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#
