathrm{t}\mathrm{m}}{\mathrm{m}\mathrm{o}\mathrm{l}}$	$\frac{\mathrm{m}\mathrm{o}\mathrm{l}}{\mathrm{L}\cdot \mathrm{a}\mathrm{t}\mathrm{m}}$	$\mathrm{a}\mathrm{t}\mathrm{m}$	dimensionless
O2	769.23	1.3Template:E	4.259Template:E	3.181Template:E
H2	1282.05	7.8Template:E	7.099Template:E	1.907Template:E
CO2	29.41	3.4Template:E	0.163Template:E	0.8317
N2	1639.34	6.1Template:E	9.077Template:E	1.492Template:E
He	2702.7	3.7Template:E	14.97Template:E	9.051Template:E
Ne	2222.22	4.5Template:E	12.30Template:E	1.101Template:E
Ar	714.28	1.4Template:E	3.955Template:E	3.425Template:E
CO	1052.63	9.5Template:E	5.828Template:E	2.324Template:E

where:
caq	= concentration (or molarity) of gas in solution (in mol/L)
cgas	= concentration of gas above the solution (in mol/L)
p	= partial pressure of gas above the solution (in atm)
x	= mole fraction of gas in solution (dimensionless)

As can be seen by comparing the equations in the above table, the Henry's law constant k_H,pc is simply the inverse of the constant k_H,cp. Since all k_H may be referred to as Henry's law constants, readers of the technical literature must be quite careful to note which version of the equation is being used.

It should also be noted, the Henry's law is a limiting law that only applies for 'sufficiently dilute' solutions. The range of concentrations in which it applies becomes narrower the more the system diverges from ideal behavior. Roughly speaking, that is the more chemically 'different' the solute is from the solvent. Typically, Henry's law is only applicable to gas solute mole fractions less than 0.03.

It also only applies simply for solutions where the solvent does not react chemically with the gas being dissolved. A common example of a gas that does react with the solvent is carbon dioxide, which forms carbonic acid (H₂CO₃) to a certain degree with water.

Temperature dependence of the Henry constant

When the temperature of a system changes, the Henry constant will also change. This is why some people prefer to name it Henry coefficient. Multiple equations assess the effect of temperature on the constant. These forms of the van 't Hoff equation are examples:

$k_{\mathrm{H},\mathrm{p}\mathrm{c}}(T)=k_{\mathrm{H},\mathrm{p}\mathrm{c}}(T^{\ominus })\exp [-C(\frac{1}{T}-\frac{1}{T^{\ominus }})]$

$k_{\mathrm{H},\mathrm{c}\mathrm{p}}(T)=k_{\mathrm{H},\mathrm{c}\mathrm{p}}(T^{\ominus })\exp \left[C(\frac{1}{T}-\frac{1}{T^{\ominus }})\right]$

where

k_H for a given temperature is Henry's constant (as defined in this article's first section). Note that the sign of C depends on whether k_H,pc or k_H,cp is used.

T is any given temperature, in K

T ^o refers to the standard temperature (298 K).

This equation is only an approximation, and should be used only when no better, experimentally derived formula is known for a given gas.

The following table lists some values for constant C (in Kelvins) in the equation above:

Table 2: Values of C (in K)

Gas	O2	H2	CO2	N2	He	Ne	Ar	CO
C	1700	500	2400	1300	230	490	1300	1300

Because solubility of permanent gases usually decreases with increasing temperature at around the room temperature, the partial pressure a given gas concentration has in liquid must increase. While heating water (saturated with nitrogen) from 25 to 95 °C, the solubility will decrease to about 43% of its initial value. This can be verified when heating water in a pot; small bubbles evolve and rise long before the water reaches boiling temperature. Similarly, carbon dioxide from a carbonated drink escapes much faster when the drink is not cooled because the required partial pressure of CO₂ to achieve the same solubility increases in higher temperatures. Partial pressure of CO₂ in the gas phase in equilibrium with seawater doubles with every 16 K increase in temperature.

The constant C may be regarded as:

$C=-\frac{{\mathrm{\Delta }}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}}H}{R}=-\frac{\mathrm{d}[\ln k_{\mathrm{H}}(T)]}{\mathrm{d}(1/T)}$

where

Δ_solvH is the enthalpy of solution

R is the gas constant.

The solubility of gases does not always decrease with increasing temperature. For aqueous solutions, the Henry's law constant usually goes through a maximum (i.e., the solubility goes through a minimum). For most permanent gases, the minimum is below 120 °C. Often, the smaller the gas molecule (and the lower the gas solubility in water), the lower the temperature of the maximum of the Henry's law constant. Thus, the maximum is about 30 °C for helium, 92 to 93 °C for argon, nitrogen and oxygen, and 114 °C for xenon.

