Question

Which of the following equations has $\Delta_f H^\circ$ and $\Delta H^\circ$ same ?

• A. $\mathrm{H_2(g) + \dfrac{1}{2}O_2(g) \rightarrow H_2O(l)}$
• B. $\mathrm{N_2(l) + O_3(g) \rightarrow N_2O_3(g)}$
• C. $\mathrm{CH_4(g) + 2Cl_2(g) \rightarrow CH_2Cl_2(g) + 2HCl(g)}$
• D. $\mathrm{2CO(g) + O_2(g) \rightarrow 2CO_2(g)}$

Hint:

$\Delta_f H^\circ$ is defined only for formation of one mole of a compound from elements in standard states.

Answer 1

The Correct Option is A

Step 1: Definition of $\Delta_f H^\circ$.
Standard enthalpy of formation ($\Delta_f H^\circ$) is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states.

Step 2: Condition for equality.
$\Delta_f H^\circ$ and $\Delta H^\circ$ are the same when the reaction represents the formation of exactly one mole of a compound directly from its elements in standard states.

Step 3: Analysis of option (A).
The reaction $\mathrm{H_2(g) + \dfrac{1}{2}O_2(g) \rightarrow H_2O(l)}$ shows formation of one mole of liquid water from hydrogen and oxygen in their standard states.

Step 4: Conclusion.
Hence, this reaction has $\Delta_f H^\circ$ equal to $\Delta H^\circ$.