Coefficient in general rate law

$aR \to bP, Rate = -\frac{1}{a} \frac{d[R]}{dt} = \frac{1}{b}\frac{d[P]}{dt}$

Tiffany Chen 2K
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Joined: Fri Sep 26, 2014 2:02 pm

Coefficient in general rate law

On page 73 of the Course Reader, the first order reaction 2A -> P is shown to have a rate law of ln[A]= -2kt+ln [A]o but in number 23c of the chapter 14 homework problems, the equation was 2A -> B+C but the solutions manual used the first order rate law of ln [A] = -kt+ln[A]0. Why do we not include the 2?

martha-1I
Posts: 76
Joined: Fri Sep 26, 2014 2:02 pm

Re: Coefficient in general rate law

23c gives us different information, so it does not require the same steps as what was described in the course reader. What makes 23c different is that we are given the amount of concentration that B rises to in 115s and given Ainitial. Since we start off with A we need to end with A, so we need to convert the concentration of B to concentration of A and subtract by Ainitial to see what is left of A after 115s. What we are left with is our final concentration of A.

martha-1I
Posts: 76
Joined: Fri Sep 26, 2014 2:02 pm

Re: Coefficient in general rate law

Once we have converted [B] to [A], we can plug what we calculated into the equation and solve for k.
The equation set up should look like this

ln[0.085] =-k(115s) + ln[0.153]

0.085 - This was calculated by converting [B] to [A] and subtraction [A]initial
115s for t - we can use the time given for decrease of [B] with respect to A since we converted to [A]
0.153 - this was given as [A]initial

Tiffany Chen 2K
Posts: 2
Joined: Fri Sep 26, 2014 2:02 pm

Re: Coefficient in general rate law

Under what conditions would we use the first equation?

martha-1I
Posts: 76
Joined: Fri Sep 26, 2014 2:02 pm

Re: Coefficient in general rate law

We use it for first order reactions (ln[A] = -kt + ln[A]initial)
Since it was stated at the beginning of the problem that all the following are first order, we use it in this case.