AIIMS 2018 Chemistry First Order Reactions MCQ Question

In a first-order reaction, the rate constant $k$ can be calculated using the formula $k = \frac{2.303}{t} \log \frac{a}{a-x}$, where $a$ is the initial concentration and $x$ is the amount reacted. Since $x$ is 80% of $a$, this means that 20% remains, so $a - x = 20\%$ of $a$. Therefore, substituting $a = 100\%$ and $a - x = 20\%$, we get $k = \frac{2.303}{60} \log \frac{100}{20}$, which corresponds to option C.

Option A incorrectly uses $100 - 80 = 20$ in the logarithm but does not express it correctly as $\frac{100}{20}$. Option B incorrectly uses $\frac{80}{100}$, which does not represent the remaining concentration. Option D also misrepresents the relationship by using $\frac{80}{20}$ instead of the correct $\frac{100}{20}$.