1. Integrated Rate Law By Chloe Dixon

2. Integrated Rate Law
The relationship between the concentration of reactants and time
To integrate, in this context, means to linearize the rate between concentration of reaction and time, in order to calculate how much time is needed to reach a certain concentration and vise versa.

3. Zero-Order Integrated Rate Law
In a zero-order reaction, the rate is proportional to the constant.
Rate = k[A]^0=k
Therefore, the zero-order integrated rate law is
= concentration over t(time) = initial concentration
-k = slope

4. First-Order Integrated Rate Law
In a first-order reaction, the rate is proportional to the concentration of the reactant
Rate = k[A]
Therefore, the first-order integrated rate law is
In order to “linearize” a first order reaction, you must take the natural log (ln) of the concentration

5. Second-Order Integrated Rate Law
In a second-order reaction, the rate is proportional to the square of the reactant concentration
Rate = [A]^2
Therefore, the second-order integrated rate law is
To integrate a second-order reaction the inverse must be taken

7. Practice Problem!

8. Half-Life of Reaction
The time required for the concentration of reactant to be one-half its initial value
Example: If a reaction has a half-life of 100 seconds and it’s initial concentration is 1.0 M, than the concentration will 0.5 M in 100 seconds.
If a reaction has a half-life of 100 seconds and it’s initial concentration is 1.0 M, than the concentration will 0.5 M in 100 seconds.

9. Practice Problem!
Molecular iodine dissociates at 625 K with a first-order rate constant of s^-1. What is the half-life of this reaction?
= 0.693/ 0.271s = 2.56s