A) \[{{t}_{1/2}}\propto {{a}^{3}}\]
B) \[{{t}_{1/2}}\propto {{a}^{2}}\]
C) \[{{t}_{1/2}}\propto a\]
D) \[{{t}_{1/2}}\propto \frac{1}{a}\]
Correct Answer: C
Solution :
Key Idea Half-life period of a reaction is defined as the time during which the concentration of a reactant is reduced to half of its initial concentration. For a reaction of nth order \[{{t}_{1/2}}\propto \frac{1}{{{a}^{n-1}}}\] ie, \[{{t}_{1/2}}\propto a\] where, \[n=\] order of reaction \[a=\] initial concentration For a zero order reaction \[{{t}_{1/2}}\propto \frac{1}{{{a}^{0-1}}}\] ie, \[{{t}_{1/2}}\propto a\] Note -For zero order, \[{{t}_{1/2}}=\frac{a}{2\,k}\] For first order, \[{{t}_{1/2}}=\frac{0.693}{k}\] For second order, \[{{t}_{1/2}}=\frac{1}{k\,.\,\,a}\]
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