62. 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)
Match the Equations with Their Names – Arrhenius, Clausius-Clapeyron, Kirchhoff and van’t Hoff Equation Explained
In this question, four well-known equations are given in one column and four famous scientific laws or equations are listed in another. The task is to correctly match each mathematical expression with its corresponding name.
Identifying Each Equation
Equation (i): Arrhenius Equation
The equation
ln k = ln A − Ea/RT
describes how the rate constant varies with temperature. It relates the activation energy, temperature, and frequency factor of a reaction.
This is the famous Arrhenius Equation.
Therefore,
(i) → (s)
Equation (ii): van’t Hoff Equation
The equation
ln K = −ΔH°/RT + ΔS°/R
connects the equilibrium constant with standard enthalpy and entropy changes.
It explains how equilibrium shifts with temperature and is known as the van’t Hoff Equation.
Therefore,
(ii) → (q)
Equation (iii): Kirchhoff’s Law
The equation
ΔrH(T2) = ΔrH(T1) + ΔCp(T2 − T1)
describes how the enthalpy of a reaction changes with temperature using the heat capacity difference.
This relationship is known as Kirchhoff’s Law.
Therefore,
(iii) → (p)
Equation (iv): Clausius-Clapeyron Equation
The equation
ln P = −ΔHvap/RT + constant
relates vapor pressure to temperature and enthalpy of vaporization.
This is the integrated form of the Clausius-Clapeyron Equation.
Therefore,
(iv) → (r)
Matching the Correct Option
The correct matching is:
(i) → (s)
(ii) → (q)
(iii) → (p)
(iv) → (r)
This corresponds to:
Option (D)
Explanation of Every Option
Option (A)
This option incorrectly matches the van’t Hoff equation with the Clausius-Clapeyron equation and Kirchhoff’s law with the wrong expression. Therefore, the sequence is incorrect.
Option (B)
This option incorrectly identifies the Arrhenius equation as Kirchhoff’s law and also mismatches the remaining thermodynamic equations. Hence, it is incorrect.
Option (C)
This option incorrectly assigns the Arrhenius equation to Kirchhoff’s law and swaps several equations. Consequently, the matching does not agree with standard physical chemistry.
Option (D)
This is the correct answer because each equation is matched with its proper scientific law:
Arrhenius Equation → Rate constant
van’t Hoff Equation → Equilibrium constant
Kirchhoff’s Law → Temperature dependence of reaction enthalpy
Clausius-Clapeyron Equation → Vapor pressure and phase equilibrium
How to Remember These Equations Conceptually
The Arrhenius equation always contains the rate constant (k) and activation energy. Whenever you see k and Ea, think of reaction kinetics.
The van’t Hoff equation always contains the equilibrium constant (K) together with enthalpy and entropy, making it an equilibrium relationship.
Kirchhoff’s law always involves the change in reaction enthalpy with temperature through heat capacity.
The Clausius-Clapeyron equation always contains vapor pressure (P) and enthalpy of vaporization, making it a phase equilibrium equation.
Final Answer
Correct Option: (D)
(i) → (s), (ii) → (q), (iii) → (p), (iv) → (r)
