Chapter 12, Problem 12.145P

(a)

Interpretation Introduction

Interpretation:

$\Delta H_{\text{vap}}$ of dimethyl ether is to be calculated.

Concept introduction:

Clausius-Clapeyron equation is used to find the vapor pressure at one temperature when vapor pressure at another temperature and heat of enthalpy is given. It determines the change in vapor pressure with a change in temperature. The expression of the Clausius-Clapeyron equation is as follows:

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

Here,

$P_1\text{ and }{P}_2$ are the vapor pressure.

$T_1\text{ and }{T}_2$ are the temperature.

$R$ is the gas constant.

$\Delta H_{\text{vap}}$ is the heat of vaporization.

The conversion factor to convert $°\text{C}$ to Kelvin is as follows:

$T\left(\text{K}\right)=T\left(°\text{C}\right)+273.2$ (2)

(b)

Interpretation Introduction

$\Delta H_{\text{f}}$ of liquid dimethyl ether is to be calculated.

Concept introduction:

Hess’s law is used to calculate the enthalpy change of an overall reaction that can be derived as a sum of two or more reaction. According to Hess’s law $\Delta H$ of an overall reaction is equal to the sum of the enthalpy change for each individual reaction. $\Delta H_{\text{overall rxn}}=\Delta H_1+\Delta H_2+\mathrm{.......}+\Delta H_{\text{n}}$

Enthalpy is a state function so the value depends upon the initial state and final state not on the path so $\Delta H$ of an overall reaction can be calculated by the addition or subtraction of the individual steps whose $\Delta H$ is known.