A) \[\log \frac{4}{3}\]
B) \[\log \frac{3}{4}\]
C) \[\frac{\log \,4}{\log 4/3}\]
D) \[\frac{\log \,4/3}{\log 4}\]
Correct Answer: C
Solution :
For a first order reaction, \[t=\frac{2.303}{k}{{\log }_{10}}\frac{a}{a-x}\] Let initial amount of reactant is 100. \[\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{\log \frac{100}{100-75}}{\log \frac{100}{100-25}}\] [k remains constant] \[=\frac{\log \frac{100}{25}}{\log \frac{100}{75}}=\frac{\log 4}{\log 4/3}\]
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