Match List-I with List-II

Choose the correct answer from the options given below:

(A)-(II), (B)-(III), (C)-(I), (D)-(IV)

The correct answer is Option (3) → (A)-(II), (B)-(III), (C)-(I), (D)-(IV)

(A) Half-life of decomposition of gaseous ammonia on hot platinum surface:

The decomposition of $NH_3$ on a platinum surface at high pressure is a classic example of a zero-order reaction. The rate is independent of the concentration because the catalyst surface becomes saturated.

• Zero-order half-life formula: $t_{1/2} = \frac{[R]_0}{2k}$
• Matches with: (II)

(B) Instantaneous rate:

In calculus-based kinetics, the instantaneous rate is the rate of reaction at a specific moment, represented by the derivative of concentration with respect to time.

• Formula: $\frac{dx}{dt}$
• Matches with: (III)

(C) Rate constant of inversion of cane sugar:

The inversion of cane sugar (sucrose) is a pseudo-first-order reaction. The rate constant ($k$) for a first-order reaction is derived from the integrated rate equation: $\ln\left(\frac{a_0}{a_t}\right) = kt$.

• Formula: $k = \frac{\ln(a_0/a_t)}{t}$
• Matches with: (I)

(D) Half-life of acid hydrolysis of methyl acetate:

Acid hydrolysis of esters like methyl acetate is also a pseudo-first-order reaction because water is present in such large excess that its concentration remains constant.

• First-order half-life formula: $t_{1/2} = \frac{\ln 2}{k}$ (or $\frac{0.693}{k}$)
• Matches with: (IV)