Question

For the gaseous elementary reaction:
$2A\left(g\right)+B\left(g\right)⟶\text{product}$ , if the pressure is increased three times keeping temperature and volume constant then the rate of reaction will be increased by how many times?

• A. $27$
• B. $9$
• C. $3$
• D. $12$

Answer 1

The correct option is A $27$

The given elementary reaction is,
$2A\left(g\right)+B\left(g\right)⟶\text{Product}$
So the rate of the reaction will be,
$r_1=k\left[A{]}^2\right[B]$
Again, $\left[A\right]=\frac{n_A}{V}$
We know, $PV=nRT$
$\therefore P=\left[A\right]RT$
So the rate in terms of pressure will be
$r_1=k{\left(\frac{P}{RT}\right)}^2\left(\frac{P}{RT}\right)\cdot \cdot \cdot \left(i\right)$
Now, if the pressure is increased $3$ times, then
$r_2=k{\left(\frac{3P}{RT}\right)}^2\left(\frac{3P}{RT}\right)\cdot \cdot \cdot \left(ii\right)$
Now, deviding $\left(ii\right)$ by (i), we get
$\frac{r_2}{r_1}=27$
Thus rate will be increased by $27$ times