Integrated Rate Equations - Half-life of a Reaction

For the first order reaction, half-life is equal to ____________.

A first order reaction takes 23.1 minutes for 50% completion. Calculate the time required for 75% completion of this reaction.

(log 2 = 0.301, log 3 = 0.4771, log 4 = 0.6021)

Sucrose decomposes in acid solution to give glucose and fructose according to the first order rate law. The half life of the reaction is 3 hours. Calculate fraction of sucrose which will remain after 8 hours.

During nuclear explosion, one of the products is ⁹⁰Sr with half-life of 28.1 years. If 1μg of ⁹⁰Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.

The half-life for radioactive decay of ¹⁴C is 5730 years. An archaeological artifact containing wood had only 80% of the ¹⁴C found in a living tree. Estimate the age of the sample.

A first order reaction takes 10 minutes for 25% decomposition. Calculate t_1/2 for the reaction.

(Given : log 2 = 0.3010, log 3 = 0.4771, log 4 = 0.6021)

Show that the time required for 99% completion is double of the time required for the completion of 90% reaction.

Calculate the half-life of a first order reaction from their rate constants given below:

(i) 200 s⁻¹ (ii) 2 min⁻¹ (iii) 4 years⁻¹