Question

For acetone (CH₃)₂CO, the normal boiling point is 56.5 °C and the enthalpy of vaporization is 31.3 kJ/mol.What is the vapor pressure of acetone at 25.0°C?

Short answer

The vapor pressure of acetone at given temperature is \(227.1{\bf{mmHg}}\).

Step-by-step solution

Define the vapour pressure  

Clausius-Clapeyron equation pertains to the relationship between the pressure and temperature. It is given by,

\(\ln \frac{{{P_1}}}{{{P_2}}} = \frac{{\Delta {H_{{\rm{vap }}}}}}{R}\left( {\frac{1}{{{T_2}}} - \frac{1}{{{T_1}}}} \right)\)

Where, \({{\bf{P}}_1}\) is the vapor pressure at \({{\bf{T}}_1}\) temperature

\({{\bf{P}}_2}\)is the vapor pressure at \({{\bf{T}}_2}\) temperature

\(\Delta {H_{vap}}\)is the enthalpy of vaporization

\({\bf{R}}\) is the universal gas constant \( = 8.314\;{\rm{J}}/{\rm{mol}}.{\rm{K}}\)

 Identify the enthalpy of vaporization for ethanol.

Now, at normal boiling point \({{\bf{T}}_2}\), vapor pressure, \({{\bf{P}}_2} = 1\;{\rm{atm}} = 760\;{\rm{mmHg}}\)

Thus, we have, \(\begin{aligned}{}{T_2} &= {56.5^\circ }{\rm{C}}\\ &= 56.5 + 273\;{\rm{K}}\\ &= 329.5\;{\rm{K}},\\{P_2} &= 760\;{\rm{mmHg}},\\\Delta {H_{{\rm{vap }}}} &= 31.3\;{\rm{kJ}}/{\rm{mol}} &= 31300\;{\rm{J}}/{\rm{mol}}\end{aligned}\),

\({T_1} = {25^\circ }{\rm{C}} = 25 + 273\;{\rm{K}} = 298\;{\rm{K}}\),

Now, substituting the values in the above relation, we have

\(\ln \frac{{{P_1}}}{{760{\rm{mmHg}}}} = \frac{{31300\;{\rm{J}}/{\rm{mol}}}}{{8.314\;{\rm{J}}/{\rm{mol}}.{\rm{K}}}}\left( {\frac{1}{{329.5\;{\rm{K}}}} - \frac{1}{{298\;{\rm{K}}}}} \right)\)

\( \Rightarrow \ln \frac{{{P_1}}}{{760{\rm{mmHg}}}} = (3764.73\;{\rm{K}}) \times \left( { - 0.000321\;{{\rm{K}}^{ - 1}}} \right)\)

\( \Rightarrow \ln \frac{{{P_1}}}{{760{\rm{mmHg}}}} = - 1.208\)

\(\begin{aligned}{} \Rightarrow \frac{{{P_1}}}{{760{\rm{mmHg}}}} &= {e^{( - 1.208)}}\\ \Rightarrow {P_1} &= {e^{( - 1.208)}} \times 760{\rm{mmHg}}\\ \Rightarrow {P_1} &= 0.299 \times 760{\rm{mmHg}}\\ &= > {P_1} = 227.1{\rm{mmHg}}\end{aligned}\)

Therefore, the vapor pressure of acetone at given temperature is \(227.1{\bf{mmHg}}\).