Question

The experimental data for the reaction \(2 A + B_2 \longrightarrow 2 AB\) is The rate equation for the above data is

Exp.	[A]	\([B_2]\)	Rate \((M\,s^{-1})\)
1	0.50	0.50	\(1.6 \times 10^{-4}\)
2.	0.05	1.00	\(3.2 \times 10^{-4}\)
3.	1.00	1.00	\(3.2 \times 10^{-4}\)

• A. rate = k $[B_2]$
• B. rate = k $[B_2]^2$
• C. rate = k $[A]^2[B]^2$
• D. rate = k $[A]^2[B]$

Answer 1

The Correct Option is A

 To determine the rate equation for the given reaction \(2 A + B_2 \longrightarrow 2 AB\), we can analyze the experimental data from the table provided.

Experiment	[A]	\([B_2]\)	Rate \((M\,s^{-1})\)
1	0.50	0.50	\(1.6 \times 10^{-4}\)
2	0.05	1.00	\(3.2 \times 10^{-4}\)
3	1.00	1.00	\(3.2 \times 10^{-4}\)

Let's derive the rate equation by analyzing changes in concentration and their effects on the rate:

1. Comparing Experiments 1 and 2, when [A] decreases from 0.50 to 0.05 (a 10-fold decrease) and [B₂] increases from 0.50 to 1.00, the rate doubles from \(1.6 \times 10^{-4}\,\text{M s}^{-1}\) to \(3.2 \times 10^{-4}\,\text{M s}^{-1}\).
2. Comparing Experiments 2 and 3 where [B₂] is held constant, increasing [A] from 0.05 to 1.00 has no effect on the rate, indicating that the rate is independent of the concentration of A.

From these observations, it is clear that the change in the concentration of A does not affect the rate, implying a zero-order dependency with respect to A. The effect of B₂ shows a direct proportional relationship indicating a first-order dependency with respect to B₂.

Therefore, the rate equation can be determined as:

\(\text{rate} = k [B_2]\)

Based on the options provided, the correct rate equation is:

rate = k \([B_2]\)