Obtain the relationship between ΔH and ΔU for gas phase reactions. - Chemistry

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Derivation

Obtain the relationship between ΔH and ΔU for gas phase reactions.

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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.

Concept: Enthalpy (H)
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Chapter 4: Chemical Thermodynamics - Exercises [Page 88]

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