Chapter 8, Problem 8.51P

Interpretation Introduction

Interpretation:

The heat of vaporization of diethyl ether at its normal boiling point is to be determined. Also, the results are to be compared with the tabulated value and then the heat of vaporization is to be calculated at ${100}^{\circ }\text{C}$ using Watson’s correlations.

Concept introduction:

According to the Trouton’s rule, entropy of vaporization at normal boiling point is same for most of the liquids which is $\Delta S_v\approx 0.088\text{ kJ/}\left(\text{mol}\cdot \text{K}\right)$. Thus, enthalpy of vaporization at normal boiling point, $T_b{}^{\circ }\text{C}$ is calculated as:

$\Delta H_v=\Delta S_v\left(T_b\right)$ ...… (1)

The Chen’s rule to calculate enthalpy of vaporization at normal boiling point is,

$\Delta H_v=R{T}_b\frac{3.978\left(T_b/T_c\right)-3.958+1.555\ln P_c}{1.07-\left(T_b/T_c\right)}$ ...… (2)

Here, $R$ is the universal gas constant with the value of $8.314\times {10}^{-3}\frac{\text{kJ}}{\text{K}\cdot \text{mol}}$, $T_b$ is the normal boiling point of the substance, $T_c$ is the critical temperature of the substance and $P_c$ is the critical pressure of the substance.

Watson’s correlation is used to calculate the heat of vaporization of any liquid at any temperature if its heat of vaporization is known at another temperature. The relation is,

$\Delta H_{v2}=\Delta H_{v1}{\left(\frac{T_c-T_2}{T_c-T_1}\right)}^{0.38}$ ...… (3)

Percentage error is calculated as:

$\%\text{ error}=\frac{Calculatedvalue-Actualvalue}{Actualvalue}\times 100$ ...… (4)