In a certain 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 6 grams. Assume a < b and y ≤ a. 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 Rate = k(ay)(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? Give your answer as a union of intervals, e.g., (- infinity,-a] U (a, 2b) ує 2. Use your graph to find the value of y at which the rate of the reaction is fastest. У =

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Chapter1: Chemical Foundations
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In a certain 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 y ≤ a. 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
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?
Give your answer as a union of intervals, e.g., (-
infinity,-a] U (a, 2b)
YE
2. Use your graph to find the value of y at which
the rate of the reaction is fastest.
У =
Transcribed Image Text:In a certain 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 y ≤ a. 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 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? Give your answer as a union of intervals, e.g., (- infinity,-a] U (a, 2b) YE 2. Use your graph to find the value of y at which the rate of the reaction is fastest. У =
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