Question

The compound Xe(CF3)2 decomposes in a first-order reaction to elemental Xe with a half-life of 30.0 min. If you place 4.5 mg of Xe(CF3)2 in a flask, calculate how long you must wait until only 0.25 mg of Xe(CF3)2 remains?

Answer 1

Answer : The time passed by the sample is, $1.2\times 10^2\text{ min}$

Explanation :

Half-life = 30.0 min

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

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

$k=\frac{0.693}{30.0\text{ min}}$

$k=0.0231\text{ min}^{-1}$

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  = $0.0231\text{ min}^{-1}$

t = time passed by the sample  = ?

a = initial amount of the reactant  = 4.5 mg

a - x = amount left after decay process =0.25 mg

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

$t=\frac{2.303}{0.0231}\log\frac{4.5}{0.25}$

$t=125.15\text{ min}=1.2\times 10^2\text{ min}$

Therefore, the time passed by the sample is, $1.2\times 10^2\text{ min}$