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

Answer:

0.6749 M is the concentration of B after 50 minutes.

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:

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

$k=\frac{0.693}{25 min}=0.02772 min^{-1}$

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

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

t = 50 minute

$[A]=[A]_o\times e^{-kt}$

$[A]=0.900 M\times e^{-0.02772 min^{-1}\times 50 minutes}$

[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.