Question

The half-life of a first-order reaction is 13 min. If the initial concentration of reactant is 0.13 M, it takes ________ min for it to decrease to 0.085 M. A) 12 B) 10. C) 8.0 D) 11 E) 5.0 Answer: C

Answer 1

Answer : The correct option is, (C) 8.0 min

Explanation :

Half-life = 13 min

First we have to calculate the rate constant, we use the formula :

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

$k=\frac{0.693}{13\text{ min}}$

$k=5.33\times 10^{-2}\text{ min}^{-1}$

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

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

where,

k = rate constant  = $5.33\times 10^{-2}\text{ min}^{-1}$

t = time passed by the sample  = ?

a = initial amount of the reactant  = 0.13 M

a - x = amount left after decay process = 0.085 M

Now put all the given values in above equation, we get

$t=\frac{2.303}{5.33\times 10^{-2}}\log\frac{0.13}{0.085}$

$t=7.97\text{ min}\aprrox 8.0\text{ min}$

Therefore, the time taken is, 8.0 min.