Question

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

A + B + C $\to$ Product
$Rate \propto \left[A\right]^{x} \left[B\right]^{y} \left[C\right]^{z}$
$\frac{R_{1}}{R_{2}} = \frac{\left(0.2\right)^{x} \left(0.1\right)^{y} \left(0.1\right)^{z}}{\left(0.2\right)^{x} \left(0.2\right)^{y} \left(0.1\right)^{z}} = \frac{6\times10^{-5}}{6\times10^{-5}}$
$\therefore \,y = 0$
Similarly x and z are calculated, $x = 1, z = 1$
Rate constant $K = \frac{6\times10^{-5}}{0.2\times0.1} = 3\times10^{-3}$
$\therefore \,$ Rate at given concentrations = $3\times10^{-3} \times \left(0.15\right)^{1} \left(0.25\right)^{0}\left(0.15\right)^{1}$
$= 6.75 \times10^{-5} mol\,dm^{-3} \,S^{-1}$
$Y = 6.75$