Question

Following is the graph between $(a-x)^{-1}$ and time $t$ for $2^{n d}$ order reaction:
Given, $\theta=\tan ^{-1}(0.5)$
$OA =2$

What is the initial rate of reaction?

• A. 0.250 mol $ltr ^{-1}\, min ^{-1}$
• B. 0.125 mol $ltr ^{-1}\, min ^{-1}$
• C. 0.375 mol $ltr ^{-1}\, min ^{-1}$
• D. None of these

Answer 1

Answer: (B)

For $2^{\text {nd }}$ order-

$k t=\frac{1}{a-x}-\frac{1}{(a)}$

$k t=(a-x)^{-1}-(a)^{-1}$

$(a-x)^{-1}=k t+(a)^{-1}$

$\downarrow$

$y=m x+c$

Slope $= k =0.5$ (given)

$c=O A=\frac{1}{a}=2 \Rightarrow a=0.5$

Initial rate of reaction $= k ( R )^{2}$

$=0.5 \times(0.5)^{2}$

$=0.125\, mol\, ltr ^{-1}\, \min ^{-1}$