Problem: For each of the following cases, identify the order with respect to the reactant, A. Case (A ----> product) 1. The half-life of A increases as the initial concentration of A decreases. 2. A twofold increase in the initial concentration of A leads to a fourfold increase in the initial rate. 3. A twofold increase in the initial concentration of A leads to a 1.41-fold increase in the initial rate. 4. The time required for [A] to decrease from [A]0 to [A]0/2 is equal to the time required for [A] to decrease from [A]0/2 to [A]0/4. 5. The rate of decrease of [A] is a constant.

FREE Expert Solution

To identify the order with respect to the reactant, A: → product


General form of Rate Law


rate law=kAxBy

k = rate constant
A & B = reactants
x & y = reactant orders


Integrated rate law for Zeroth order reaction:


[A]t=-kt+[A]0


Integrated rate law for First order reaction: 

  • t1/2 = half-life

ln[A]t=-kt+ln[A]0        t1/2=ln2k


Integrated rate law for Second order reaction:


1[A]t=kt+1[A]0  t1/2=1k[A]0


1. The half-life of A increases as the initial concentration of A decreases.

  •  For a 2nd order reaction → the half-life t1/2 depends on initial concentration [A]0
  • t1/2=1k[A]0
  • second-order reaction
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Problem Details

For each of the following cases, identify the order with respect to the reactant, A. Case (A ----> product) 

1. The half-life of A increases as the initial concentration of A decreases. 

2. A twofold increase in the initial concentration of A leads to a fourfold increase in the initial rate. 

3. A twofold increase in the initial concentration of A leads to a 1.41-fold increase in the initial rate. 

4. The time required for [A] to decrease from [A]0 to [A]0/2 is equal to the time required for [A] to decrease from [A]0/2 to [A]0/4. 

5. The rate of decrease of [A] is a constant.

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