The vapor pressure of a dilute solution of a non-volatile solute and the vapor pressure of the pure solvent at the same temperature are P and P*, respectively. \(\frac{P^*-P}{P^*}\) is equal to
(Assume that the vapor phase behaves as an ideal gas)
(Assume that the vapor phase behaves as an ideal gas)
- molality of the solution
- mole fraction of the solvent
weight fraction of the solute
- mole fraction of the solute
The Correct Option is D
Solution and Explanation
The problem given is related to colligative properties in physical chemistry, specifically Raoult's Law, which is used to determine the vapor pressure of solutions.
Raoult's Law states that the vapor pressure of a solution, \( P \), is directly proportional to the mole fraction of the solvent in the solution. When a non-volatile solute is dissolved in a solvent, the vapor pressure of the solution decreases compared to the vapor pressure of the pure solvent, \( P^* \). The relationship is given by:
\(P = x_{\text{solvent}} P^*\)
where \( x_{\text{solvent}} \) is the mole fraction of the solvent.
The difference in vapor pressure between the pure solvent and the solution is given by:
\(P^* - P = P^* - x_{\text{solvent}} P^*\)
This difference can be further expressed as:
\(P^* - P = P^*(1 - x_{\text{solvent}})\)
Dividing by the vapor pressure of the pure solvent \( P^* \), we have:
\(\frac{P^* - P}{P^*} = 1 - x_{\text{solvent}}\)
The term \( 1 - x_{\text{solvent}} \) is equivalent to the mole fraction of the solute \( x_{\text{solute}} \) in the solution, as the sum of the mole fractions in a solution must equal 1:
\(x_{\text{solvent}} + x_{\text{solute}} = 1\)
Therefore,
\(\frac{P^* - P}{P^*} = x_{\text{solute}}\)
Hence, the expression \(\frac{P^* - P}{P^*}\) is equal to the mole fraction of the solute.
The correct option is: mole fraction of the solute.
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