Chapter 15, Problem 86A

Heating with Coal How much heat is liberated when5.00 kg of coal is burned if the coal is 96.2% carbon bymass and the other materials in the coal do not react? $\Delta H_{comb}$ of carbon is -394 kJ/mol.

Interpretation Introduction

Interpretation:

The heat during combustion of coal needs to be calculated.

Concept introduction:

Molar mass: It is the sum of the total mass in grams of all the atoms that make a mole of a particular molecule.

Answer to Problem 86A

Heat released during the combustion of 5.00kg coal is $\text{-1}{\text{.58×10}}_{}^{\text{5}}\text{kJ}$.

Explanation of Solution

First, balanced thermochemical equation for the combustion of one mole of C.

${\text{C(s)+O}}_{\text{2}}^{}\text{(g)}\to {\text{CO}}_{\text{2}}^{}\text{(g)}$

${\text{ΔH}}_{\text{comb}}^{}=\text{-394kJ/mol}$

First convert kilograms to grams.

The percentage of C refers to the number of grams of C per 100grams.

Use the molar mass of C as a conversion factor to convert grams to mole.

Use the molar heat of combustion of C as conversion factor to convert mole to kJ.

$\begin{array}{c}\text{Heat release}=\text{50}\times \frac{\text{1000g}}{\text{1kgcoal}}\times \frac{\text{96}\text{.2}}{\text{100gcoal}}\times \frac{\text{1}}{\text{12}\text{.0107gC}}\times \frac{\text{-394}}{\text{1molC}}\\ \text{=}-\text{1}{\text{.58×10}}_5\text{kJ}\end{array}$

Conclusion

Use conversion factors and the table to refers the number.