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Question
Obtain the relationship between ΔH and ΔU for gas phase reactions.
Solution
i. At constant pressure, ΔH and ΔU are related as
ΔH = ΔU + PΔV ...(1)
ii. For reactions involving gases, ΔV cannot be neglected.
Therefore, ΔH = ΔU + PΔV
= ΔU + P(V2 – V1)
ΔH = ΔU + PV2 – PV1 ...(2)
where, V1 is the volume of gas-phase reactants and V2 that of the gaseous products.
iii. 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)
iv. 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.
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