Question

A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm at 300 K. The vapour pressure of propyl alcohol is 200 mm. If the mole fraction of ethyl alcohol is 0.6, its vapour pressure (in mm) at the same temperature will be
A ) 300
B ) 700
C ) 360
D ) 350

Answer 1

Hint: The total pressure of a binary solution is equal to the sum of the partial pressures of two components. Use the following formula for the total vapour pressure of the binary mixture of ethyl alcohol and propyl alcohol.
Total pressure = Partial pressure of ethyl alcohol + Partial pressure of propyl alcohol

Complete step by step answer:
Total vapour pressure of the mixture of ethyl alcohol and propyl alcohol is \[290{\text{ mm}}\].
Propyl alcohol has the vapour pressure of 200 mm.
The ethyl alcohol has the mole fraction of 0.6.
Subtract the mole fraction of ethyl alcohol from 1 and calculate the mole fraction of propyl alcohol
\[{\text{1}} - 0.{\text{6}} = 0.{\text{4}}\]
The total pressure of a binary solution is equal to the sum of the partial pressures of two components. The partial pressure of each component is the product of the mole fraction of that component in the solution and partial pressure of the pure component. Write the equation for the total pressure of binary solution.
Total pressure = partial pressure of ethyl alcohol + partial pressure of propyl alcohol
\[{{\text{P}}_{{\text{total}}}}{\text{ }} = {\text{ }}\left( {{{\text{X}}_{{\text{ethyl alcohol}}}}{\text{ }} \times {{\text{P}}_{{\text{pure ethyl alcohol}}}}} \right) + {\text{ }}\left( {{{\text{X}}_{{\text{propyl alcohol}}}}{\text{ }} \times {{\text{P}}_{{\text{pure propyl alcohol}}}}} \right)\]
Substitute values in the above expression
\[{\text{290 }} = {\text{ }}\left( {{\text{0}}{\text{.4 }} \times {\text{200}}} \right){\text{ + }}\left( {{\text{0}}{\text{.6 }} \times {{\text{P}}_{{\text{pure propyl alcohol}}}}} \right) \\
{\text{290 }} = {\text{ }}\left( {{\text{0}}{\text{.4 }} \times {\text{200}}} \right){\text{ + }}\left( {{\text{0}}{\text{.6 }} \times {{\text{P}}_{{\text{pure propyl alcohol}}}}} \right) \\
{{\text{P}}_{{\text{pure propyl alcohol}}}} = \dfrac{{290 - \left( {{\text{0}}{\text{.4 }} \times {\text{200}}} \right)}}{{0.6}} \\
= 350{\text{ mm}} \\ \]
Hence, the vapor pressure of pure ethyl alcohol is \[350{\text{ mm}}\].

Hence, the option D ) 350 is the correct answer.

Note: For an ideal solution, the total pressure of a binary solution is equal to the sum of the partial pressures of two components. However for non ideal solutions, the total pressure of a binary solution is not equal to the sum of the partial pressures of two components. For non ideal solutions the total pressure of a binary solution is either greater than or less than to the sum of the partial pressures of two components.