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 = k2
After: (Rate)4 = k2= k
So this would be 2nd order reaction
iii) Rate = k[A]x
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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