Question

Among the following, which are examples of first-order reactions?

(A) \(^{226}_{88}\text{Ra} \rightarrow {}^{4}_{2}\text{He} + {}^{222}_{86}\text{Rn}\) 

(B) \(2\text{NH}_3 \xrightarrow[\text{Pt catalyst}]{1130\,\text{K}} \text{N}_2\text{(g)} + 3\text{H}_2\text{(g)}\) 

(C) \(2\text{N}_2\text{O}_5\text{(g)} \rightarrow 2\text{N}_2\text{O}_4\text{(g)} + \text{O}_2\text{(g)}\) 

(D) \(\text{C}_2\text{H}_4\text{(g)} + \text{H}_2\text{(g)} \rightarrow \text{C}_2\text{H}_6\text{(g)}\) 

Choose the correct answer from the options given below:

• A. (A), (B) and (D) only
• B. (A) and (C) only
• C. (B), (C) and (D) only
• D. (A), (C) and (D) only

Hint:

Examples to remember for CUET:
- First Order: All radioactive decays, decomposition of \(\text{N}_2\text{O}_5\), decomposition of \(\text{SO}_2\text{Cl}_2\), hydrogenation of ethene.
- Zero Order: Decomposition of \(\text{NH}_3\) on Pt at high pressure, decomposition of \(\text{HI}\) on Au.

Answer 1

The Correct Option is D

Concept:
A first-order reaction has a rate that is directly proportional to the first power of the reactant concentration:
\[ \text{Rate} = k [R]^1 \] Many common chemical transformations and all natural nuclear decay processes obey first-order kinetics.

Step 1: Assessing Radioactive Decay (Reaction A):
The disintegration of radium into radon and an alpha particle:
\[ ^{226}_{\phantom{0}88}\text{Ra} \rightarrow ^{\phantom{0}4}_{\phantom{0}2}\text{He} + ^{222}_{\phantom{0}86}\text{Rn} \] is a nuclear decay process. All natural and artificial radioactive decays obey first-order kinetics.
Hence, (A) is a first-order reaction.

Step 2: Assessing Ammonia Decomposition (Reaction B):
The decomposition of ammonia on a hot platinum catalyst at \(1130\text{ K}\) and elevated pressure is a classic example of a zero-order reaction:
\[ 2\text{NH}_3(\text{g}) \xrightarrow{\text{Pt, } 1130\text{ K}} \text{N}_2(\text{g}) + 3\text{H}_2(\text{g}) \] Under high pressure, the metal catalyst surface is completely saturated with adsorbed ammonia molecules, so varying the concentration of \(\text{NH}_3\) does not affect the rate.
Hence, (B) is zero-order and not first-order.

Step 3: Assessing Decomposition of \(\text{N}_2\text{O}_5\) (Reaction C):
The thermal decomposition of dinitrogen pentoxide in the gas phase proceeds with the rate law:
\[ \text{Rate} = k [\text{N}_2\text{O}_5] \] This is a standard example of a first-order chemical reaction in the NCERT syllabus.
Hence, (C) is a first-order reaction.

Step 4: Assessing Hydrogenation of Ethene (Reaction D):
The catalytic hydrogenation of ethene to ethane:
\[ \text{C}_2\text{H}_4(\text{g}) + \text{H}_2 \rightarrow \text{C}_2\text{H}_6(\text{g}) \] follows first-order kinetics with \(\text{Rate} = k[\text{C}_2\text{H}_4]\).
Hence, (D) is a first-order reaction.
Final Answer:
The first-order reactions are (A), (C), and (D), which corresponds to option (D).