Question

For the non-stoichiometric reaction \(\mathrm{2A + B \rightarrow C + D}\), the following kinetic data were obtained in three separate experiments, all at 298 K.

Initial Concentration (A)	Initial Concentration (B)	Initial rate of formation of C (mol L-1 s-1)
0.1 M	0.1 M	\(1.2\times 10^{-3}\)
0.1 M	0.2 M	\(1.2\times 10^{-3}\)
0.2 M	0.1 M	\(2.4\times 10^{-3}\)

The rate law for the formation of C is :

• A. \(\frac{dc}{dt} = k[A][B]\)
• B. \(\frac{dc}{dt} = k[A]^2[B]\)
• C. \(\frac{dc}{dt} = k[A][B]^2\)
• D. \(\frac{dc}{dt} = k[A]\)

Hint:

Compare the experiments in which only one concentration changes.

Answer 1

The Correct Option is D

Let rate = \(k[A]^m[B]^n\).
Experiments 1 and 2: [A] fixed, [B] doubled, rate unchanged, so \(2^n = 1\) and \(n = 0\).
Experiments 1 and 3: [B] fixed, [A] doubled, rate doubles (\(1.2\times 10^{-3} \to 2.4\times 10^{-3}\)), so \(2^m = 2\) and \(m = 1\).
Rate law: \(\frac{dc}{dt} = k[A]\).
Answer: (4) \(\frac{dc}{dt} = k[A]\)