Derive the relationship between $\Delta H$ and $\Delta U$ for an ideal gas. Explain each term involved in the equation.

(N/A) From the first law of thermodynamics,$q = \Delta U + p \Delta V$.
For an ideal gas,enthalpy is defined as $H = U + pV$.
For a change at constant temperature and pressure,the change in enthalpy is given by $\Delta H = \Delta U + \Delta(pV)$.
Since $pV = nRT$ for an ideal gas,at constant temperature,$\Delta(pV) = \Delta(nRT) = RT \Delta n_g$.
Substituting this into the enthalpy equation,we get $\Delta H = \Delta U + \Delta n_g RT$.
Here,$\Delta H$ is the change in enthalpy,$\Delta U$ is the change in internal energy,$\Delta n_g$ is the difference between the number of moles of gaseous products and gaseous reactants $(n_2 - n_1)$,$R$ is the universal gas constant,and $T$ is the absolute temperature.