For a first order reaction A $\to$ products, slope of a graph plotted between $\log \frac{[A_{o}]}{[A_{t}]}$ (y-axis) vs time(x-axis in minutes) is 0.001. Half life of the reaction is ( where [A₀] = initial concentration of ‘A’ and [A_t] = concentration of ‘A’ after time ‘t’)

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301 minutes

30.1 minutes

230.3 minutes

23.03 minutes

answer is C.

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Detailed Solution

For a first order reaction

$K = \frac{2.303}{t} \log \frac{[A_{o}]}{[A_{t}]} \underset{y}{\log \frac{[A_{o}]}{[A_{t}]}} = \underset{m}{\frac{K}{2.303}} \times \underset{x}{t} slope = \frac{K}{2.303} K = 2.303 (10^{- 3}) K = 2.303 \times 10^{- 3} \min^{- 1} t_{\frac{1}{2}} = \frac{0.693}{K} minutes = 301 minutes .$