Chemical Thermodynamics Chapter 4 Chemistry Class 12 Textbook Solution

i. At constant pressure, \( \Delta H \) and \( \Delta U \) are related as:

\[ \Delta H = \Delta U + P\Delta V \quad \text{(1)} \]

ii. For reactions involving gases, \( \Delta V \) cannot be neglected.

Therefore, \( \Delta H = \Delta U + P\Delta V \)

\[ = \Delta U + P(V_2 - V_1) \quad \text{(2)} \]

where \( V_1 \) is the volume of gas-phase reactants and \( V_2 \) is that of the gaseous products.

iii. We assume reactant and product behave ideally. Applying an ideal gas equation, \( PV = nRT \). Suppose that \( n_1 \) moles of gaseous reactants produce \( n_2 \) moles of gaseous products. Then,

iv. Substituting equation (3) into equation (2) yields

\[ \Delta H = \Delta U + n_2RT - n_1RT \] \[ = \Delta U + (n_2 - n_1)RT \] \[ = \Delta U + \Delta n_g RT \quad \text{(4)} \]

where \( \Delta n_g \) is the difference between the number of moles of products and those of reactants.