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

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#### Question

A first order reaction takes 40 minutes for 30% decomposition. Calculate t1/2 for this reaction. (Given log 1.428 = 0.1548)

#### Solution

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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.

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A first order reaction takes 30 minutes for 50% completion. Calculate the time required for 90% completion of this reaction.

(log 2 = 0.3010)

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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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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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#### Reference Material

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