Question

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

(A) \({}^{226}_{88}\text{Ra} \to {}^{4}_{2}\text{He} + {}^{222}_{86}\text{Rn}\)
(B) \(2NH_3 \xrightarrow[\text{Pt catalyst}]{1130\,K} N_2(g) + 3H_2(g)\)
(C) \(2N_2O_5(g) \to 2N_2O_4(g) + O_2(g)\)
(D) \(C_2H_4(g) + H_2(g) \to C_2H_6(g)\)

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:

Radioactive decay and N2O5 decomposition are first order. The NTA key also counts ethene hydrogenation as first order.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We must pick all the first order reactions among (A) to (D).

Step 2: Check (A):
Radioactive decay of radium is always first order.

Step 3: Check (B):
The decomposition of ammonia on a hot Pt catalyst is zero order, so (B) is not first order.

Step 4: Check (C):
The decomposition of \(N_2O_5\) follows rate = k[\(N_2O_5\)], so it is first order.

Step 5: Check (D):
As in the previous question of this paper, the NTA key treats the hydrogenation of ethene as first order, so (D) is included.

Step 6: Match with the options:
(A), (C) and (D) are first order, which is option 4.

Final Answer:
The first order reactions are (A), (C) and (D), which is option 4 (as per the NTA final answer key). \[ \boxed{\text{(A), (C) and (D) only}} \]