The boiling temperature of a binary solution of A and B of concentration xA= 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.

Question

The boiling temperature of a binary solution of A and B of concentration [latex]x_{A}[/latex] = 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.

Accepted Answer

The equilibrium partial pressures of the components of an ideal mixture can be calculated using Raoult’s law:

[latex]P_{ ext {tot }}=x_{ A } p_{ A }^{*}+\left(1-x_{ A } ight) p_{ B }^{*}=102.955 kPa[/latex]

As 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

[latex]y_{A} = \frac{P_{A} }{P_{A} + P_{B}}[/latex] and [latex]y_{B} = \frac{P_{B} }{P_{A} + P_{B}}[/latex]

After substitution, we get [latex]x _{A}[/latex] = 0.52 and [latex]x _{B}[/latex] = 0.48.

Question 7.3: The boiling temperature of a binary solution of A and B of c...

Related Answered Questions

The equilibrium vapor pressure of a single component liquid at 300 K was found to be 0.2 bar. The heat of vaporization of the liquid is 40 kJ/mol. Assume the vapor to be an ideal gas, its density to be much less than that of the liquid. Estimate the temperature at which the equilibrium vapor ...

Verified Answer:

Verified Answer:

Verified Answer: