A solution of methanol and water has a mole fraction of water of 0.312 and a total vapor pressure of 211 torr at 39.9 °C. The vapor pressures of pure methanol and pure water at this temperature are 256 torr and 55.3 torr, respectively. Is the solution ideal? If not, what can be inferred about the relative strengths of the solute–solvent interactions compared to the solute–solute and solvent–solvent interactions?

Verified step by step guidance

1. Identify the components of the solution: methanol and water.
2. Use Raoult's Law to calculate the expected vapor pressure of the solution if it were ideal. Raoult's Law states that the partial vapor pressure of each component in an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.
3. Calculate the partial vapor pressure of methanol: \( P_{\text{methanol}} = X_{\text{methanol}} \times P^0_{\text{methanol}} \), where \( X_{\text{methanol}} = 1 - X_{\text{water}} \).
4. Calculate the partial vapor pressure of water: \( P_{\text{water}} = X_{\text{water}} \times P^0_{\text{water}} \).
5. Add the partial pressures of methanol and water to find the total vapor pressure of the ideal solution and compare it to the given total vapor pressure to determine if the solution is ideal. If the calculated total vapor pressure is different from the given total vapor pressure, the solution is not ideal, indicating that the solute-solvent interactions differ in strength from the solute-solute and solvent-solvent interactions.