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

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#### Question

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)

#### Solution

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

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

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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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#### 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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