Chapter 6, Problem 6.52P

The constituent partial pressures of a gas in equilibrium with a liquid solution at 30°C and 1 atm containing $\text{2}{\text{lb}}_{\text{m}}{\text{SO}}_{\text{2}}\text{/100}{\text{lb}}_{\text{m}}{\text{H}}_{\text{2}}\text{O}$are $p_{{\text{H}}_{\text{2}}\text{O}}\text{=31}\text{.6}\text{mm}\text{Hg}$and $p_{{\text{SO}}_2}\text{=176}\text{mm}\text{Hg}$. The balance of the gas is air.

(a) Calculate the partial pressure of air. If you make any assumptions, state what they are.

(b) Suppose the only data available on this system gave $p_{{\text{SO}}_2}\text{=176}\text{mm}\text{Hg}$, but there was no information given on the equilibrium partial pressure of water. Use Raoult's law to estimate a value for this quantity. Assuming that the value given in the problem statement is correct, what percentage error results from using Raoult’s law?

(c) The same system was examined in Example 6.4-1. What percentage errors in the two calculated quantities would result from using Raoult's law for the partial pressure of water?