Chemistry Practice Problems Identifying Reaction Order Practice Problems Solution: For each of the following cases, identify the orde...

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Solution: For each of the following cases, identify the order with respect to the reactant, A. Case (A → products) Orderi) The half-life of A is independent of the initial concentration of [A].   ii) A two fold increase in the initial concentration of A leads to a four fold increase in the initial rate.   iii) A two fold increase in the initial concentration of A leads to a 1.41-fold increase in the initial rate.  iv) 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. v) The rate of decrease of [A] is a constant.

Problem

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

Case (A → products) Order

i) The half-life of A is independent of the initial concentration of [A].   

ii) A two fold increase in the initial concentration of A leads to a four fold increase in the initial rate.   

iii) A two fold increase in the initial concentration of A leads to a 1.41-fold increase in the initial rate.  

iv) 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

v) The rate of decrease of [A] is a constant.

Solution

i) t1/2=ln2/k  This is the only half life equation which is not dependent on the initial concentration of a reactant, and it corresponds to 1st order reaction.

ii) Rate = k[A]x where x is the rate of [A] and overall reaction.
 If we increase [A] by 2, the only way for rate to increase by 4 would be if rate or x= 2.

Before: Rate = k[1]2
After: (Rate)4 = k[2]2= k[4]

So this would be 2nd order reaction

iii) Rate = k[A]x

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