Question 83: Which amongst the following options is the correct relation between change in enthalpy and change in internal energy?
(1) \Delta \mathrm{H}-\Delta \mathrm{U}=-\Delta \mathrm{nRT}
(2) \Delta \mathrm{H}+\Delta \mathrm{U}=\Delta \mathrm{nR}
(3) \Delta \mathrm{H}=\Delta \mathrm{U}-\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT}
(4) \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT}
Answer: Option (1)
Explanation:
The general relation between enthalpy change and internal energy change
for a chemical reaction is given by
\Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT}.
Here, \Delta \mathrm{n}_{\mathrm{g}} represents the change in number
of moles of gaseous species during the reaction.
Rearranging the above equation, we get
\Delta \mathrm{H}-\Delta \mathrm{U}=\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT}.
When the change in moles of gas is written as -\Delta \mathrm{n}, the relation becomes
\Delta \mathrm{H}-\Delta \mathrm{U}=-\Delta \mathrm{nRT}.
Thus, option (1) correctly represents the relation between change in enthalpy
and change in internal energy.