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The reaction between $\mathrm{A\: and\: B}$ is carried out for different initial concentrations and the corresponding half life times are measured

$\mathrm{\left [ A \right ]_0}$ $\mathrm{\left [ B \right ]_0}$ $\mathrm{1y_2}$

500 10 60

500 20 60

10 500 60

20 500 30

the rate law of reaction will be:-
Option: 1
$\mathrm{rate\Rightarrow K \left [ A \right ]\left [ B \right ]}$

Option: 2
$\mathrm{rate\Rightarrow K \left [ A \right ]^{1}\left [ B \right ]}$

Option: 3
$\mathrm{rate\Rightarrow K \left [ A \right ]\left [ B \right ]^{3}}$

Option: 4
$\mathrm{rate\Rightarrow K \left [ A \right ]^{2}\left [ B \right ]^{2}}$

Answers (1)

best_answer

Experiment -1

$\mathrm{\left([A]_0\right)_2=500 }$ $\mathrm{(t1 / 2)_2=60}$

$\mathrm{\left.[ B]_0\right)_2=10}$

$\mathrm{ t_1/2 \propto \frac{1}{[A]_0^{n-1}} }$

Experiment -2

$\mathrm{ \left([A]_0\right)_2=500 }$ $\mathrm{ \quad\left(t \frac{1}{2}\right)_2=60 }$

$\mathrm{ \left([B)_0\right)_2=20 }$

$\mathrm{{\left[\frac{[B_0]_2}{\left[B_0\right]_1}\right]^{n-1}=\left(\frac{\left[t_ 1/2\right]_1}{\left[t_ 1/2\right]_2}\right)} }$

$\mathrm{{\left[\frac{20}{10}\right]^{n-1}=\left(\frac{60}{60}\right)} }$

$\mathrm{\left ( 2 \right )^{n-1}\Rightarrow 1 }$

$\mathrm{\left ( 2 \right )^{n-1}\Rightarrow 2^{0} }$

$\mathrm{n-1 =0 }$

$\mathrm{n=1}$ [First order w.r.t.[B] ]

Here $\mathrm{[A]_0}$ concentration doesn't change so half life depends on $\mathrm{[B]_0}$ only.

Experiment-3 Experiment-4

$\mathrm{{\text { }}{\left\{[A]_0\right\}_3= 10}}$ $\mathrm{\left ( \left [ A \right ]_0 \right )_4=20}$

$\mathrm{{\{[B_0]\}_3=500}}$ $\mathrm{\left ( \left [ B \right ]_0 \right )_4=500}$

$\mathrm{{\left(t _1/2\right)_3=60}}$ $\mathrm{\left ( t_1/2 \right )_4=30}$

$\mathrm{\frac{\left([A]_0\right)_4}{\left((A]_0\right)_3}=\left(\frac{\left ( t_1/2 \right )_3}{\left(t_1/2\right)_4}\right)^{n-1} }$

$\mathrm{ \frac{20}{10} \Rightarrow\left(\frac{60}{30}\right)^{n-1} }$

$\mathrm{ (2) \Rightarrow(2)^{n-1} }$

$\mathrm{ n-1=1 }$

$\mathrm{ n=2 }$ [Second order w.r.t.[A] ]

$\mathrm{ \text { So\, rate }=K[A]^2[B]^1}$

Hence option 2 is correct.

.

Posted by

chirag

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