3C + 2D ---> 2F + G A reaction between the gaseous substances C and D proceeds a

Question

3C + 2D ---> 2F + G A reaction between the gaseous substances C and D proceeds at a measurable rate. When 1.0 x 10^-3 mol G/L forms a sudden color change occurs. The following set of data was collected for the reaction: [C] [D] Time for Color change (s) Rate= change in [G]/change in time .01 1.0 30 ? .01 3.0 10 ? .02 3.0 1.3 ? .02 1.0 3.7 ? .03 3.0 0.37 ? a) What is the (whole number) order of C in the reaction? ____; of D in the reaction? ______ b) What is the rate law? c) What is the specific rate constant, k? d) At any given instant during the reaction, - the rate of appearance of F is _____ times the rate of disappearance of C. - the rate of disappearance of D is _____ times the rate of appearance of G. - the rate of appearance of G is _____ time the rate of appearance of F.

Explanation / Answer

The formula for the average rate of change is:
(f(t + h) - f(t))/h
The t + h in f(t + h) means that you plug in t + h instead of t. Plug in t = 1 and simplify it:

(f(1 + h) - f(1))/h
= (220 + 30(1 + h)^3 - (220 + 30(1)^3))/h
= (220 + 30(1 + 3h + 3h^2 + h^3) - (220 + 30(1)))/h
= (220 + 30 + 90h + 90h^2 + 30h^3 - (220 + 30))/h
= (250 + 90h + 90h^2 + 30h^3 - 250)/h
= (90h + 90h^2 + 30h^3)/h
= h(90 + 90h + 30h^2)/h
= 90 + 90h + 30h^2

Now, lug in h = 1, 0,1, and 0.01:

90 + 90(1) + 30(1)^2
= 90 + 90 + 30(1)
= 180 + 30
= 210

90 + 90(0.1) + 30(0.1)^2
= 90 + 9 + 30(0.01)
= 99 + 0.3
= 99.3

90 + 90(0.01) + 30(0.01)^2
= 90 + 0.9 + 30(0.0001)
= 90.9 + 0.003
= 90.9003

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