For each of the following cases, identify the order with respect to the reactant

Question

For each of the following cases, identify the order with respect to the reactant, A The half-life of A increases as the initial concentration of A decreases. A threefold increase in the initial concentration of a leads to a ninefold increase in the initial rate. A threefold increase in the iritial concentration of a leads to a 1.73-fold increase in the initial rate. The time required for [A] to decrease for [A]_2 to [A]_0/2 is equal to the time required for [A] to decrease from [A]_0/2 to [A]_04. The rate of decrease of [A]_0/2 [A]_0/4.

Explanation / Answer

The half-life of A increases as the initial concentration of A decreases. : Second order reaction

For a second order reaction, the half life is inversely proportional to initial concentration of A.

t1/2 = 1/k[A]

A threefold increase in the initial concentration of A leads to a nine-fold increase in the intial rate : Second order reaction.

For a second order reaction,

rate = k[A]^2

when, A = 1 ; rate = k

when A = 3 ; rate = 9k

So the rate increases to nine-folds by threefold increase in initial concentration of A

A threefold increase in the intial concentration of A leads to a 1.73-fold increase in the intial rate : 1/2 order

say,

rate = k[A]^x

with k being the rate constant, x being the order with respect to A

when [A] = 1 ; rate = 1 ---(a)

when [A] = 3 ; rate = 1.73 ----(b)

taking ratios,

rate a/rate b = (1/1.73) = (1/3)^x

x = 0.5

So order is 1/2 with respect to [A]

The time required for [A] to decrease from [A]o to [A]o/2 is equal to the time required for [A] to decrease from [A]o/2 to [A]o/4 : First order reaction

For a first order reaction, rate of reaction is directly proportional to the initial concentration.

Another easy way to confirm this is plot, data points ln[A] : 0 0.5 0.25 vs time : 0 2 4. We get a straight line which confirms it follows a first order kinetics.

The rate of decrease of [A] is a constant : Zero order reaction

For a zero order reaction, rate = k = constant.

So change in [A] does not effect the rate of reaction

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