Match the equations in the left column with their names in the right column

• (A) (i)-(s), (ii)-(r), (iii)-(p), (iv)-(q)
• (B) (i)-(p), (ii)-(q), (iii)-(r), (iv)-(s)
• (C) (i)-(p), (ii)-(q), (iii)-(s), (iv)-(r)
• (D) (i)-(s), (ii)-(q), (iii)-(p), (iv)-(r)

  The equations match as:
  (i) Arrhenius equation (s), (ii) van’t Hoff equation (q), (iii) Kirchhoff’s law (p), (iv) Clausius–Clapeyron equation (r), so the correct option is (D).

  Introduction

  Matching thermodynamic and kinetic equations with their correct names is a common CSIR NET and GATE question, and it tests conceptual understanding more than memory. This article explains how to match each given equation with Arrhenius, van’t Hoff, Kirchhoff’s law and the Clausius–Clapeyron equation, and discusses why the other options are incorrect.

  Step‑by‑step matching of equations

  Equation (i): ln k = ln A − Ea/RT

  • The form k=Ae−Ea/RTk=Ae−Ea/RT relates rate constant $k$ to temperature $T$, where EaEa is activation energy and $A$ is the pre‑exponential factor.

  • Taking natural log gives ln⁡k=ln⁡A−Ea/(RT)lnk=lnA−Ea/(RT), which is the Arrhenius equation, so (i) matches with (s).

  Equation (ii): ln K = −ΔrH⁰/RT + ΔrS⁰/R

  • For an equilibrium constant $K$, thermodynamics gives K=exp⁡(−ΔrG∘/RT)K=exp(−ΔrG∘/RT); using ΔrG∘=ΔrH∘−TΔrS∘ΔrG∘=ΔrH∘−TΔrS∘ leads to ln⁡K=−ΔrH∘/RT+ΔrS∘/RlnK=−ΔrH∘/RT+ΔrS∘/R.

  • This linear relation between $\ln K$ and $1/T$ is known as the van’t Hoff equation, so (ii) matches with (q).

  Equation (iii): ΔrH₂ − ΔrH₁ = ΔCp(T₂ − T₁)

  • Kirchhoff’s law describes how the enthalpy (heat) of reaction changes with temperature, giving ΔrH2−ΔrH1=ΔCp(T2−T1)ΔrH2−ΔrH1=ΔCp(T2−T1), where ΔCpΔCp is the difference in heat capacities of products and reactants.

  • Therefore equation (iii) is Kirchhoff’s law, so (iii) matches with (p).

  Equation (iv): ln P = −ΔH/RT + constant

  • For phase transitions such as vaporization, integrating the Clausius–Clapeyron relation yields ln⁡P=−ΔHvap/(RT)+ClnP=−ΔHvap/(RT)+C, where $P$ is vapour pressure and ΔHvapΔHvap is enthalpy of vaporization.

  • This is the integrated Clausius–Clapeyron equation, so (iv) matches with (r).

  Evaluation of given options

  Option	(i)	(ii)	(iii)	(iv)	Correct?	Reason
  (A)	(s) Arrhenius	(r) C–C	(p) Kirchhoff	(q) van’t Hoff	No	(ii) and (iv) swapped; ln K form is van’t Hoff, ln P form is Clausius–Clapeyron.
  (B)	(p) Kirchhoff	(q) van’t Hoff	(iii) (r) C–C?	(iv) (s) Arrhenius	No	(i) is not Kirchhoff, and (iv) is not Arrhenius because it uses pressure rather than rate constant.
  (C)	(p) Kirchhoff	(q) van’t Hoff	(s) Arrhenius	(r) C–C	No	Again mislabels (i) and (iii); ΔH₂ − ΔH₁ form belongs to Kirchhoff, not Arrhenius.
  (D)	(s) Arrhenius	(q) van’t Hoff	(p) Kirchhoff	(r) C–C	Yes	Correctly assigns each standard equation to its name.

  Only option (D) simultaneously gives Arrhenius for the kinetic rate equation, van’t Hoff for the temperature dependence of equilibrium, Kirchhoff for the temperature dependence of reaction enthalpy, and Clausius–Clapeyron for vapour pressure versus temperature.