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 $[A]/mol\ L^{-1}$ $[B]/mol\  L^{-1}$ $\text{Initial rate/mol L}^{-1} min^{-1}$
$I$ $0.1$ $0.1$ $2.0 \times 10^{-2}$
$II$ $-$ $0.2$ $4.0 \times 10^{-2}$
$III$ $0.4$ $0.4$ $-$
$IV$ $-$ $0.2$ $2.0 \times 10^{-2}$

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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