Question

For the non-stoichiometric reaction $2A+B\to C+D$, the following kinetic data were obtained in three separate experiments, all at 298 K

Initial Concentration (A)	Initial Concentration (B)	Initial rate of function of C $\left(mol{L}^{-1}{s}^{-1}\right)$
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 of the formation of $C$ is:

• A. $\frac{dc}{dt}=K\left[A\right][B{]}^2$
• B. $\frac{dc}{dt}=K\left[A\right]$
• C. $\frac{dc}{dt}=K\left[A\right]\left[B\right]$
• D. $\frac{dc}{dt}=K\left[A{]}^2\right[B]$

Answer 1

The correct option is B $\frac{dc}{dt}=K\left[A\right]$

From first and second experiment, it is observed that when the initial concentration of $A$ is held constant and the initial concentration of $B$ is doubled, the rate of the formation of $C$ is unaffected.
Hence, the rate of formation of $C$ is independent of the initial concentration of $B$.
From first and third experiment, it is observed that when the initial concentration of B is held constant and the initial concentration of $A$ is doubled, the rate of formation of $C$ is doubled.
Hence, the rate of formation of $C$ is directly proportional to the initial concentration of $A$.
Hence, the rate of formation of $A$ is given by the expression $\frac{dc}{dt}=K\left[A\right]$.