Question

Derive the expression for work done in chemical reaction. Write the relationship between ∆H and ∆U for an isochoric process.

Answer 1

Expression for work done in a chemical reaction:

The work done by a system at constant temperature and pressure is given by

W = - P_ext ΔV            .....(1)

Assuming P_ext = P,

W = – PΔV

= – P (V₂ – V₁) W

= – PV₂ + PV₁       ......(2)

If the gases were ideal, at constant temperature and pressure.,

PV₁ = n₁RT and PV₂ = n₂RT     …(3)

Substitution of equation (3) into equation (2) yields

W = – n₂RT + n₁RT

= – (n₂ – n₁) RT

= – Δn_g RT            …(4)

Equation (4) gives the work done by the system in chemical reactions.

Relationship between ∆H and ∆U for an isochoric process:

For an isochoric process, ∆V = 0.

∆H = ∆U + P∆V = ∆U + 0 = ∆U

∴ ∆H = ∆U