Question

Select the rate law that corresponds to the data shown for the following reaction:
$A+B⟶C$

Exp	$\left[A\right]$	$\left[B\right]$	$InitialRate$
$1$	$0.012$	$0.035$	$0.10$
$2$	$0.024$	$0.070$	$0.80$
$3$	$0.024$	$0.035$	$0.10$
$4$	$0.012$	$0.070$	$0.80$

• A. Rate$=k{\left[B\right]}^3$
• B. Rate$=k{\left[B\right]}^4$
• C. Rate$=k\left[A\right]{\left[B\right]}^3$
• D. Rate$=k{\left[A\right]}^2{\left[B\right]}^2$

Answer 1

The correct option is A Rate$=k{\left[B\right]}^3$

Let the rate law be $r=k{\left[A\right]}^x{\left[B\right]}^y$

Divide (3) by (1)

$\frac{0.10}{0.10}=\frac{{\left[0.024\right]}^x{\left[0.035\right]}^y}{{\left[0.012\right]}^x{\left[0.035\right]}^y}$

$\therefore 1={\left[2\right]}^x,x=0$

Divide (4) by (1)

$\frac{0.80}{0.10}=\frac{{\left[0.024\right]}^x{\left[0.070\right]}^y}{{\left[0.024\right]}^x{\left[0.035\right]}^y}$

$\therefore 8={\left(2\right)}^y,y=3$

hence, rate equation, $R=k{\left[A\right]}^0{\left[B\right]}^3=k{\left[B\right]}^3$