Chapter 13, Problem 13.88QP

Interpretation Introduction

Interpretation: The fuel values of liquid propanol and isopropanol are to be calculated. The comparison of their fuel values is to be done.

Concept introduction: Fuel value is defined as the amount of energy which is generated by the complete combustion of a particular mass of the fuel. The fuel value of alcohols increases with increase in number of carbon atoms in the alcohol.

To determine: The fuel value of propanol and isopropanol and the comparison of their fuel values.

Answer to Problem 13.88QP

The fuel value of diethyl ether is $\underset{\_}{36.77kJ/g}$. The fuel value of butanol is $\underset{\_}{36.02kJ/g}$. The fuel value of diethyl ether is greater than butanol.

Explanation of Solution

The structure of propanol is,

Figure 1

The structure of isopropanol is,

Figure 2

The fuel value is calculated by the formula,

$\text{Fuel}\text{value}=\frac{\text{Heat}\text{of}\text{combustion}}{\text{Mass}\text{of}\text{substance}}$ (1)

Propanol ( ${\text{C}}_3{\text{H}}_8\text{O}$) burns according to the thermochemical equation:

${\text{2C}}_3{\text{H}}_8\text{O}\left(l\right)+9{\text{O}}_{\text{2}}\left(g\right)\to 6{\text{CO}}_{\text{2}}\left(g\right)+8{\text{H}}_{\text{2}}\text{O}\left(l\right)$

According to the above reaction, $2$ moles of propanol are consumed in the process of combustion.

Molar mass of propanol is $60.09\text{g/mol}$.

Since, mass of $1$ mol of ${\text{C}}_3{\text{H}}_8\text{O}\left(l\right)$ is $60.09\text{g}$.

Therefore, mass of $2$ moles of ${\text{C}}_3{\text{H}}_8\text{O}\left(l\right)$ is $\begin{array}{c}2\times 60.09\text{g}\\ =\text{120}\text{.18}\text{g}\end{array}$.

The heat of combustion of propanol is $-2021\text{kJ/mol}$.

Substitute the value of heat of combustion of propanol and its mass in equation (1).

$\begin{array}{c}\text{Fuel}\text{value}=\frac{2021\text{kJ/mol}}{\text{120}\text{.18}\text{g/mol}}\\ =16.81\text{kJ/g}\end{array}$

Isopropanol ( ${\text{C}}_3{\text{H}}_8\text{O}$) burns according to the thermochemical equation:

${\text{2C}}_3{\text{H}}_8\text{O}\left(l\right)+9{\text{O}}_{\text{2}}\left(g\right)\to 6{\text{CO}}_{\text{2}}\left(g\right)+8{\text{H}}_{\text{2}}\text{O}\left(l\right)$

According to the above reaction, $2$ moles of isopropanol are consumed in the process of combustion.

Molar mass of isopropanol is $60.01\text{g/mol}$.

Since, mass of $1$ mol of ${\text{C}}_3{\text{H}}_8\text{O}\left(l\right)$ is $60.01\text{g/mol}$.

Therefore, mass of $2$ moles of ${\text{C}}_3{\text{H}}_8\text{O}\left(l\right)$ is $\begin{array}{c}2\times 60.01\text{g}\\ =\text{120}\text{.02}\text{g}\end{array}$.

The heat of combustion of isopropanol is $-2005\text{kJ/mol}$.

Substitute the value of heat of combustion of isopropanol and its mass in equation (1).

$\begin{array}{c}\text{Fuel}\text{value}=\frac{2005\text{kJ/mol}}{\text{120}\text{.02}\text{g/mol}}\\ =16.70\text{kJ/g}\end{array}$

The fuel value of diethyl ether is $\underset{\_}{36.77kJ/g}$. The fuel value of butanol is $\underset{\_}{36.02kJ/g}$. The fuel value of diethyl ether is greater than butanol.

Conclusion

The fuel value of diethyl ether is $\underset{\_}{36.77kJ/g}$. The fuel value of butanol is $\underset{\_}{36.02kJ/g}$. The fuel value of diethyl ether is greater than butanol.