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Chemical Kinetics — Chemistry STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceChemistryChemical Kinetics5 Marks
Question
Write the rate law for a first order reaction. Justify the statement that half life for a first order reaction is independent of the initial concentration of the reactant.
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Answer

Consider the first order reaction,

R → P

For this reaction, rate law which relates the rate of reaction to the concentration of reactants can be given as:

$\text{Rate}=\frac{\text{d|R|}}{\text{dt}}=\text{k|R|}$

For a first order reaction,

$\text{t}=\frac{2.303}{\text{k}} \log\frac{\text{|R|}_0}{\text{|R|}}$, Where [R]0 = initial concentration,[R] = concentration at time t.

At t1/2, [R] = [R]0/2

So, the above equation becomes:

$\text{t}_{1/2}=\frac{2.303}{\text{k}}\log\frac{\text{|R|}_0}{\text{|R|}_0/2}$

$\text{t}_{1/2}=\frac{2.303}{\text{k}}\log2 \text{ or}\text{ t}_{1/2}=\frac{2.303}{\text{k}}\times0.3010$

$\text{t}_{1/2}=\frac{0.693}{\text{k}}$

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