Question

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

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

The rate law for the formation of $C$ is__________.

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

Answer 1

Answer: (D)

$\frac{dc}{dt}=k\left[A\right]$

$2A+B\to C+D$

Given table

$\left(A\right)$ $\left(B\right)$ rate of $C$

(1) $0.1m$ $0.1M$ $1.2\times {10}^{-3}$

(2) $0.1$ $0.2$ $1.2\times {10}^{-3}$

(3) $0.2$ $0.1$ $2.4\times {10}^{-3}$

Suppose $r=K{\left[A\right]}^a{\left[B\right]}^b$

rate in (1)

$1.2\times {10}^{-3}=K{\left(0.1\right)}^a{\left(0.1\right)}^b\to \left(4\right)$

rate in (2)

$1.2\times {10}^{-3}=K{\left(0.1\right)}^a{\left(0.2\right)}^b\to \left(5\right)$

rate in (3)

$2.2\times {10}^{-3}=K{\left(0.2\right)}^a{\left(0.1\right)}^b\to \left(6\right)$

Dividing (4) & (5) gives $b=0$

Dividing (4) & (6) gives $a=1$

$r=K\left(A\right)$