Question

The enthalpy of vaporization for acetone is 32.0kJ/mol. The normal boiling point for acetone is 56.5⁰C. What is the vapor pressure of acetone at 23.5⁰C?

Short answer

The vapor pressure of acetone at 23.5⁰C is 270 torr.

Step-by-step solution

The boiling point of acetone

Use the Clausius-Clapeyron equation:

$\ln \left(\frac{p_1}{p_2}\right)=\frac{\Delta H_{vap}}{R}\times \left(\frac{1}{T_1}-\frac{1}{T_2}\right)$

P₁ is the pressure at the boiling point of acetone:$56.5°C=329.5K$

$\Delta H_{vap}$ is the enthalpy of vaporization for acetone: $32.0\text{kJ/mol}$

R is the universal gas constant: $R=8.314\text{J/K mol}$

$T_2=23.5^{\circ }C=329.5K$

T₁ is the boiling point of acetone: $56.5^{\circ }Cor329.5K$

Calculating the vapor pressure of acetone at 23.50C

Rearrange the equation and plug in the numbers:

$\ln p_2=\frac{\Delta H_{vap}}{R}\times \left(\frac{1}{T_1}-\frac{1}{T_2}\right)+\ln p_1$

$\ln p_2=\frac{32.000 \text{J/mol}}{8.314 \text{J/K} \text{mol}}\times \left(\frac{1}{329.5 K}-\frac{1}{296.5 K}\right)+\ln 760 \text{torr}$

$$\begin{gathered} \ln p_2=-1.30+6.633 \\ \ln p_2=5.333 \\ {p}_2=207 \text{torr} \end{gathered}$$