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.

Step-by-step explanation:

All the radioactive reactions follows first order kinetics.

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

`t_(1/2)=(0.693)/(k)`

We are given:

`t_(1/2)=62.1s`

Putting values in above equation, we get:

`k=(0.693)/(62.1)=0.011s^(-1)`

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

`k=(2.303)/(t)\log([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)=(2.303)/(84.2s)\log(250)/([A])`

`[A]=99.05g`

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