Question

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

What is the initial rate of reaction?

• A. 0.250 mol $lt{r}^{-1}mi{n}^{-1}$
• B. 0.125 mol $lt{r}^{-1}mi{n}^{-1}$
• C. 0.375 mol $lt{r}^{-1}mi{n}^{-1}$
• D. None of these

Answer 1

Answer: (B)

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

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

$kt=(a-x{)}^{-1}-(a{)}^{-1}$

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

$\downarrow$

$y=mx+c$

Slope $=k=0.5$ (given)

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

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

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

$=0.125mollt{r}^{-1}{\min }^{-1}$