Question

In a chemical reaction, substance A combines with substance B to form substance Y. At the start of the reaction, the quantity of A present is a grams, and the quantity of B present is b grams. Assume a><b> and <img src=. At time t seconds after the start of the reaction, the quantity of Y present is y grams. For certain types of reactions, the rate of the reaction, in grams/sec, is given by
\hbox{Rate}=k(a-y)(b-y),
where k is a positive constant. 1. Sketch a graph of the rate against y. For what values of y is the rate nonnegative?</b>

Answer 1

If we expect the rate to be nonnegative, we must have 0 ≤ y ≤ a and 0 ≤ y ≤ b.
Since we assume a < b, we restrict y to 0 ≤ y ≤ a.
In fact, the expression for the rate is nonnegative for y greater than b, but these
values of y are not meaningful for the reaction.


(b) From the graph, we see that the maximum rate occurs when y = 0; that is, at the
start of the reaction.

Answer 2

a) y E ________(0,a)________

b) y = ___0____

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Answer 3

a) [0,a]
b) 0

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