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For the reaction $\mathrm{A + B + C \rightarrow D}$ , experimental data for the measured initial rates is given below. The order of the reaction with respect to $\mathrm{A, B \: and \: C}$ respectively is :

Expt. Initial Con.A Initial Con.B Initial Con.C Initial Rate $\mathrm{Ms^{-1}}$

1 0.4 1.0 0.8 $\mathrm{8.0\times10^{-5}}$

2 0.8 1.0 0.8 $\mathrm{3.2\times10^{-4}}$

3 0.8 4.0 0.8 $\mathrm{1.28\times10^{-3}}$

4 0.2 0.5 3.2 $\mathrm{4.0\times10^{-5}}$

Option: 1
$2,2,1$

Option: 2
$2,1,2$

Option: 3
$2,1,1$

Option: 4
$1,1,2$

Answers (1)

best_answer

$\mathrm{\text { Rate } =k[A]^x[B]^y [C]^z }$

$\mathrm{x =\text { Order w.r.t } A }$

$\mathrm{y =\text { Order w.r.t } B }$

$\mathrm{z =\text { Order w.r.t } C }$

$\mathrm{(1) 8 \times 10^{-5}=(0.4)^x(1)^y(0.8)^z }$

$\mathrm{(2) 3.2 \times 10^{-4}=(0.8)^x(1)^y(0.8)^z }$

$\mathrm{(3) 1.28 \times 10^{-3}=(0.8)^x(4)^y(0.8)^z }$

$\mathrm{(4) 4 \times 10^{-5}=(0.4)^x(0.4)^y(3.2)^z }$

from eq^n(1) & (2)

$\mathrm{\frac{3.2\times10^{-4}}{8\times10^{-5}}=\frac{\left ( 0.8 \right )^{x}\left ( 1 \right )^{y}\left ( 0.8 \right )^{z}}{\left ( 0.4 \right )^{x}\left ( 1 \right )^{y}\left ( 0.8 \right )^{z}} }$

$\mathrm{4=2^{x}\quad \quad x=2 }$

from eq^n(1) & (4)

$\mathrm{ \frac{8\times10^{-5}}{4\times 10^{-5}}=\left ( 2 \right ) ^{z}\left ( 4 \right )\left ( 2 \right )}$

$\mathrm{ z=1}$

from eq^n (2) & (3)

$\mathrm{ \frac{1.28 \times 10^{-3}}{3.2 \times 10^{-4}}=(4)^y \quad y=1 }$

$\mathrm{over\: all \: order 2,1,1 }$
Hence option 3 is correct.

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