Influence of electrolytes

The influence of electrolytes on the solubility of gases is sometimes given by Sechenov (often spelled Setchenov) equation which accounts for the "salting out" (i.e., decreasing the solubility) or "salting in" (i.e., increasing the solubility) effect (see the article on activity coefficient). The Sechenov equation can be written as:

$\log (*z_1/z_1)=k_{syz}y$

where:

• *z₁ is the solubility of gas 1 in pure solvent
• z₁ is the solubility of gas 1 in an electrolyte solution
• y expresses the salt composition

In geophysics

In geophysics, a version of Henry's law applies to the solubility of a noble gas in contact with silicate melt. One equation used is

$C_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}/C_{\mathrm{g}\mathrm{a}\mathrm{s}}=\exp [-\beta ({\mu }_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}^{\mathrm{E}}-{\mu }_{\mathrm{g}\mathrm{a}\mathrm{s}}^{\mathrm{E}})]$

where:

C = the number concentrations of the solute gas in the melt and gas phases

β = 1/k_BT, an inverse temperature scale: k_B = the Boltzmann constant

µ^E = the excess chemical potentials of the solute gas in the two phases.

Comparison to Raoult's law

For a dilute solution, the concentration of the solute is approximately proportional to its mole fraction x, and Henry's law can be written as:

$p=k_{\mathrm{H}}x$

This can be compared with Raoult's law:

$p=p^{\star }x$

where p* is the vapor pressure of the pure component.

At first sight, Raoult's law appears to be a special case of Henry's law where k_H = p*. This is true for pairs of closely related substances, such as benzene and toluene, which obey Raoult's law over the entire composition range: such mixtures are called "ideal mixtures".

The general case is that both laws are limit laws, and they apply at opposite ends of the composition range. The vapor pressure of the component in large excess, such as the solvent for a dilute solution, is proportional to its mole fraction, and the constant of proportionality is the vapor pressure of the pure substance (Raoult's law). The vapor pressure of the solute is also proportional to the solute's mole fraction, but the constant of proportionality is different and must be determined experimentally (Henry's law). In mathematical terms:

Raoult's law: $\underset{x\to 1}{\lim }\left(\frac{p}{x}\right)=p^{\star }$

Henry's law: $\underset{x\to 0}{\lim }\left(\frac{p}{x}\right)=k_{\mathrm{H}}$

Raoult's law can also be related to non-gas solutes.

Standard chemical potential

Henry's law has been shown to apply to a wide range of solutes in the limit of "infinite dilution" (x→0), including non-volatile substances such as sucrose or even sodium chloride. In these cases, it is necessary to state the law in terms of chemical potentials. For a solute in an ideal dilute solution, the chemical potential depends on the concentration:

$\mu ={\mu }_c^{\ominus }+RT\ln \left(\frac{{\gamma }_{c}c}{c^{\ominus }}\right)$, where ${\gamma }_c=\frac{k_{\mathrm{H},c}}{p^{\star }}$ for a volatile solute; c^o = 1 mol/L.

For non-ideal solutions, the activity coefficient γ_c depends on the concentration and must be determined at the concentration of interest. The activity coefficient can also be obtained for non-volatile solutes, where the vapor pressure of the pure substance is negligible, by using the Gibbs–Duhem relation:

$\sum _i{n}_i\mathrm{d}{\mu }_i=0$

By measuring the change in vapor pressure (and hence chemical potential) of the solvent, the chemical potential of the solute can be deduced.

The standard state for a dilute solution is also defined in terms of infinite-dilution behavior. Although the standard concentration c^o is taken to be 1 mol/l by convention, the standard state is a hypothetical solution of 1 mol/l in which the solute has its limiting infinite-dilution properties. This has the effect that all non-ideal behavior is described by the activity coefficient: the activity coefficient at 1 mol/l is not necessarily unity (and is frequently quite different from unity).

All the relations above can also be expressed in terms of molalities b rather than concentrations, e.g.:

$\mu ={\mu }_b^{\ominus }+RT\ln \left(\frac{{\gamma }_{b}b}{b^{\ominus }}\right)$, where ${\gamma }_b=\frac{k_{\mathrm{H},b}}{p^{\star }}$ for a volatile solute; b^o = 1 mol/kg.

The standard chemical potential μ_m^o, the activity coefficient γ_m and the Henry's law constant k_H,b all have different numerical values when molalities are used in place of concentrations.

See also

• Bunsen solubility coefficient
• Dalton's law
• Partial pressure
• Pervaporation
• Sieverts' law
• Henry adsorption constant

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

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• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
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• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang (An example of isotopic effect on solubility)