Question

Consider a binary solution of two volatile liquid components 1 and 2. \(x_1\) and \(y_1\) are the mole fractions of component 1 in the liquid and vapor phase, respectively. The slope and intercept of the linear plot of \( \frac{1}{x_1} \) vs \( \frac{1}{y_1} \) are given respectively as:

• A. \( \frac{p_1^0}{p_2^0} - \frac{p_1^0}{p_2^0} \)
• B. \( \frac{p_2^0}{p_1^0} - \frac{p_1^0}{p_2^0} \)
• C. \( \frac{p_1^0}{p_2^0} - \frac{p_2^0}{p_1^0} \)
• D. \( \frac{p_2^0}{p_1^0} - \frac{p_2^0}{p_1^0} \)

Hint:

For binary solutions, Raoult's Law governs the relationship between mole fractions in the liquid and vapor phases. The slope of the plot of \( \frac{1}{x_1} \) vs \( \frac{1}{y_1} \) depends on the vapor pressures of the components.

Answer 1

The Correct Option is A

For a binary solution of volatile components, the relationship between the mole fractions of components in the liquid (\( x_1 \)) and vapor phases (\( y_1 \)) is governed by Raoult's Law: \[ y_1 = \frac{p_1^0}{p_1} x_1, \] Where \( p_1^0 \) is the vapor pressure of component 1, and \( p_1 \) is the partial pressure of component 1. Rearranging the equation gives a linear relationship: \[ \frac{1}{x_1} = \left( \frac{p_1^0}{p_2^0} - \frac{p_1^0}{p_2^0} \right) \frac{1}{y_1}. \] Thus, the slope is given by \( \frac{p_1^0}{p_2^0} - \frac{p_1^0}{p_2^0} \), and the correct answer is option (1).