chemistry physical

Question

The rate constant is 7.5 × 10-3 dm3mol–1s. Given that the initial number of moles of

A is 0.05 moles in a volume of 2 litres.

Calculate the time (s) taken for [A] to be reduced by 20 %.

Answer 1

From the units for the rate constant (M^-1s^-1), we know the reaction is second order.

The integrated rate law for a 2nd order reaction is 1/[A] = 1/[A]₀ + kt

[A]₀ = 0.05 mol/2 L = 0.025 M

[A] = 0.20 x 0.025 = 0.005 M

k = 7.5x10^-3 M^-1s^-1

t = ?

Substituting and solving for t, we have...

1/0.005 = 1/0.025 + 7.5x10^-3 t

200 = 40 + 7.5x10^-3 t

t = 160 / 7.5x10^-3

t = 21,333 s = 356 min = 5.9 hours