## 15.23 (c)

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

Andy Liao 1B
Posts: 52
Joined: Thu Jul 13, 2017 3:00 am

### 15.23 (c)

Problem:
15.23 Determine the rate constant for each of the following first-order reactions, in each case expressed for the rate of loss
of A: (c) 2A -> B + C, given that [A]0 = 0.153 mol.L^-1 and that after 115 s the concentration of B rises to 0.034 mol.L^-1.

I know which equation to use and understand that I first have to solve for [A]t. However, I do not understand how [A]t was calculated in the solutions manual: [A]t = [A]0 - [(2 mol A/1 mol B)(.034 mol B/L)]. Why is it necessarily to subtract [A]0 with [(2 mol A/1 mol B)(.034 mol B/L)]? Can someone please explain?

Kelly Seto 2J
Posts: 30
Joined: Thu Jul 27, 2017 3:00 am

### Re: 15.23 (c)

The increase in the concentration of B is directly linked to a decrease in the concentration of A, and this decrease is modeled by (2 mol A/1 mol B)(.034 mol B/L), which is the amount of A that had to be used to produce the 0.34 M of B. Subtracting this amount from the initial concentration allows us to find the concentration of A after those 115 seconds