Question
The reaction between $A$ and $B$ is first order with respect to $A$ and zero order with respect to $B$. Fill in the blanks in the following table:
Experiment $[A]/mol\ L^{-1}$ $[B]/mol\ L^{-1}$ Initial rate$/mol\ L^{-1}\ min^{-1}$
$I$ $0.1$ $0.1$ $2.0 \times 10^{-2}$
$II$ $-$ $0.2$ $4.0 \times 10^{-2}$
$III$ $0.4$ $0.4$ $-$
$IV$ $-$ $0.2$ $2.0 \times 10^{-2}$

Answer

The given reaction is of the first order with respect to $A$ and of zero order with respect to $B.$
Therefore, the rate of the reaction is given by,
Rate $= k[A]^1 [B]^0$
Rate $= k[A]$
From experiment I, we obtain
$2.0 \times 10^{-2} \  mol\ L^{-1} \ \min^{-1} = k(0.1\ \ mol\ L^{-1})$
$k = 0.2\ \min^{-1}$
From experiment II, we obtain
$4.0 \times 10^{-2} \ mol\ L^{-1} \min^{-1} = 0.2 \min^{-1} [A]$
$[A] = 0.2 \ mol\ L^{-1}$
From experiment III, we obtain
Rate $= 0.2 \min^{-1} \times 0.4 \ mol\ L^{-1}$
$= 0.08 \ mol\ L^{-1}\ min^{-1}$
From experiment IV, we obtain
$2.0 \times 10^{-2} \ mol\ L^{-1}\ \min^{-1} = 0.2 \min^{-1}[A]$
$[A] = 0.1 \ mol\ L^{-1}$

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