Question

The half-life of a first-order reaction is $10$ min. What % of the reaction will be completed in 100 min?

• A. $25$%
• B. $99.9$%
• C. $75$%
• D. $80$%

Answer 1

The correct option is B $99.9$%

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{10}$

$k=0.0693$ minutes${}^{-1}$

Rate law expression for first order kinetics is given by:

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

where,

k = rate constant

t = time taken for the decay process

a = initial amount of the reactant

a - x = amount left after decay process

Putting values in above equation, we get:

$100=\frac{2.303}{0.0693}\log \frac{100}{100-x}$

$x=99.9$

Thus the amount decomposed is 9.9 and thus the percentage of the reaction completion is 99.9%.

Hence, the correct option is $\text{B}$