Question

use the molar bond enthalpy data in the table to estimate the value of \\( \delta h_{\mathrm{mm}}^{\circ} \\) for the equation \\( \mathrm{ch}_{4}(g)+4 \mathrm{cl}_{2}(g) \
ightarrow \mathrm{ccl}_{4}(g)+4 \mathrm{hcl}(g) \\) the bonding in the molecules is shown.

Explanation:

Step1: Calculate the energy required to break bonds

• For \(CH_4\): There are \(4\) \(C - H\) bonds. Energy to break \(C - H\) bonds: \(4\times414\space kJ\cdot mol^{-1}\)
• For \(4Cl_2\): There are \(4\) \(Cl - Cl\) bonds. Energy to break \(Cl - Cl\) bonds: \(4\times243\space kJ\cdot mol^{-1}\)
• Total energy to break bonds: \(4\times414+4\times243=(414 + 243)\times4=657\times4 = 2628\space kJ\cdot mol^{-1}\)

Step2: Calculate the energy released when bonds are formed

• For \(CCl_4\): There are \(4\) \(C - Cl\) bonds. Energy released from \(C - Cl\) bonds: \(4\times331\space kJ\cdot mol^{-1}\)
• For \(4HCl\): There are \(4\) \(H - Cl\) bonds. Energy released from \(H - Cl\) bonds: \(4\times431\space kJ\cdot mol^{-1}\)
• Total energy released when bonds are formed: \(4\times331+4\times431=(331 + 431)\times4=762\times4=3048\space kJ\cdot mol^{-1}\)

Step3: Calculate \(\Delta H_{rxn}^{\circ}\)

Using the formula \(\Delta H_{rxn}^{\circ}=\text{Energy to break bonds}-\text{Energy released when bonds are formed}\)
\(\Delta H_{rxn}^{\circ}=2628 - 3048=- 420\space kJ\cdot mol^{-1}\)

Answer:

\(-420\space kJ\cdot mol^{-1}\)