The formation enthalpies, Hf^ for H2 and O2 are 220.0 kJ mol^-1 and 250.0 kJ mol^-1, respectively, at 298.15 K, and Hf^ for H2 O (g) is -242.0 kJ mol^-1 at the same temperature. The average bond…

Given: Hf^ ( H2) = 220.0 kJ mol^-1, Hf^ ( O2) = 250.0 kJ mol^-1, and Hf^ ( H2 O) = -242.0 kJ mol^-1 at 298.15 K. Find: The average bond enthalpy of the O-H bond in water. Using Hess's law: Hf^ ( H2 O) = Bond enthalpy of O-H 2 - ( Hf^ ( H2) + Hf^ ( O2)) Substituting the given values: -242 = 2 Bond enthalpy of O-H - (220 + 250) -242 = 2 Bond enthalpy of O-H - 470 2 Bond enthalpy of O-H = 228 Bond enthalpy of O-H = 114 kJ/mol Therefore, the average bond enthalpy of the O-H bond in water is 114 kJ/mol.

The formation enthalpies, Hf^ for H2 and O2 are 220.0 kJ mol^-1 a… — Solution | JEE Chemistry

NVAEasyJEE 2025Enthalpies (Bond, Combustion, Formation…)

The formation enthalpies, $\Delta H_f^\circ$ for $\text{H}_2$ and $\text{O}_2$ are $220.0 \, \text{kJ mol}^{-1}$ and $250.0 \, \text{kJ mol}^{-1}$ , respectively, at $298.15 \, \text{K}$ , and $\Delta H_f^\circ$ for $\text{H}_2\text{O}$ $\text{(g)}$ is $-242.0 \, \text{kJ mol}^{-1}$ at the same temperature. The average bond enthalpy of the O-H bond in water at $298.15 \, \text{K}$ is:

Answer

Correct answer:114

Step-by-step solution

Standard Method

Given: $\Delta H_f^\circ(\text{H}_2) = 220.0 \, \text{kJ mol}^{-1}$ , $\Delta H_f^\circ(\text{O}_2) = 250.0 \, \text{kJ mol}^{-1}$ , and $\Delta H_f^\circ(\text{H}_2\text{O}) = -242.0 \, \text{kJ mol}^{-1}$ at $298.15 \, \text{K}$ .

Find: The average bond enthalpy of the O-H bond in water.

Using Hess's law:

\Delta H_f^\circ(\text{H}_2\text{O}) = \text{Bond enthalpy of O-H} \times 2 - \left( \Delta H_f^\circ(\text{H}_2) + \Delta H_f^\circ(\text{O}_2) \right)

Substituting the given values:

-242 = 2 \times \text{Bond enthalpy of O-H} - (220 + 250)

-242 = 2 \times \text{Bond enthalpy of O-H} - 470

2 \times \text{Bond enthalpy of O-H} = 228

\text{Bond enthalpy of O-H} = 114 \, \text{kJ/mol}

Therefore, the average bond enthalpy of the O-H bond in water is $114 \, \text{kJ/mol}$ .

Common mistakes

Using the formation enthalpy values without applying Hess's law correctly. This is wrong because the solution explicitly relates product and reactant enthalpies through a balance equation. Instead, write the Hess's law relation first and then substitute the values.
Forgetting that water contains two O-H bonds. This is wrong because the bond enthalpy term must be multiplied by $2$ . Instead, use $2 \times$ bond enthalpy of O-H before solving.
Making a sign error with $\Delta H_f^\circ(\text{H}_2\text{O}) = -242.0 \, \text{kJ mol}^{-1}$ . This is wrong because changing the negative sign changes the final numerical value completely. Instead, substitute the value with its correct negative sign.

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