To solve this problem, we need to understand the relationship between enthalpy change $(\Delta H)$ and internal energy change $(\Delta U). \\$The enthalpy $(H)$ of a system is defined as:$\\ H = U + PV \\$where $U$ is the internal energy, $P$ is the pressure, and $V$ is the volume.$\\$For a process occurring at constant pressure, the change in enthalpy is given by:$\\ \Delta H = \Delta U + \Delta (PV) \\$If we consider an ideal gas, the term $\Delta (PV)$ can be expressed as:$\\ \Delta (PV) = \Delta (nRT) \\$where $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is the temperature.$\\$For a reaction involving gases, we focus on the change in moles of gas, $\Delta n_g. \\$Thus, the change in $(PV)$ for gases can be written as:$\\ \Delta (PV) = \Delta n_g RT \\$Substituting this into the enthalpy change equation, we get:$\\ \Delta H = \Delta U + \Delta n_g RT \\$Therefore, the correct relation between change in enthalpy and change in internal energy is:$\\ \Delta H = \Delta U + \Delta n_g RT \\$This corresponds to Option 2.