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Which amongst the following options is the correct relation between change in enthalpy and change in internal energy?
By definition, enthalpy is H = U + PV. For a chemical reaction involving gases behaving ideally, Δ(PV) = Δ(n_g RT) = Δn_g RT. Therefore, ΔH = ΔU + Δn_g RT! Instant 3-second answer: Option (3)!
Enthalpy (H) is defined as the sum of internal energy (U) and pressure-volume energy (PV):
For a process involving an initial state (1) and final state (2):
For reactions involving ideal gases at constant temperature T, let n₁ be moles of gaseous reactants and n₂ be moles of gaseous products. Since P₁V₁ = n₁RT and P₂V₂ = n₂RT:
Substituting Δ(PV) = Δn_g RT into the enthalpy change expression yields:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Algebraically incorrect relation that omits temperature T and adds ΔH and ΔU.
Sign error on the expansion energy term; confuses expansion work with PV energy.
Accurate: Canonical thermodynamic expression relating ΔH and ΔU for gaseous systems.
Rearranges with a negative sign: ΔH - ΔU must equal +Δn_g RT, not -Δn_g RT.
Because expansion work done by gas is w = -PΔV = -Δn_g RT, students sometimes confuse work with enthalpy and write ΔH = ΔU - Δn_g RT. Since H = U + PV, the PV term has a positive sign, so ΔH = ΔU + Δn_g RT.
"Enthalpy change of a gaseous reaction at constant temperature is related to internal energy change by ΔH = ΔU + Δn_g RT."
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