A. How fast a reaction proceeds:

1. change in something vs. change in time - rate
2. chemistry: change in amount of substance vs. time

B. Compare to thermodynamics

1. DG determines spontaneity
- a reaction is favored or not favored
- when or how fast the reaction will occur is not known
2. The rate of a reaction (kinetics) tells when and how fast

A. Measure of reaction rate? e.g. 2 NO₂ --> 2 NO + O_{2 (g)}

1. Measurable quantities:

a. concentration of a substance ([ ] = moles/L)
b. time of [ ] measurement

2. rate = D[ ]/Dt = D[NO₂]/Dt or D[NO]/Dt or D[O₂]/Dt
3. Determining reaction rate

a. expected result:

rate defined as -D[NO₂]/Dt = D[NO]/Dt = 2D[O₂]/Dt
=> NO₂ disappears \ the rate is negative.
=> NO appears at the same rate as NO₂, but it is being formed, \ rate is positive.
=> O₂ appears at half the rate of NO (stoichiometry), \ must double obsvd. rate of O₂ appearance to get rate of NO appearance.

b. Actual result:

c. Reason? LeChatlier's Principle

1. rewrite the reaction to show reversibility:

2. as the rxn proceeds in the forward direction, it slows down.
3. Analogy with weak acids: ionization of acetic acid

=> acetic acid is always ionized to a small extent in solution; it is at equilibrium.
=> what if add H⁺? Rxn. would shift to the left, and less acetic acid would be ionized, but [H⁺]_f ~ [H⁺]_i
4. Return to NO₂ rxn.:
=> as [NO] and [O₂] increase, it becomes more difficult to form NO and O₂, so the ratesof formation of NO and O₂ decrease (rateis proportionate to [NO₂]).
=> The system is at eq. when the rates are unchanging.
d. Can determine rates at any time

1. Instantaneous rate: slope of tangent to curve at time t.
2. Average rate:
-D[NO₂]/Dt = -([NO₂]_f - [NO₂]_o)/(t_f - t_o)
3. Initial rate: average rate over very small time interval at the beginning of the reaction.

e. Determining the exact rate expression => differential rate law

n = order of the rxn. with respect to (WRT) NO₂
f. n = order of the rxn WRT [R]

1. Zero Order: no dependence of rate on [R]
2. First Order: dependence of rate on [R]
3. Second Order: dependence of rate on [R]²
4. Overall Order: add up all exponents in rate expression

B. Determining the order of a reaction: what is n?

1. Method of initial rates
=> avoid problems associated with LeChatlier's Principle
=> no significant [P], so forward rxn. dominates; negligible back rxn.
=> [R]_f ~ [R]_o
=> curve along such a small interval is approximately a straight line; rate = slope.

a. Vary [R] and determine initial rate to determine n

Rate is proportional to [NO]ⁿ[Cl₂]^m
Rate = k[NO]ⁿ[Cl₂]^m

1. From trial 2 to trial 3 [NO]_o is doubled while [Cl₂]_o is constant, \Drate is proportionate to D[NO]_o.

Rate is proportional to [NO]²
2. From trial 1 to trial 2 [Cl₂]_o is doubled while [NO]_o is constant, \D rate is proportional to D[Cl₂]_o.

3. Put it together: Rate = k[NO]²[Cl₂]
4. Solve for k:
1.45 M/min = k(0.20 M)²(0.20 M)
k = 181 1/M² min (2 sf)
=> Units of k indicate order of reaction (order= -exp+1 of M)
=> Reaction is third order overall (n+m); second order in [NO]² plus first order in [Cl₂].

C. Determining k and the rate expression, via integration of the rate law

1. Zero Order Reaction

a. Rate = k; handling is straightforward
b. Example: CH₃NNCH₃ --> C₂H₆ + N_{2 (g)}
plot [CH₃NNCH₃] vs. time and get a straight line \ rate = k[CH₃NNCH₃]¡ = k
Equation of line: [CH₃NNCH₃] = kt + [CH₃NNCH₃]_o
determine k (slope) from graph.

2. First Order Reaction: A --> B + C

a. Rate = k[A]
-D[A]/Dt = k[A] ; -D[A]/[A] = kDt

ln[A] - ln[A]_o = -kt ; ln[A] = -kt + ln[A]_o
=> equation for a straight line; plot ln[A] vs. t and determine k (-slope) and ln[A]_o (y-int, already known!).
b. Example: Radioactive Decay (always first order)

Plot ln(cpm) vs. time to get straight line: ln[A] = -kt + ln[A]_o

c. Unique result of first order kinetics:Half-life equation
t_1/2 is defined as the time interval required for [A] to decrease to half its initial value.

3. Second Order Reaction: be aware of rate laws, but will not be tested beyond using raw data directly (shown earlier).

III. Arrhenius Equation

A. The dependence of rate on temperature: k = A_e-E_A/RT
- Experimentally derived equation: A_e = Arrhenius constant (empirical)
B. Explanation of the Arrhenius equation

1. Temp. is a measure of K.E. of molecules
2. On a molecular level, a reaction is seen as a result of a collision of two or more molecules (unless truly zero or first order)
3. In the collision model of chemical kinetics, molecules use K.E. to break bonds; new bonds form as a result of the reaction.

C. Example 2 NO₂ --> 2 NO + O₂

1. Proposed molecular mechanism

2. Energy profile of reaction

3. Determination of E_A and A

a. Plot ln(k) vs. 1/T
ln(k) = -E_A/RT + ln(A)
m = -E_A/R ; b = ln(A)
b. Use two determinations of k at two temperatures
ln(k₂/k₁) = E_A/R(1/T₁- 1/T₂)

A. Reaction Mechanism: A hypothesis of how molecules actually react based upon observed rate law and chemical equation of reaction.

B. Law of Mass Action

C. An Example: NO₂ + CO --> NO + CO₂ (g)

1. Propose a mechanism and rate laws for each step.

2. Assign step 1 as the slow step, \ the rate is determined by step 1 and Rate = k₁[NO₂]².

3. Tie in Arrhenius Equation

V. Catalysis

A. Function of a catalyst

1. Lower E_A of the reaction
2. Not be consumed or generated in the reaction
=> The catalyst interacts with reactants to make it easier for them to form products.

B. Example - depletion of the ozone layer by CFCs

C. Example - catalytic converters in automobiles

1. Function: to convert CO and NO to CO₂ and N₂.
In an engine, if it gets too hot, nitrogen will be oxidized to NO.
NO will go on to produce tropospheric ozone and acid rain.
2. Reaction: CO + NO --> CO₂ + 1/2 N_{2 (g)}
catalyst: heterogeneous noble metals; e.g. Pt, Pd.