Question

1. estimate \\( \delta h^{\circ} \\) for the following reaction from the bond energies given. \\( ch_{4}(g)+2 o_{2}(g) \

ightarrow co_{2}(g)+2 h_{2} o(g) \\)

a. -923 kj/mol
b. -785 kj/mol
c. 1212 kj/mol
d. 818 kj/mol
e. -1615 kj/mol

Explanation:

Step1: Calculate energy required to break bonds

• For \(CH_4\): There are \(4\) \(C - H\) bonds. Energy to break \(C - H\) bonds: \(4\times414\) kJ/mol.
• For \(O_2\): There are \(2\) \(O = O\) bonds. Energy to break \(O = O\) bonds: \(2\times498.7\) kJ/mol.
• Total energy to break bonds: \(4\times414+2\times498.7\) \(=1656 + 997.4=2653.4\) kJ/mol.

Step2: Calculate energy released when bonds form

• For \(CO_2\): There are \(2\) \(C = O\) bonds. Energy released for \(CO_2\): \(2\times799\) kJ/mol.
• For \(H_2O\): There are \(2\) \(H_2O\) molecules, each with \(2\) \(H - O\) bonds. Energy released for \(H_2O\): \(2\times2\times460\) kJ/mol.
• Total energy released: \(2\times799+2\times2\times460\) \(=1598+1840 = 3438\) kJ/mol.

Step3: Calculate \(\Delta H^{\circ}\)

Using the formula \(\Delta H^{\circ}=\text{Energy to break bonds}-\text{Energy released when bonds form}\)
\(\Delta H^{\circ}=2653.4 - 3438=- 784.6\approx - 785\) kJ/mol.

Answer:

B. -785 kJ/mol