# Explain how Henry's law works?

##### 1 Answer

*Henry's Law only applies to the solute in ideally-dilute solutions, where a gas has been dissolved into a liquid to a small extent, and it is obvious which is the solvent and which is the solute (Raoult's law applies to the solvent in either an ideal or ideally-dilute solution).*

**Henry's Law** for ideally-dilute solutions states:

#bb(P_i = chi_i^lk_(H,i))#

or for real, dilute solutions:

#bb(P_i = gamma_(II,i)chi_i^lk_(H,i) = a_(II,i)k_(H,i))# where:

#P_i# is the**partial pressure**of the*vapor*above the solution.#chi_i^l# is the#bb("mol")# **fraction**of the gas that is dissolved in the liquid.#k_(H,i)# is the**Henry's Law constant**, and it is equal to#P_i^"*"# , the partial pressure of the pure gas, when one extrapolates back to#chi_i^l = 0# .#gamma_(II,i)# is the**activity coefficient**of the gas in solution in reference to the ideally-dilute solution (rather than an ideal solution).#a_(II,i) = gamma_(II,i)chi_i^l# is the**activity**of the gas in solution in reference to the ideally-dilute solution.

The partial pressure of the vapor above the solution is also related to the

#bb(P_i = chi_i^v P)# where

#chi_i^v# is the#"mol"# fraction of the vapor that is above the solution and#P# is the total pressure.

*This assumes that the gas is ideal**(which is a pretty good assumption compared to assuming a liquid is "ideal"), and that the solution is highly dilute.*

Using this information, you can, for example, solve the following problem for an **ideally-dilute solution**:

A solution of ethanol (eth) and chloroform (chl) at

#45^@ "C"# with#chi_(eth) = 0.9900# has a vapor pressure of#"177.95 torr"# . At this high dilution of chloroform, the solution can be assumed to be essentially ideally dilute. The vapor pressure of pure ethanol at#45^@ "C"# is#"172.76 torr"# .

#a)# Find the partial pressures of the gases in equilibrium with the solution.

#b)# Find the mole fractions in the vapor phase.

#c)# Find the Henry's Law constant for chloroform in ethanol at#45^@ "C"# .

#d)# Predict the vapor pressure and vapor-phase mole fractions at#45^@ "C"# for a chloroform-ethanol solution with#chi_(eth) = 0.9800# (using the Henry's Law constant from part c). Compare with the experimental values of#P = "183.38 torr"# and#chi_(eth)^v = 0.9242# .

**ANSWERS**

#a)# #P_(eth) = "171.03 torr"# ,#P_(chl) = "6.92 torr"#

#b)# #chi_(eth)^v = 0.9611_1# ,#chi_(chl)^v = 0.0388_9#

#c)# #k_(H,chl) = "692 torr"#

#d)# #P = "183.14 torr"# ,#chi_(eth)^v = 0.9244#