Solution - Integrated Rate Equations - Half-life of a Reaction



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Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law with t1/2= 3 hours. What fraction of the sample of sucrose remains after 8 hours?


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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.

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The experimental data for decomposition of N2O5

[`2N_2O_5 -> 4NO_2 + O_2`] in gas phase at 318K are given below:

t(s 0 400 800 1200 1600 2000 2400 2800 3200
`10^2xx[N_2O_5]mol L^(-1)` 1.63 1.36 1.14 0.93 0.78 0.64 0.53 0.43 0.35

(i) Plot [N2O5] against t.

(ii) Find the half-life period for the reaction.

(iii) Draw a graph between log [N2O5] and t.

(iv) What is the rate law?

(v) Calculate the rate constant.

(vi) Calculate the half-life period from and compare it with (ii).

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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

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Derive the relation between half life and rate constant for a first order reaction

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The integrated rate equation for first order reaction is A → products

(a) ``

(b) `k=-1/tl_n[A]_t/[A]_0`

(c) `k=2.303/t log_10 ([A]_t/[A]_0 )`

(d) `k=l/tl_n[A]_t/[A]_0`

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Solution for concept: Integrated Rate Equations - Half-life of a Reaction. For the courses 12th HSC Science (Computer Science), 12th HSC Science (Electronics), 12th HSC Science (General)