Import Question JSON

\textbf{Hint:} \text{Change in number of moles of gases should be Zero} \Delta H = \Delta U + \Delta n_g RT \Delta n = 0 \Delta H = \Delta U \Delta n_g = \sum \text{Gaseous P} - \sum \text{Gas R} \text{Let us calculate } \Delta n_g \text{ for each reaction:} \textbf{1. } \text{PCl}_5(\text{g}) \to \text{PCl}_3(\text{g}) + \text{Cl}_2(\text{g}) \Delta n_g = (1 + 1) - 1 = +1 \textbf{2. } 2\text{CO}(\text{g}) + \text{O}_2(\text{g}) \to 2\text{CO}_2(\text{g}) \Delta n_g = 2 - (2 + 1) = -1 \textbf{3. } \text{H}_2(\text{g}) + \text{Br}_2(\text{g}) \to 2\text{HBr}(\text{g}) \Delta n_g = 2 - (1 + 1) = 0 \textbf{4. } \text{C}(\text{s}) + 2\text{H}_2\text{O}(\text{g}) \to 2\text{H}_2(\text{g}) + \text{CO}_2(\text{g}) \Delta n_g = (2 + 1) - 2 = +1 \text{For } \Delta H = \Delta U, \text{ we need } \Delta n_g = 0 \text{Only reaction 3 has } \Delta n_g = 0, \text{ therefore only for this reaction } \Delta H = \Delta U. \text{The relationship between enthalpy and internal energy is:} \Delta H = \Delta U + \Delta n_g RT \text{When } \Delta n_g = 0 \text{ (no change in number of gaseous moles), the } \Delta n_g RT \text{ term becomes zero, making } \Delta H = \Delta U. \text{Therefore, option (3) is correct.}