Question

For the reaction: $A+B\to C+D$, doubling the concentration of both the reactants increases the reaction rate by 8 times and doubling the concentration of only B simply doubles the reaction rate. The rate law is given as:

• A. $r=k\left[A{]}^{\frac{1}{2}}\right[B{]}^{\frac{1}{2}}$
• B. $r=k\left[A\right][B{]}^2$
• C. $r=k\left[A{]}^2\right[B]$
• D. $r=k\left[A\right]\left[B\right]$

Answer 1

The correct option is C $r=k\left[A{]}^2\right[B]$

$r=k{a}^{\alpha }{b}^{\beta }...\left(i\right)$
$8r=k\left(2a{)}^{\alpha }\right(2b{)}^{\beta }..\left(ii\right)$
$2r=k{a}^{\alpha }(2b{)}^{\beta }...(iii)$
Dividing $e{q}^n\left(ii\right)$ by $e{q}^n\left(iii\right)$ gives $\frac{8}{2}=2^{\alpha }$
$2^{\alpha }=4=2^2,\alpha =2$

Dividing $e{q}^n\left(iii\right)$ by $e{q}^n\left(i\right)$ gives $2=2^{\beta }\text{or}\beta =1$
Hence, rate = $k\left[A{]}^2\right[B]$