Question

The reaction between X and Y is first order with respect to X and second order with respect to Y. If the concentration of X is halved and the concentration of Y is doubled the rate of reaction will be ______.

Options

• same as the initial value.

• three times the initial value.

• double the initial value.

• half the initial value.

Answer 1

The reaction between X and Y is first order with respect to X and second order with respect to Y. If the concentration of X is halved and the concentration of Y is doubled the rate of reaction will be double the initial value.

Explanation:

We are given:

Order with respect to X = 1

Order with respect to Y = 2

So the rate law is:

Rate = k[X]¹[Y]²

Now, suppose initially 

[X] = x, [Y] = y

Then

Initial Rate = kxy²

Now the changes

[X] is halved → x/2

[Y] is doubled → 2y

∴ New rate = `k * x/2 * (2y)^2`

= `k * x/2 * 4y^2`

= 2kxy²

∴ New Rate = 2 × (Initial Rate)