Obtain the relationship between ΔH and ΔU for gas phase reactions.
1. At constant pressure, ΔH and ΔU are related as
ΔH = ΔU + PΔV …(1)
2. For reactions involving gases, ΔV cannot be neglected. Therefore,
ΔH = ΔU + PΔV
= ΔH + P(V2 – V1)
ΔH = ΔU + PV2 – PV1 …(2)
where, V1 is the volume of gas-phase reactants and V2 that of the gaseous products.
3. We assume reactant and product behave ideally. Applying an ideal gas equation, PV = nRT. Suppose that n1 moles of gaseous reactants produce n2 moles of gaseous products. Then,
PV1 = n1RT and PV2 = n2RT …(3)
4. Substitution of equation (3) into equation (2) yields
ΔH = ΔU + n2RT – n1RT
= ΔU + (n2 – n1) RT
= ΔU + Δng RT ....(4)
where, Δng is the difference between the number of moles of products and those of reactants.