Question

The rate law of a reaction is given by

Rate = k[A][B]²

Which of the following will react fastest?

Options

• 1 mol of A and 2 mol of B in 1 L vessel.

• 2 mol of A and 1 mol of B in 500 ml vessel.

• 3 mol of A and 2 mol of B in 2 L vessel.

Answer 1

2 mol of A and 1 mol of B in 500 ml vessel.

Explanation:

We are given the rate law

Rate = k[A][B]²

1. 1 mol of A and 2 mol of B in 1 L vessel:

`[A] = 1/1 = 1` mol/L,

`[B] = 2/1 = 2` mol/L

Rate₁ ​= k × 1 × (2)² = 4 k

2. 2 mol of A and 1 mol of B in 0.5 L vessel:

`[A] = 2/0.5 = 4` mol/L,

`[B] = 1/0.5 = 2` mol/L

Rate₂ ​= k × 4 × (2)² = 16 k

3. 3 mol of A and 2 mol of B in 2 L vessel:

`[A] = 3/2 = 1.5` mol/L,

`[B] = 2/2 = 1` mol/L

Rate₁ ​= k × 1.5 × (1)² = 1.5 k

1.5 k < 4 k < 16 k

∴ 2 mol of A and 1 mol of B in 500 ml vessel will react faster.