Question

Consider the kinetic data given in the following table for the reaction $A+B+C\to$ Product.

Experiment No.	[A](mol dm${}^{-3}$)	[B](mol dm${}^{-3}$	[C](mol dm${}^{-3}$	Rate of reaction (mol dm${}^{-3}{s}^{-3}$)
1	0.2	0.1	0.1	6.0 x 10${}^{-5}$
2	0.2	0.1	0.2	6.0 x 10${}^{-5}$
3	0.2	0.1	0.2	6.0 x 10${}^{-4}$
4	0.3	0.1	0.2	9.0 x 10${}^{-5}$

The rate of the reaction for [A] = 0.15 mol dm${}^{-3}$, [B] = 0.25 mol dm${}^{-3}$ and [C] = 0.15 mol dm${}^{-3}$ is found to be Y x 10${}^{-5}$ mol dm${}^{-3}$ s${}^{-1}$. The value of Y is _____

Answer 1

Answer: 6.75

A + B + C $\to$ Product
$Rate\propto {\left[A\right]}^x{\left[B\right]}^y{\left[C\right]}^z$
$\frac{R_1}{R_2}=\frac{{\left(0.2\right)}^x{\left(0.1\right)}^y{\left(0.1\right)}^z}{{\left(0.2\right)}^x{\left(0.2\right)}^y{\left(0.1\right)}^z}=\frac{6\times 10^{-5}}{6\times 10^{-5}}$
$\therefore y=0$
Similarly x and z are calculated, $x=1,z=1$
Rate constant $K=\frac{6\times 10^{-5}}{0.2\times 0.1}=3\times 10^{-3}$
$\therefore$ Rate at given concentrations = $3\times 10^{-3}\times {\left(0.15\right)}^1{\left(0.25\right)}^0{\left(0.15\right)}^1$
$=6.75\times 10^{-5}mold{m}^{-3}{S}^{-1}$
$Y=6.75$