CHEM 220 - Chemical Kinetics Notes

Collision Model of Reactions:
- Molecules need to collide with sufficient kinetic energy (KE). and correct orientation for a reaction to occur.
- If the KE is sufficient and the orientation is correct, a reaction occurs, leading to product formation.
- If either the KE is insufficient or the orientation is incorrect, no reaction occurs.
Activation Energy ( $E_a$ ):
- $E_a$ is the minimum energy required for a reaction to proceed.
- This energy is needed to break bonds.
- $E_a$ is needed to form the least stable substance during the reaction.
Rate (R):
- Rate (R) is the measure of change in concentration per unit time.
- Average Rate ( $R{avg}$ ) and Instantaneous Rate ( $Rt$ ) are types of rates.
- For a reaction $A + 2B \rightarrow 3C$ , the rate expression is $R = -\frac{d[A]}{dt} = -\frac{1}{2}\frac{d[B]}{dt} = \frac{1}{3}\frac{d[C]}{dt}$ .
Lab and Homework (HW) Assignments:
- There is a lab today on kinetics.
- HW 5, which assigns kinetics, electrochemistry, and nuclear chemistry, is due next Tuesday (05/13).
- All late work is due the day before the final (05/21).
- The post-lab crystal violet report is due next Monday by 11:59 pm.
- Notebook Report for Part A of Electrochemistry is due next lab.
- Final Exam focuses on kinetics, electrochemistry, and nuclear chemistry.

Rate Definition:
- The rate can be defined as the change in reactant or product concentration over the change in time:
- $Rate = -\frac{\Delta[Reactant]}{\Delta t} = \frac{\Delta[Product]}{\Delta t}$ .
Rate Law:
- The rate law is an expression of rate in terms of concentration dependence.
- It shows how the rate (R) is affected by changes in concentration.
- For a reaction $A + B \rightarrow Product$ , the rate law is $R = k[A]^m[B]^n$ , where k is the rate constant.
- The overall order of the reaction is the sum of the exponents (m + n).
- The order can’t be determined via stoichiometry
- The order can be determined experimentally.
- First order in A and B means $R = k[A][B]$ , second order overall.

Zero Order Reaction:
- For a reaction $A \rightarrow Product$ , a zero-order reaction has a rate law $R = k[A]^0 = k$ .
- The rate (R) does not depend on the concentration of A.
- $[A]t = [A]0 - kt$

First Order Reactions:
- For a reaction $A \rightarrow Product$ , a first-order reaction has a rate law $R = k[A]^1$ .
- The rate is directly proportional to [A].
- Exponential Decay

Second Order Reactions:
- For a reaction $A \rightarrow Product$ , a second-order reaction has a rate law $R = k[A]^2$ .
- There is a quadratic sensitivity of Rate on [A].
- \frac{1}{[A]t} = \frac{1}{[A]0} + kt

Integrated Rate Law:
- The integrated form of the rate law models how concentration changes with time, integrated over the time interval from t=0 to t.
- Integrated First Order
- ln[A]t = -kt + ln[A]0

Zero Order:
- For $R = k[A]^0 = k$ , integration yields $[A]t = [A]0 - kt$ .
- There is a proportional decrease in [A] over time.

First Order:
- ln[A]t = -kt + ln[A]0
- 1st order kinetics. Exponential decay of crystal violet.

Second Order:
- The integrated rate law is $\frac{1}{[A]t} = \frac{1}{[A]0} + kt$ .
- [A] decreases inversely with time.

	Zero Order	First Order	Second Order
Rate Law	$R = k$	$R = k[A]$	$R = k[A]^2$
Units of k	$M \cdot s^{-1}$	$s^{-1}$	$M^{-1} \cdot s^{-1}$
Rate vs. [A]	Rate is independent of [A]	Rate is directly proportional to [A]	Rate has a quadratic dependence on [A]
Integrated Rate Law	[A]t = [A]0 - kt	ln[A]t = ln[A]0 - kt	1/[A]t = 1/[A]0 + kt
Decay Model	Linear decay of [A] over time	Exponential decay of [A] over time	Inverse decay of [A] over time