Question

A first-order reaction (A → B) has a half-life of 25 minutes. If the initial concentration of A is 0.900 M, what is the concentration of B after 50 minutes?

Answer 1

0.6749 M is the concentration of B after 50 minutes.

Step-by-step explanation:

A → B

Half life of the reaction =
`t_(1/2)=25 minutes`

Rate constant of the reaction = k

For first order reaction, half life and half life are related by:

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

`k=(0.693)/(25 min)=0.02772 min^(-1)`

Initial concentration of A =
`[A]_o=0.900 M`

Final concentration of A after 50 minutes =
`[A]=?`

t = 50 minute

`[A]=[A]_o* e^(-kt)`

`[A]=0.900 M* e^{-0.02772 min^(-1)* 50 minutes}`

[A] = 0.2251 M

The concentration of A after 50 minutes = 0.2251 M

The concentration of B after 50 minutes = 0.900 M - 0.2251 M = 0.6749 M

0.6749 M is the concentration of B after 50 minutes.