Question

For $2A+B+C\to 2D$, determine the rate law for the reaction based on the following data.

Exp	$\left[A\right]$	$\left[B\right]$	$\left[C\right]$	Rate of disappearance (M/s)
$1$	$0.1$	$0.1$	$0.1$	$X$
$2$	$0.2$	$0.2$	$0.1$	$8X$
$3$	$0.2$	$0.1$	$0.1$	$4X$
$4$	$0.2$	$0.1$	$0.2$	$32X$

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

Answer 1

The correct option is B $Rate=k\left[A{]}^2\right[B\left]\right[C{]}^3$

Let the rate law be, $R=K{\left[A\right]}^x{\left[B\right]}^y{\left[C\right]}^z$

From experiment 1,

$X=K{\left[0.1\right]}^x{\left[0.1\right]}^y{\left[0.1\right]}^z⟶\left(i\right)$

From experiment 2,

$8X=K{\left[0.2\right]}^x{\left[0.2\right]}^y{\left[0.1\right]}^z⟶\left(ii\right)$

From experiment 3,

$4X=K{\left[0.2\right]}^x{\left[0.1\right]}^y{\left[0.1\right]}^z⟶\left(iii\right)$

From experiment 4,

$32X=K{\left[0.2\right]}^x{\left[0.1\right]}^y{\left[0.2\right]}^z⟶\left(iv\right)$

Dividing (i) by (iii),

$\frac{1}{4}={\left(\frac{0.1}{0.2}\right)}^x\Rightarrow x=2$

Dividing (ii) by (iii)

$2={\left(\frac{0.2}{0.1}\right)}^y⟹y=1$

Dividing (iii) by (iv)

$\frac{1}{8}={\left(\frac{1}{2}\right)}^z⟹z=3$

$\therefore$ Rate law$=K{\left[A\right]}^2\left[B\right]{\left[C\right]}^3$