A) For first order reaction, straight line graph of log (a - x) versus t is obtained for which slope \[=-k/2.303\].
B) A plot of log k vs 1/T gives a straight line graph for which slope \[=-{{E}_{a}}2.303R.\]
C) For third order reaction, the product of \[{{t}_{1/2}}\] and initial concentration a is constant.
D) Units of k for the first order reaction are independent of concentration units.
Correct Answer: C
Solution :
[c] : \[\log k=-\frac{{{E}_{a}}}{2.303RT}+\log A\](straight line) Slope \[=-\frac{{{E}_{a}}}{2.303R}\]First order reaction, \[k=\frac{2.303}{t}\log \frac{C}{C-x}\](straight line) Slope \[=-\frac{k}{2.303}\] \[{{t}_{1/2}}\propto {{a}^{1-n}};n=3,{{t}_{1/2}}\propto \frac{1}{{{a}^{2}}}\] \[{{t}_{1/2}}=\frac{k'}{{{a}^{2}}}\Rightarrow {{t}_{1/2}}.{{a}^{2}}=k'\]k' is a proportionality constant. Units of k for the first order reaction are independent of concentration units.
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