Which of the following relations are correct?
(A) Δ U=q+pΔ V
(B) Δ G=Δ H-TΔ S
(C) Δ S=qᵣₑᵥ/T
(D) Δ H=Δ U-Δ nRT
Choose the most appropriate answer from the options given below :

Solution

Chemistry ma’am · 3 steps

Check the sign of every term: expansion work takes energy out, and Δ H is Δ U plus the gas term.

1. Work sign. The first law is Δ U = q + w. When a gas expands against pressure p, the system does work and loses energy, so w = -pΔ V and Δ U = q - pΔ V.
2. Enthalpy link. From H = U + pV at constant T and p, for ideal gases pΔ V = Δ n_g RT. That gives the relation below, with a plus sign.

   Δ H = Δ U + Δ n_g RT

   Relation	Correct form	Verdict
   (A) Δ U = q + pΔ V	Δ U = q - pΔ V	wrong sign on work
   (B) Δ G = Δ H - TΔ S	same, the Gibbs equation	correct
   (C) Δ S = qᵣₑᵥ/T	same, the definition of entropy change	correct
   (D) Δ H = Δ U - Δ nRT	Δ H = Δ U + Δ n_g RT	wrong sign on gas term

3. So. Only B and C are correct, which is option (b).

The idea to keep. Expansion work removes energy, so it enters Δ U as -pΔ V. More gas moles mean Δ H exceeds Δ U, so it is Δ U + Δ n_g RT.

Answer from the NTA final answer key. Solution by PrepWiser.