The half-life of a reaction, t 1/2, is the time it takes for the reactant concen

Question

The half-life of a reaction, t1/2, is the time it takes for the reactant concentration [A] to decrease by half. For example, after one half-life the concentration falls from the initial concentration [A]0 to [A]0/2, after a second half-life to [A]0/4, after a third half-life to [A]0/8, and so on. on.

Part A

Part complete

A certain second-order reaction (Bproducts) has a rate constant of 1.20×103M1s1 at 27 C and an initial half-life of 230 s . What is the concentration of the reactant B after one half-life?

Please, provide thorough explanation.

Explanation / Answer

Given:
k = 1.20*10^-3 M-1.s-1
use relation between rate constant and half life of 2nd order reaction

t1/2 = 1/([B]o*k)
230 = 1/([B]o*1.20*10^-3)
[B]o= 230*1.20*10^-3
= 0.276 M

This is the initial concentration

After 1 half life,
concentration = [B]o / 2
= 0.276 / 2
= 0.138 M

Answer: 0.138 M

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