# Henry's law

Henry's law is one of the gas laws and was formulated by the British chemist, William Henry, in 1803. It states that:
At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

## Formula and Henry constant

Henry's law may be mathematically expressed as:[1] [2] [3] [4]
• $p = k_{\rm H}\cdot c$
• where:
• p is the partial pressure of the solute above the solution
• c is the concentration of the solute in the solution (in one of its many units)
• kH is the Henry's Law constant, which has units such as L··atm/mol or atm/(mole fraction) or Pa · m3/mol

Some values for kH include:
• oxygen (O2): 769.2 L · atm/mol
• carbon dioxide (CO2): 29.4 L · atm/mol
• hydrogen (H2): 1282.1 L · atm/mol
when these gases are dissolved in water at a temperature of 298 K.

As shown in Table 1 below, there are other forms of Henry's law each of which defines the constant kH differently and requires different dimensional units.[5] The form of the equation presented above is consistent with the example numerical values presented for oxygen, carbon dioxide and hydrogen and with their corresponding dimensional units.

Note that for the above values, the unit of concentration, c , was chosen to be molarity (i.e., mol/L). Hence the dimensional units: L is liters of solution, atm is the partial pressure of the gaseous solute above the solution (in atmospheres of absolute pressure), and mol refers to a mol of the gaseous solute in the solution. Also note that the Henry's law constant, kH varies with the solvent and with the temperature.

## Forms of Henry's Law

There are various forms Henry's law which are discussed in the technical literature.[6] [7] [8]

• where:
• caq = moles of gas per liter of solution
• Lsoln = liters of solution
• pgas = partial pressure above the solution, in atmospheres of absolute pressure
• xaq = mole fraction of gas in solution ≈ moles of gas per mole of water
• atm = atmospheres of absolute pressure

As can be seen by comparing the equations in the above Table 1, the Henry's law constant kHp, c is simply the inverse of the constant kHc, p. Since all kH values may be referred to as the Henry's law constants, readers of the technical literature must be quite careful to note which version of the Henry's law equation is being used.[9]

It should also be noted the Henry's law is a limiting law that only applies for 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.

It also only applies 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 (CO2), which rapidly forms hydrated carbon dioxide and then carbonic acid (H2CO3) with water.

## Temperature dependence of Henry's law constant

When the temperature of a system changes, the Henry's law constant will also change.[10] [11] This is why some people prefer to name it the Henry's law coefficient. There are multiple equations assessing the effect of temperature on the constant. These forms of the van't Hoff equation are examples:[12]
• $k_{\rm H,pc} = k_{\rm H,pc}^\Theta \; \exp \left[ -C \cdot \left( \frac{1}{T}-\frac{1}{T^\Theta}\right)\right]$
• $k_{\rm H,cp} = k_{\rm H,cp}^\Theta\; \exp \left[ C \cdot \left( \frac{1}{T}-\frac{1}{T^\Theta}\right)\right]$
• where:
• kH = Henry's law constant as defined in the first section of this article.
• C = A constant, in kelvins. Note that the correct sign of C depends on whether kHp, c or kHc, p is used.
• T = Any given temperature, in kelvins
• T Θ = the standard state temperature of 298 K

The above equation is an approximation only and should be used only when no better experimentally derived formula for a given gas exists.

The following Table 2 lists some values for the constant C in the equation above:

Because the solubility of gases usually decreases with increasing temperature, the partial pressure a given gas concentration has in a liquid must increase. While heating water (saturated with nitrogen) from 25 °C to 95 °C, the solubility will decrease to about 43% of its initial value. The partial pressure of CO2 in seawater doubles with every 16 K increase in temperature.[13]

The constant C may be regarded as:
• $C = \frac{\Delta_{\rm{\,solv}}\,H}{R} = - \frac{d\ln k_{\rm{H}}}{d(1/T)}$
• where:
• Δsolve H = the enthalpy of solution
• R = the universal ideal gas constant

## References

1. ^ F.F. Lee (2007). Comprehensive analysis, Henry's law constant determination, and photocatalytic degradation of polychlorinated biphenyls (PCBs) and/or other persistent organic pollutants (POPs), Ph.D. dissertation, State University of New York at Albany, pp. 199-201. Published by ProQuest.
2. ^ Robert G. Mortimer (2000), Physical Chemistry, Second Edition, Academic Press, ISBN 0-12-508345-9
3. ^ Editors: D.W. Green and Robert H. Perry (1984), Perry's Chemical Engineers' Handbook, 6th Edition, McGraw-Hill, page=14-9, ISBN 0-07-049479-7
4. ^ Online Introductory Chemistry: Solubility of gases in liquids
5. ^ Francis L. Smith and Allan H. Harvey (Sept. 2007), "Avoid Common Pitfalls When Using Henry's Law", Chemical Engineering Progress (CEP), pp. 33-39
6. ^ Same as Reference 5
7. ^ North Carolina State University CH 431/Lecture 14
8. ^ An extensive list of Henry's law constants, and a conversion tool
9. ^ Same as Reference 5
10. ^ Same as Reference 5
11. ^ Same as Reference 3. See pages 3-101 to 3-103 for tabulated Henry's law constant values versus temperature for various gases.
12. ^ Same as Reference 8
13. ^ T. Takahashi et al (2002), "Global sea-air CO2 flux based on climatological surface ocean pCO2 and seasonal biological and temperature effect", Deep Sea Res. II, 49, (9-10), pp. 1601– 1622.