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

Sum

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

#### Solution

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.

Concept: Enthalpy (H)
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#### APPEARS IN

Balbharati Chemistry 12th Standard HSC for Maharashtra State Board
Chapter 4 Chemical Thermodynamics
Exercises | Q 4.02 | Page 88