Question

The decomposition of a compound in a first-order solution, with an activation energy of 52.3 kJ mol-1. A solution with 10% A decomposes 10% in 10 min at 10 ° C. What percentage of decomposition can be found with a 20% solution after 20 min at 20 ° C? Answer: 36.21%

Answer 1

decomposition of a compound in a first-order solution

A ? B

Given that

10% A decomposes 10% in 10 minute at 10° C

Initial amount of A

a = 10

Amount left after time t = 10 min

(a - x) = 10 * (90/100) = 9

Rate constant at 10°C

K₁₀ = (2.303/t) * log₁₀(a/a-x)

= (2.303/10) * log₁₀(10/9)

= 0.0105

Now calculate the rate constant at 20°C

2.303 * log₁₀(K₂₀/K₁₀) = (Ea/R)[(T₂ – T₁)/T₁T₂]

2.303 * log₁₀(K₂₀/K₁₀) = {(52.3 * 10³)/8.314}[(293 - 283)/(293 * 283]

(K₂₀/K₁₀) = 2.135

K₂₀ = 2.135 * 0.0105 = 0.0224175

Let amount left 20% solution after 20 minute at 20° C = z

K₂₀ = (2.303/t) * log₁₀{a/(a – x)}

0.0224175 = (2.303/20) * log₁₀(20/z)

0.19468 = log₁₀(20/z)

20/z = 1.5655

z = 12.775

% decomposition = (a – z)*100/a

= (20 – 12.775)*100/20

= 36.125%