Chapter 9, Problem 42E

Interpretation Introduction

Interpretation:

The amount required (in grams) of each of given items to produce $7.8\times {10}^3\text{ kJ}$ of energy is to be calculated.

Concept introduction:

The power generated by utilizing chemical or physical resources for providing heat and light or for carrying out various processes, is known as energy. The SI unit of energy is joule.

Unit conversion is defined as the process in which multiple steps are used to convert the unit of measurement for the same given quantity. It is determined by multiplication with a conversion factor.

The fraction in which numerator and denominator are the same quantities but are determined in different units, is known as a conversion factor.

Answer to Problem 42E

Solution:

$3.7\times {10}^2\text{ g}$

$1.8\times {10}^2\text{ g}$

$2.6\times {10}^2\text{ g}$

$2.8\times {10}^2\text{ g}$

$1.6\times {10}^2\text{ g}$

Explanation of Solution

a) Pine wood

The combustion of pinewood produces heat energy. The energy produced during combustion is $-7.8\times {10}^3\text{ kJ}$.

The heat of combustion for pinewood is $-21\text{ kJ}$(From table $9.6$ ).

The amount used to produce $-7.8\times {10}^3\text{ kJ}$ energy is calculated as follows:

$\begin{array}{c}m=\left(-7.8\times {10}^3\cancel{\text{kJ}}\times \frac{1\text{ g}}{-21\cancel{\text{kJ}}}\right)\\ =3.7\times {10}^2\text{ g}\end{array}$

Therefore, the quantity of pinewood used to produce $7.8\times {10}^3\text{ kJ}$ energy is $3.7\times {10}^2\text{ g}$.

b) Octane

The combustion of octane produces heat energy. The energy produced during combustion is $-7.8\times {10}^3\text{ kJ}$.

The heat of combustion for octane is $-44.5\text{ kJ}$(From table $9.6$ ).

The amount used to produce $-7.8\times {10}^3\text{ kJ}$ energy is calculated as follows:

$\begin{array}{c}m=\left(-7.8\times {10}^3\cancel{\text{kJ}}\times \frac{1\text{ g}}{-44.5\cancel{\text{kJ}}}\right)\\ =1.8\times {10}^2\text{ g}\end{array}$

Therefore, the quantity of octane used to produce $7.8\times {10}^3\text{ kJ}$ energy is $1.8\times {10}^2\text{ g}$.

c) Ethanol

The combustion of ethanol produces energy. The energy produced during combustion is $-7.8\times {10}^3\text{ kJ}$.

The heat of combustion for ethanol is $-30\text{ kJ}$(From table $9.6$ ).

The amount used to produce $-7.8\times {10}^3\text{ kJ}$ energy is calculated as follows:

$\begin{array}{c}m=\left(-7.8\times {10}^3\cancel{\text{kJ}}\times \frac{1\text{ g}}{-30\cancel{\text{kJ}}}\right)\\ =2.6\times {10}^2\text{ g}\end{array}$

Therefore, the quantity of ethanol used to produce $7.8\times {10}^3\text{ kJ}$ energy is $2.6\times {10}^2\text{ g}$

d) Coal

The combustion of coal produces heat energy. The energy produced during combustion of coal is $-7.8\times {10}^3\text{ kJ}$.

The heat of combustion for coal is $-28\text{ kJ}$(From table $9.6$ ).

The amount used to produce $-7.8\times {10}^3\text{ kJ}$ energy is calculated as follows:

$\begin{array}{c}m=\left(-7.8\times {10}^3\cancel{\text{kJ}}\times \frac{1\text{ g}}{-28\cancel{\text{kJ}}}\right)\\ =2.8\times {10}^2\text{ g}\end{array}$

Therefore, the quantity of coal used to produce $7.8\times {10}^3\text{ kJ}$ energy is $2.8\times {10}^2\text{ g}$.

e) Natural gas

The combustion of natural gas produces heat energy. The energy produced during combustion is $-7.8\times {10}^3\text{ kJ}$.

The heat of combustion for natural gas is $-49.3\text{ kJ}$(From table $9.6$ ).

The amount used to produce $-7.8\times {10}^3\text{ kJ}$ energy is calculated as follows:

$\begin{array}{c}m=\left(-7.8\times {10}^3\cancel{\text{kJ}}\times \frac{1\text{ g}}{-49.3\cancel{\text{kJ}}}\right)\\ =1.6\times {10}^2\text{ g}\end{array}$

Therefore, the quantity of natural gas used to produce $7.8\times {10}^3\text{ kJ}$ energy is $1.6\times {10}^2\text{ g}$.