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 $k=2.31\times {10}^{-3}se{c}^{-1}$. (in sec). (Answer in the form of 100X)

Answer 1

$A+B⟶C+Drate=k{\left[A\right]}^{1/2}{\left[B\right]}^{1/2}\frac{dx}{dt}=k\sqrt{(a-x)(a-x)}\frac{dx}{dt}=k(a-x)\Rightarrow t=\frac{2.303}{k}{\log }_{10}\left(\frac{a}{a-x}\right)t=\frac{2.303}{2.31\times {10}^{-3}}{\log }_{10}\left(\frac{1}{0.25}\right)t=600sec.$