Question 7.3: The boiling temperature of a binary solution of A and B of c...
The boiling temperature of a binary solution of A and B of concentration x_{A} = 0.45 is 100°C at 1.016 atm. At this temperature, the vapor pressures of pure A and B are 120.1 and 89.0 kPa, respectively. Prove that the solution is ideal and calculate the composition of the vapor when boiling begins.
The equilibrium partial pressures of the components of an ideal mixture can be calculated using Raoult’s law:
P_{\text {tot }}=x_{ A } p_{ A }^{*}+\left(1-x_{ A }\right) p_{ B }^{*}=102.955 kPaAs 1.016 atm = 102.9462 kPa, the solution can be considered as ideal. The composition of the vapor is easy to determine from the above data using the equations for the mole fractions in the vapor
y_{A} = \frac{P_{A} }{P_{A} + P_{B}} and y_{B} = \frac{P_{B} }{P_{A} + P_{B}}
After substitution, we get x _{A} = 0.52 and x _{B} = 0.48.