Question 9.8: Use tabulated data to find the heat of combustion of one mol......
Use tabulated data to find the heat of combustion of one mole of propane, C_3H_8, to form gaseous carbon dioxide and liquid water.
Strategy We will need values for the heats of formation of the reactants and products to determine the desired heat of combustion. First, we must write a balanced chemical equation for the process. Then we can use Equation 9.12 to calculate the heat of the reaction (in this case the heat of combustion) by looking up heats of formation in the table in Appendix E. The stoichiometric coefficients needed will be obtained from the balanced equation. Remember that the heat of formation of an element in its standard state—like the O_2 in this equation—will always be zero.
\Delta H^{\circ}=\sum_{i}\nu_{i}\Delta H_{f}^{\circ}\,(\mathrm{product})_{i}-\sum_{j}\nu_{j}\Delta H_{f}^{\circ}\,(\mathrm{reactant})_{j} (9.12)
{\mathrm C}_{3}{\mathrm H}_{8}({\mathrm g})+5~{\mathrm O}_{2}({\mathrm g})\longrightarrow3~{\mathrm C}{\mathrm O}_{2}({\mathrm g})+4~{\mathrm H}_{2}{\mathrm O}(\ell)
\Delta H° = 3\text{ mol }\Delta H_f^°(\text{CO}_2) + 4\text{ mol }\Delta H_f^°(\mathrm{H_2O}) – 1\text{ mol }\Delta H_f^°(\mathrm{C_3H_8}) – 5\text{ mol }(0)
= 3 mol (–393.5 kJ/mol) + 4 mol (–285.8 kJ/mol) – 1 mol (–103.8 kJ/mol)
= –2219.9 kJ
Discussion We use units of kJ/mol for the heat of formation of a substance. But in writing the enthalpy change of a chemical reaction, we will use kJ as our preferred unit, not kJ/mol. The reaction in this example illustrates why we do this. The value we calculated, ΔH° = –2219.9 kJ, is for a reaction in which one mole of propane reacts with five moles of oxygen to form three moles of carbon dioxide and four moles of water. So if we were to say “–2219.9 kJ/mol,” we would need to specify carefully which substance that “mol” refers to. We choose to write the ΔH value in kJ, with the understanding that it refers to the reaction as written. This is also dimensionally consistent with Equation 9.12, provided that we treat the stoichiometric coefficients as carrying units of moles. You may see other texts that refer to values as “per mole of reaction.”
Check Your Understanding Use heat of formation data from Appendix E to calculate ΔH° for the following reaction: ClO_2(g) + O(g) → ClO(g) + O_2(g)