Hi Nayi, just for review, I'll work the first problem in two steps. The average rate of formation of a product, or consumption of a reactant, is
Average Rate = Final Concentration - Initial Concentration
Final Time - Initial Time
For the first problem this will be
Average Rate
of Disappearance = 0.9746 M - 0.9986 M = -3.03 X 10-5 Ms-1
of Reactant B 792 s - 0 s
Note that the value of the average rate is a negative number. Physically, we cannot actually have a "negative" rate any more than you can go negative 35 miles per hour in a car. But in this calculation, a negative answer means we are talking about the rate of disappearance of a reactant, while a positive rate indicates we are looking at the rate of formation of a product. Normally, all rates are expressed as positive numbers and the given information should always clarify what substance in the reaction the rate is based on. If your book or teacher wants you to put the sign on your rates, just check that it makes sense according to the above convention.
The second step is the calculation of the average rate of disappearance of reactant A based on the rate of disappearance of reactant B just calculated. From the stoichiometry of the reaction, we see that A disappears at one-third of the rate that B does, so the average rate of disappearance of A will be the 1.01 X 10-5 Ms-1 that you got. The problem should have specifically asked for the rate of disappearance of reactant A. The phrase "rate of reaction" alone ain't good enough!
In the second question, it looks like they just want the average rate of disappearance of reactant A, which will be
Average Rate
of Disappearance = 0.3187M - 0.3629 M = -8.93 X 10-5 Ms-1
of Reactant A 495 s - 0 s
If they wanted the rate of disappearance of reactant B, we would divide our answer by 2 as you did, since the rate of disappearance of B is half the rate of disappearance of A. But it looks like in this problem, they just want the rate of disappearance of A, 8.93 X 10-5 Ms-1.
Just a reminder, once you know the rate of disappearance or appearance of one substance in the reaction, you can calculate the rate for any other substance:
For the reaction aA + bB --> cC + dD,
(1/a)(Rate of Disappearance of A) = (1/b)(Rate of Disappearance of B)
= (1/c)(Rate of Formation of C) = (1/d)(Rate of Formation of D)
and, for example, "Rate of Disappearance of A" is written symbolically as "D [A] / D t" as you did. To make the signs come out right, you would have to put a negative sign in front of the first two terms (which are rates of disappearance of reactants which should be "negative"). That can be confusing enough, so I personally always simply use positive rate values in these calculations, and put a negative sign in afterwards if it is asked for, if the rate is of the disappearance of something.
Steve
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