Question

To translate the provided text:

An ideal solution has a vapor pressure of 80 torr and contains a non-volatile solute with a mole fraction of 0.2. What is the vapor pressure of the pure solvent at the same temperature?

A 64 torr

B 80 torr

C 100 torr

D 400 torr

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Answer

To determine the vapor pressure of the pure solvent, we can use Raoult's Law for an ideal solution:

Raoult's Law states that: $$ P_{\text{solution}} = X_{\text{solvent}} \times P^0_{\text{solvent}} $$ where:

  • $P_{\text{solution}}$ is the vapor pressure of the solution.
  • $X_{\text{solvent}}$ is the mole fraction of the solvent.
  • $P^0_{\text{solvent}}$ is the vapor pressure of the pure solvent.

Given:

  • Vapor pressure of the solution, $P_{\text{solution}} = 80 \text{ टोर}$.
  • Mole fraction of the solute, $X_{\text{solute}} = 0.2$.

The mole fraction of the solvent, $X_{\text{solvent}}$, can be calculated as: $$ X_{\text{solvent}} = 1 - X_{\text{solute}} = 1 - 0.2 = 0.8 $$

Using Raoult's Law: $$ 80 \text{ टोर} = 0.8 \times P^0_{\text{solvent}} $$

Solving for $P^0_{\text{solvent}}$, $$ P^0_{\text{solvent}} = \frac{80 \text{ टोर}}{0.8} = 100 \text{ टोर} $$

Therefore, the vapor pressure of the pure solvent is 100 टोर.

Final Answer

Option C: 100 टोर


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