Tamil Nadu Board of Secondary EducationHSC Science Class 11

Derive the relation between ∆H and ∆U for an ideal gas. Explain each term involved in the equation. - Chemistry

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Numerical

Derive the relation between ∆H and ∆U for an ideal gas. Explain each term involved in the equation.

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Solution

When the system at constant pressure undergoes changes from an initial state with H1, U1, V1 and P parameters to a final state with H2, U2, V2 and P parameters, the change in enthalpy ∆H, is given by

H = U + PV

At initial state H1 = U1 + PV1    ...(1)

At final state H2 = U2 + PV2    ...(2)

change in enthalpy is (2) – (1)

⇒ (H2 – H1) = (U2 – U1) + P(V2 – V1)

∆H = ∆U + P∆V     ...(3)

As per first law of thermodynamics,

∆U = q + w; w = - P∆V 

Equation (3) becomes

∆H = q + w + P∆V

∆H = qp – P∆V + P∆V

∆H = qp    ...(4)

qp is the heat absorbed at constant pressure and is considered as heat content.

Consider a closed system of gases which are chemically reacting to form gaseous products at constant temperature and pressure with Vi and Vf, as the total volumes of the reactant and product gases respectively, and ni and nf as the number of moles of gaseous reactants and products, then,

For reactants: P Vi = ni RT   ...(5)

For products: P Vf = nf RT   ...(6)

(6) - (5)

P (Vf – Vi) = (nf – ni) RT

P∆V = ∆ng RT   ...(7)

Substituting in (7) in (3)

∆H = ∆U + P∆V

∆H = ∆U + ∆ng RT 

Concept: Enthalpy (H)
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Chapter 7: Thermodynamics - Evaluation [Page 225]

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Tamil Nadu Board Samacheer Kalvi Class 11th Chemistry Volume 1 and 2 Answers Guide
Chapter 7 Thermodynamics
Evaluation | Q II. 25. | Page 225

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