Question

Diethyl ether ( ${\mathbf{CH}}_3{\mathbf{CH}}_2{\mathbf{OCH}}_2{\mathbf{CH}}_3$) was one of the first chemicals used as an anesthetic. At $\mathbf{34}\mathbf{.}\mathbf{6}\mathbf{°}\mathbf{C}$, diethyl ether has a vapor pressure of 760torr, and at$\mathbf{17}\mathbf{.}\mathbf{9}\mathbf{°}\mathbf{C}$it has a vapor pressure of 400. torr. What is the ∆H of vaporization for diethyl ether?

Short answer

The ${\mathrm{\Delta H}}_{\mathrm{vap}}$ of diethyl ether is 28.6 kJ/mol.

Step-by-step solution

Enthalpy of vaporization

The enthalpy of vaporization mainly depends upon the intermolecular forces between the molecules. In these two molecules, heavy has a stronger intermolecular force as compared to water.

Calculation of enthalpy of vaporization

The relation between vapor pressures (P_vap) of a substance at temperatures T₁, and T₂, is given by the equation:

$\begin{array}{c}{\mathrm{lnP}}_{\mathrm{vap}}=-\frac{{\mathrm{\Delta H}}_{\mathrm{vap}}}{\mathrm{R}}\left(\frac{1}{\mathrm{T}}\right)+\mathrm{C}\\ \ln \left(\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}\right)=\frac{{\mathrm{\Delta H}}_{\mathrm{vap}}}{\mathrm{R}}\left(\frac{1}{{\mathrm{T}}_1}-\frac{1}{{\mathrm{T}}_2}\right)\end{array}$

${\mathrm{\Delta H}}_{\mathrm{vap}}$is the heat of vaporization of the substance, and R is the gas constant

For diethyl ether, the vapor pressures at temperatures T₁ and T₂ are

$\begin{array}{l}{\mathrm{P}}_1=400\mathrm{torr}\\ \\ {\mathrm{P}}_2=760\mathrm{torr}\\ \\ {\mathrm{T}}_1\text{=}290.9\mathrm{K}\\ \\ \mathrm{T}₂=307.6\mathrm{K}\\ \\ \mathrm{R}=8.3145\mathrm{J}.{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}\end{array}$

$\begin{array}{c}\ln \left(\frac{400\mathrm{torr}}{760\mathrm{torr}}\right)=\frac{{\mathrm{\Delta H}}_{\mathrm{vap}}}{8.314\mathrm{J}/\mathrm{mol}.\mathrm{K}}\left(\frac{1}{307.6\mathrm{K}}-\frac{1}{290.9\mathrm{K}}\right)\\ -0.642=\frac{{\mathrm{\Delta H}}_{\mathrm{vap}}}{8.314\mathrm{J}/\mathrm{mol}.\mathrm{K}}(-1.866\times {10}^{-4})\\ {\mathrm{\Delta H}}_{\mathrm{vap}}=28.6\mathrm{kJ}/\mathrm{mol}\end{array}$