Question

For the reaction, $2NO+C{l}_2⟶2NOCl$ at $300K$ following data are obtained

Exp No	$\frac{InitialConcentration}{\left[NO\right]\left[C{I}_2\right]}$	initial rate
$1$	$0.010$ $0.010$	$1.2\times {10}^4$
$2$	$0.010$ $0.020$	$2.4\times {10}^4$
$3$	$0.020$ $0.020$	$9.6\times {10}^4$

Write rate law for the reaction. What is the order of the reaction? Also calculate the specific rate constant.

Answer 1

Let the rate law be given by;

Rate= $K\left[NO{]}^x\right[C{l}_2{]}^y$

$x+y$= Order of the reaction

$1.2\times {10}^4=K\left[0.01{]}^x\right[0.01{]}^y...\left(1\right)$

$2.4\times {10}^4=K\left[0.01{]}^x\right[0.02{]}^y...\left(2\right)$

$9.6\times {10}^4=K\left[0.02{]}^x\right[0.02{]}^y...\left(3\right)$

From (1) and (2), $\frac{1}{2}={\left(\frac{1}{2}\right)}^y\Rightarrow y=1$

From (2) and (3), $\frac{2}{8}=\frac{1}{4}={\left(\frac{1}{2}\right)}^x\Rightarrow x=2$

$\therefore$ Order of the reaction= $2+1=3$

Rate= $K\left[NO{]}^2\right[C{l}_2]$

From (1), $1.2\times {10}^{-4}=K\left(0.01{)}^2\right(0.01)$

$\therefore K=1.2\times {10}^{10}$= Specific rate constant