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. Case (A ---> products) Order The half-life of A increases as the initial concentration of A decreases. A twofold increase in the concentration of A leads to a fourfold increase in the initial rate. Number A twofold increase in the initial concentration of A leads to a 1.41-fold increase in the initial rate. The time required for [A] to decrease from [A0] to [A]0/2 is equal to the time required for [A] to decrease from [A]0/2 to [A]0/4. The rate of decrease of [A] is a constant.

Explanation / Answer

1) Second order. The half-life of second order reaction is given by, t1/2 = 1/[A]o*1/K. Thus, t1/2 increases with decreasing initial concentration of A.

2) Second order. rate = K[A]2 When A = 2A, then rate = K[2A]2, => rate = 4K[A]2.

3) Let r1 = Kxa, x is the concentration of A, when this increased to two fold, r2 = 1.41r1 = K(2x)a , solving for a,

r2/r1 = 1.41 = (2x)a/xa, => 1.41 = 2a, Therefore a = 0.496.

Order of reaction is 0.5

4) First-order. The half-life of first order reaction is given by, t1/2 = (1/K)*ln([A]o/[A]). The term ln([A]o/[A]) always results 0.693, when the initial concentration reduces to half of that.

5) Zero-order. For this zero order reaction rate law is, rate = Kt which is independent of [A].

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