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Q. For the reaction $A+B \rightarrow C$ ; starting with different initial concentration of $A$ and $B$ , initial rate of reaction were determined graphically in four experiments.
$3.2\times 10^{- 3}$
S.NO. $\left[\right.A\left]\right._{0}/M$ (Initial conc.) $\left[\right.B\left]\right._{0}/M$ (Initial conc.) $rate/M \,\sec^{-1}$
$1$ $1.6\times 10-3$ $5\times 10-2$ $10-3$
$2$ $3.2\times 10-3$ $5\times 10-2$ $4\times 10-3$
$3$ $1.6\times 10-3$ $10-1$ $2\times 10-3$
$4$ $3.2\times 10^{- 3}$ $10^{- 1}$ $8\times 10^{- 3}$
Rate law for reaction from above data is

NTA AbhyasNTA Abhyas 2022

Solution:

$R=K[A]^m[B]^n$
$10^{-3}=K\left(1.6 \times 10^{-3}\right)^m\left(5 \times 10^{-2}\right)^n$
$3.2 \times 10^{-3}=K\left(3.2 \times 10^{-3}\right)^m\left(5 \times 10^{-2}\right)^n$
$1.6 \times 10^{-3}=K\left(10^{-1}\right)^m\left(2 \times 10^{-3}\right)^n$
$3.2 \times 10^{-3}=K\left(10^{-1}\right)^m\left(8 \times 10^{-3}\right)^n$
Solving $R=K[A]^2[B]$