For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.

Question 4.18: For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.
Answer
Given that
Order of reaction = first
Let Initial amount = 100 g
Amount in % after 90 % completion = 100 - 90 = 10%
Amount in g [R]= 10% of 100g = 10g
Amount in % after 99 % completion = 100 - 99 = 1%
Amount in g [R]= 1% of 100g = 1g
Use the formula of first order reaction

We observe that t₂ = 2t₁
Hence, for a first order reaction, time required for 99% completion is twice the time required for the completion of 90% of reaction