Kinetics Questions

[indianjatt]

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I have two questions regarding rate of appearances and rate constants.

1)
From MCAT Success 2004
It says the reaction goes from A + 3B -> 2 C. Concentration of C increases by .002M in 20 secs. What is the rate of appearance in M/s?
What I thought:
rate of appearance = 1/2(delta[C]/deltat) = 1/2(.002M/20s) = .00005 M/s
Answer:
rate of appearance = (delta [C]/deltat) = .002/20s = .0001 M/s

2)
The reaction A^2 -> is zero order. in 40 secs, concentration A goes from .096M to .098M. What is rate constant?
What I thought:
At = -kt + A0
.098M-.096M = -k40s
k=-.0005 M/s

But can a rate constant be negative? Why doesn't this method work?
Answer:
-da/dt = k = 1/2(.002/40s) = 2.5 x 10^-5 M/s

Thanks!
Source: MCAT success 2004 Bosworth, Stefon

 

[MT Headed]

For part 1, you are confusing rate of appearance with rate constant. You did a good job of solving for the rate constant for the reaction as written. They just wanted the rate of appearance of the product, and told you how many molarities appear every second. Just divide.

For part 2, you did exactly the reverse. You correctly solved for the rate of appearance of A (and it is negative because A isn't appearing, it is disappearing). But they wanted the rate constant for the reaction, so you'll need to divide the rate by the coefficient of A (which I will assume was 2, it wasn't very clear from your question). Also, since this is a reactant and it is disappearing, you want to multiply by -1 in order to create a rate constant for the reaction as a whole.

You are almost there, just focus on the difference between rate of appearance/disappearance of a chemical, and the rate of the reaction itself.

I teach my students that the rate of the reaction is the rate of the "arrow" so to speak. Sometimes that helps them with the concept.