14.28 Consider a hypothetical reaction between A, B, and C that is zero order in

Question

14.28 Consider a hypothetical reaction between A, B, and C that is zero order in A, second order in B, and first order in C. (a) Write the rate law for the reaction. (b) How does the rate change when [A] is doubled and the other reactant concentra- tions are held constant? (c) How does the rate change when [B) is tripled and the other reactant concentrations are held con- stant? (d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant? (e) By what factor does the rate change when the concentrations of all three reactants are tripled? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

Explanation / Answer

14.28

reaction is zero-order in A

reaction is second-order in B

reaction is first-order in C

(a) rate law,

rate = k[B]^2.[C]

with k = rate constant

(b) when [A] is doubled, no change in rate of reaction as in zero-order dependence, the rate is a constant term, independent of concentration of substrate [A].

(c) when [B] is tripled while keeping others constant, the rate would increase 9-times.

say the initial concentration of [B] = 2 M, changed to 6 M

then, initial rate = (2)^2 = 4

after tripled, rate = (6)^2 = 36

the ratio, 36/4 = 9

So the rate change was 9-times

(d) when [C] is tripled while keeping others constant, the rate would also increase 3-times. For first order reaction, the rate is directly proportional to the substrate concentration.

(e) When concentrations of all three are tripled.

with [B] it is increased by 9-times

with [C] it is increased by 3-times

So overall the rate would increase by 27-times

(f) When the concentration of all three are cut to half,

with [B] it is decreased by 4-times

with [C] it is decreased by half-times

So overall the rate would decrease by 2-times

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