Question

For a reaction $A+B⟶C+D$, rate $=K\left[A{]}^{\frac{-1}{2}}\right[B{]}^{\frac{3}{2}}$. On doubling the concentration of A and B, the rate will be:

• A. Quadrupled
• B. Doubled
• C. Tripled
• D. The same

Answer 1

The correct option is B Doubled

The rate law for the reaction $A+B⟶C+D$ is given by Rate $=K\left[A{]}^{\frac{-1}{2}}\right[B{]}^{\frac{3}{2}}$ when [A] and [B] is doubled,
$R_{intial}=K\left(A{)}^{\frac{-1}{2}}\right(B{)}^{\frac{3}{2}}$
$R_{final}=K\left[2{]}^{\frac{-1}{2}+\frac{3}{2}}\right(A{)}^{\frac{-1}{2}}(B{)}^{\frac{3}{2}}$
$=K\left(2{)}^{\frac{2}{2}}\right(A{)}^{\frac{-1}{2}}(B{)}^{\frac{3}{2}}$
$R_{final}=2K\left(A{)}^{\frac{-1}{2}}\right(B{)}^{\frac{3}{2}}$
$\therefore R_{final}=2\left(R_{intial}\right)$
Hence the rate is doubled