Problem 15.35 (half life)

$\frac{d[R]}{dt}=-k[R]^{2}; \frac{1}{[R]}=kt + \frac{1}{[R]_{0}}; t_{\frac{1}{2}}=\frac{1}{k[R]_{0}}$

Shivangi_2J
Posts: 65
Joined: Fri Sep 28, 2018 12:15 am

Problem 15.35 (half life)

given the half-life, how do we calculate the time needed for a certain amount of the reactant's concentration to decrease using the half-life equation

for example : (problem 15.35)
The half-life for the second-order reaction of a substance A is 50.5 s when [A]0 = 0.84 mol/L. Calculate the time needed for the concentration of A to decrease to (a) one-sixteenth; (b) one-fourth; (c) one-fifth of its original value.

is there a way to calculate these values more quickly using only the half-life equation? or do we have to solve for k using the half-life equation and then solve for time using the integrated rate law

Ethan Breaux 2F
Posts: 63
Joined: Sat Sep 29, 2018 12:16 am

Re: Problem 15.35 (half life)

first you solve for k then you use the formula to solve for t and you get t = (1/[A]t - 1/[A]o)/k to solve for t in which [A]t can be replaced by (1/16)[A]o , (1/4)[A]o , and (1/5)[A]o which gives you something like for 1/16th : t = (16/[A]o - 1/[A]o)/k