Match List-I with List-II
|
List-I Reaction property |
List-II Formula |
|
(A) Half-life of decomposition of gaseous ammonia on hot platinum surface |
(I) \( \frac{ln(\frac{a_0}{a_t})}{t} \) |
|
(B) Instantaneous rate |
(II) \( [R]_0/2k \) |
|
(C) Rate constant of inversion of cane sugar |
(III) \( \frac{dx}{dt} \) |
|
(D) Half-life of acid hydrolysis of methyl acetate |
(IV) \( (ln2)/k \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
Each formula in List-II belongs to a particular order of reaction: \( t_{1/2} = [\mathrm{R}]_0/2k \) for a zero order reaction; \( k = \frac{1}{t}\ln\frac{a_0}{a_t} \) and \( t_{1/2} = \ln 2/k \) for a first order reaction. So each reaction in List-I is matched by its order, and the rate itself by its definition.
(A) Half-life of decomposition of gaseous ammonia on hot platinum surface — This matches (II) \([R]_0/2k\). At high pressure the platinum surface is fully covered by ammonia, so the rate does not depend on its concentration: rate = k, a zero order reaction, whose half-life is \( [\mathrm{R}]_0/2k \).
\( \displaystyle \ce{2NH3(g)} \xrightarrow[\text{1130 K}]{\ce{Pt}} \ce{N2(g) + 3H2(g)} \)
(B) Instantaneous rate — This matches (III) \(\frac{dx}{dt}\). The rate at a particular moment is the rate of change of the amount reacted, x, over an infinitesimally small time interval, the slope of the tangent to the concentration–time curve.
(C) Rate constant of inversion of cane sugar — This matches (I) \(\frac{ln(\frac{a_0}{a_t})}{t}\). Water is present in large excess, so the rate depends only on the sucrose concentration: a pseudo first order reaction, whose rate constant is \( k = \frac{1}{t}\ln\frac{a_0}{a_t} \).
\( \displaystyle \ce{C12H22O11 + H2O} \xrightarrow{\ce{H+}} \ce{C6H12O6}\,(\text{glucose}) + \ce{C6H12O6}\,(\text{fructose}) \)
(D) Half-life of acid hydrolysis of methyl acetate — This matches (IV) \((ln2)/k\). With water in large excess this is also pseudo first order, and the half-life of a first order reaction is \( \ln 2/k = 0.693/k \).
\( \displaystyle \ce{CH3COOCH3 + H2O} \xrightarrow{\ce{H+}} \ce{CH3COOH + CH3OH} \)
Shortcut: (B)-(III) appears only in Option (3).