Question

For the first order process: AB The half-life of A is 62.1 seconds. If a sample of A initially has 250.0 g, what mass (in g) of A will remain after 84.2 seconds?

Answer 1

Answer: The mass of sample A after given time is 99.05 g.

Explanation:

All the radioactive reactions follows first order kinetics.

The equation used to calculate half life for first order kinetics:

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

We are given:

$t_{1/2}=62.1s$

Putting values in above equation, we get:

$k=\frac{0.693}{62.1}=0.011s^{-1}$

Rate law expression for first order kinetics is given by the equation:

$k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}$

where,

k = rate constant = $0.011s^{-1}$

t = time taken for decay process = 84.2 s

$[A_o]$ = initial amount of the reactant = 250 g

[A] = amount left after decay process =  ?

Putting values in above equation, we get:

$0.011s^{-1}=\frac{2.303}{84.2s}\log\frac{250}{[A]}$

$[A]=99.05g$

Hence, the mass of sample A after given time is 99.05 g.