Match List-I with List-IIList-IList-II(A) Collision Theory(I) k=([R]_…

Match List-I with List-II

List-I	List-II
(A) Collision Theory	(I) \( \displaystyle k=\frac{[\mathrm{R}]_0-[\mathrm{R}]}{t} \)
(B) Arrhenius Equation	(II) \( \displaystyle k=\mathrm{A}\,e^{-E_a/RT} \)
(C) Rate constant for zero order	(III) \( \displaystyle k=\frac{1}{t}\ln\frac{[\mathrm{R}]_0}{[\mathrm{R}]} \)
(D) Rate constant for first order	(IV) \( \displaystyle \text{Rate}=PZ_{AB}\,e^{-E_a/RT} \)

Choose the correct answer from the options given below:

Answer & explanation

Correct answer: option 2

The correct answer is Option (2) → (A) - (IV), (B) - (II), (C) - (I), (D) - (III)

Two of the items describe how the rate depends on temperature and on collisions (Arrhenius equation, collision theory). The other two are integrated rate equations, which come from integrating the rate law of a zero order and a first order reaction.

(A) Collision Theory — This matches (IV) Rate = PZ_ABe^−E_a/RT. A reaction occurs only when molecules collide. Z_AB is the collision frequency of A and B, e^−E_a/RT is the fraction of molecules with energy equal to or more than E_a, and P, the probability or steric factor, allows for the proper orientation of the colliding molecules.
\( \displaystyle \text{Rate}=P\,Z_{AB}\,e^{-E_a/RT} \)
(B) Arrhenius Equation — This matches (II) k = A e^−E_a/RT. It gives the temperature dependence of the rate constant. A is the Arrhenius (pre-exponential) factor and E_a is the activation energy; k increases when T increases or E_a decreases.
\( \displaystyle k=A\,e^{-E_a/RT} \)
(C) Rate constant for zero order — This matches (I) k = ([R]₀ − [R])/t. In a zero order reaction the rate does not depend on concentration, so [R] falls linearly with time:
    \( \displaystyle -\frac{d[R]}{dt}=k \)
    \( \displaystyle [R]=[R]_0-kt \)
    \( \displaystyle k=\frac{[R]_0-[R]}{t} \)
(D) Rate constant for first order — This matches (III) k = (1/t) ln([R]₀/[R]). In a first order reaction the rate is proportional to [R], so integration gives a logarithmic expression:
    \( \displaystyle -\frac{d[R]}{dt}=k[R] \)
    \( \displaystyle \ln\frac{[R]_0}{[R]}=kt \)
    \( \displaystyle k=\frac{1}{t}\ln\frac{[R]_0}{[R]} \)

Match List-I with List-II

List-I	List-II
(A) Collision Theory	(I) \( \displaystyle k=\frac{[\mathrm{R}]_0-[\mathrm{R}]}{t} \)
(B) Arrhenius Equation	(II) \( \displaystyle k=\mathrm{A}\,e^{-E_a/RT} \)
(C) Rate constant for zero order	(III) \( \displaystyle k=\frac{1}{t}\ln\frac{[\mathrm{R}]_0}{[\mathrm{R}]} \)
(D) Rate constant for first order	(IV) \( \displaystyle \text{Rate}=PZ_{AB}\,e^{-E_a/RT} \)

Choose the correct answer from the options given below:

Answer & explanation

Correct answer: option 2

The correct answer is Option (2) → (A) - (IV), (B) - (II), (C) - (I), (D) - (III)

(A) Collision Theory — This matches (IV) Rate = PZ_ABe^−E_a/RT. A reaction occurs only when molecules collide. Z_AB is the collision frequency of A and B, e^−E_a/RT is the fraction of molecules with energy equal to or more than E_a, and P, the probability or steric factor, allows for the proper orientation of the colliding molecules.
\( \displaystyle \text{Rate}=P\,Z_{AB}\,e^{-E_a/RT} \)
(B) Arrhenius Equation — This matches (II) k = A e^−E_a/RT. It gives the temperature dependence of the rate constant. A is the Arrhenius (pre-exponential) factor and E_a is the activation energy; k increases when T increases or E_a decreases.
\( \displaystyle k=A\,e^{-E_a/RT} \)
(C) Rate constant for zero order — This matches (I) k = ([R]₀ − [R])/t. In a zero order reaction the rate does not depend on concentration, so [R] falls linearly with time:
    \( \displaystyle -\frac{d[R]}{dt}=k \)
    \( \displaystyle [R]=[R]_0-kt \)
    \( \displaystyle k=\frac{[R]_0-[R]}{t} \)
(D) Rate constant for first order — This matches (III) k = (1/t) ln([R]₀/[R]). In a first order reaction the rate is proportional to [R], so integration gives a logarithmic expression:
    \( \displaystyle -\frac{d[R]}{dt}=k[R] \)
    \( \displaystyle \ln\frac{[R]_0}{[R]}=kt \)
    \( \displaystyle k=\frac{1}{t}\ln\frac{[R]_0}{[R]} \)