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**Problem**: 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.

###### FREE Expert Solution

###### FREE Expert Solution

i) t_{1/2}=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}

###### Problem Details

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.

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