Explain how Henry's law works?

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 #"mol"# fraction of the vapor that is above the solution and the total pressure:

#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#