50 % of a first order reaction completes in 20 minutes. What will be the time taken for 100% completion of the same reaction?

Infinite time

For first order reaction,

t_1/2 = \(\frac{0.693}{k}\) 

20 = \(\frac{0.693}{k}\) 

k = \(\frac{0.693}{20}\) = 0.03465 s^-1 

t = \(\frac{2.303}{k}\)log\(\frac{a}{a-x}\)

t_100% = \(\frac{2.303}{0.03465}\)log\(\frac{100}{0}\)

t_100% = \(\frac{2.303}{0.03465}\)log∞

t_100% = ∞ (infinite time)