Question 10.15: Calculating an Enthalpy of Reaction from Bond Energies The r...
Calculating an Enthalpy of Reaction from Bond Energies
The reaction of methane (CH_4) and chlorine produces a mixture of products called chloromethanes. One of these is monochloromethane, CH_3Cl, used in the preparation of silicones. Calculate ΔH for the reaction
CH_4 (g) + Cl_2 (g) \longrightarrow CH_3 Cl(g) + HCl(g)
Analyze
To identify which bonds are broken and formed, it helps to draw structural formulas (or Lewis structures), as in Figure 10-17. To apply expression (10.26) literally, we would break four \begin{matrix} C-H \end{matrix} bonds and one \begin{matrix} Cl-Cl \end{matrix} bond and form three \begin{matrix} C-H \end{matrix} bonds, one \begin{matrix} C-Cl \end{matrix} bond, and one \begin{matrix} H-Cl \end{matrix} bond. The net change, however, is the breaking of one \begin{matrix} C-H \end{matrix} bond and one \begin{matrix} Cl-Cl \end{matrix} bond, followed by the formation of one \begin{matrix} C-Cl \end{matrix} bond and one \begin{matrix} H-Cl \end{matrix} bond.
\Delta H =\Delta H(\text { bond breakage })+\Delta H \text { (bond formation) } \approx \Sigma BE \text { (reactants) } – \Sigma BE \text { (products) }(10.26)
\begin{array}{r c}\begin{matrix}\text{ΔH for net bond breakage:}\\\text{ } \\ \text{ } \end{matrix} &\begin{matrix} \text{1 mol } \begin{matrix} C-H \end{matrix} \text{bonds} & +414 kJ \\ \text{1 mol} \begin{matrix} Cl-Cl \end{matrix} \text{bonds} & +243 kJ \\ \hline \text{sum:} & +657 kJ \end{matrix} \end{array}
\begin{array}{r c} \begin{matrix}\text{ΔH for net bond formation:} \\\text{ } \\ \text{ } \end{matrix} \begin{matrix} \text{1 mol} \begin{matrix} C-Cl \end{matrix} \text{bonds} & -339 kJ \\ \text{1 mol} \begin{matrix} H-Cl \end{matrix} \text{bonds} & -431 kJ \\ \hline \text{sum:} & -770 kJ \end{matrix} \end{array}
Enthalpy of reaction: ΔH = 657 – 770 = -113 kJ
Assess
A number of terms cancel out because some of the same types of bonds appear in both reactants and products. Such a situation is not uncommon.