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### 15.23 (c)

Posted: Tue Feb 27, 2018 6:10 pm
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?

### Re: 15.23 (c)

Posted: Tue Feb 27, 2018 6:58 pm
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