Question

Reaction $A+B⟶C+D$ follow's following rate law rate $=k={\left[A\right]}^{\frac{1}{2}}{\left[B\right]}^{\frac{1}{2}}$. Starting with initial conc. of one mole of A and B each, what is the time taken for amount of A of become 0.25 mole. Given $k=2.31\times {10}^{-3}se{c}^{-1}$.

• A. 300 sec
• B. 600 sec
• C. 900 sec
• D. none of these

Answer 1

The correct option is B 600 sec

$A+B⟶C+D$

$rate=k{\left[A\right]}^{1/2}{\left[B\right]}^{1/2}$

$\frac{dx}{dt}=k\sqrt{(a-x)(a-x)}$

$\frac{dx}{dt}=k(a-x)$

$\Rightarrow t=\frac{2.303}{k}{\log }_{10}\left(\frac{a}{a-x}\right)$

$t=\frac{2.303}{2.31\times {10}^{-3}}{\log }_{10}\left(\frac{1}{0.25}\right)$

$t=600sec.$

Hence, the correct option is $\text{B}$