# Problem: Diethyl ether (C2H5OC2H5, molar mass = 74.12 g/mol) has a vapor pressure of 400.0 torr at 18.0°C. When a sample of benzoic acid (C6H5COOH, molar mass = 122.12 g/mol) is dissolved in diethyl ether, the vapor pressure of the solution is 342.0 torr at 18.0°C. Calculate the mole fraction of benzoic acid in the solution

###### FREE Expert Solution

We’re being asked to determine the mole fraction of a benzoic acid. Recall that the vapor pressure of a solution can be given by Raoult’s Law.

The given solutions are composed of water and glycerol. For a solution with volatile solute, Raoult’s Law is given as:

$\overline{){{\mathbf{P}}}_{{\mathbf{solution}}}{\mathbf{=}}{{\mathbf{X}}}_{{\mathbf{solvent}}}{{\mathbf{P}}}_{{\mathbf{solvent}}}^{{\mathbf{°}}}}$

where Xsolvent represents the mole fraction of the solvent and Psolvent is the vapor pressure of water in torr.

We can substitute the obtained values into the Raoult's Law equation and solve for Psolution:

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###### Problem Details

Diethyl ether (C2H5OC2H5, molar mass = 74.12 g/mol) has a vapor pressure of 400.0 torr at 18.0°C. When a sample of benzoic acid (C6H5COOH, molar mass = 122.12 g/mol) is dissolved in diethyl ether, the vapor pressure of the solution is 342.0 torr at 18.0°C. Calculate the mole fraction of benzoic acid in the solution

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