Question

A first order reaction takes 100 minutes for completion of 60% of the reaction. Find the time when 90% of the reaction will be completed.

Answer 1

If a first order reaction is 60% complete in 100 min.

Let [x]₀ = 100M, [x]_60% = 100 − 60 = 40M and t = 100 min

\(k = \frac{2.303}t \log \frac{x_0}x\)

\(= \frac{2.303}{100} \log \frac{100}{40}\)

= 0.02303 log 2.5

0.02303 × 0.397 = 0.009 min⁻¹

Time taken to complete 90% reaction = ?

[x]₀ = 100M, [x]_90% = 100 − 90 = 10M

k = 0.009 min⁻¹

\(t = \frac{2.303}k \log \frac{x_0}x\)

\(= \frac{2.303}{0.009} \log \frac{100}{10}\)

= 251.4 log10

= 251.4 min

Answer 2

(a) For the reaction of first order,

= 0.00916

(b)

= 251.4 minutes