Class/Kinetics/kinetics-notes.org

[2019-01-15 mar]

Thermodynamics

Whether something is likely to happen

Kinetics

how fast it will happen

T v.s v v.s. kinetic energy

• Graphite is less thermodynamically stable than diamond
Ideal gas

• # of molecules colliding to surface A
\frac{1}{2} n^{*}A
• Temperature is a direct indication of kinetic energy
• The energy is the same for two (ideal) gases E = 3/2 k T
• The velocity and the mass are different

Distribution

Review

Chapter 2

rate las (rate) = \underbrace{k}_{rate constant} [A]^{a} [B]^{b}...

• differential

\frac{[P]}{t} = k f([A], [B])

the function can be simple or complicated as desired, and

• integral

P(t) =

[2019-02-22 vie +2d]
• 1st order
• 2nd order
• Higher order (3rd order; partial fraction)
• Equilibrium (forward & reverse)
• Parallel A →(k1) B
(k2)↓ C \frac{k1}{k2}: branching ratio

• Consecutive

(k1) (k2) A --→ B --→ C

• k1 >> k2: B --→C 1st order (A is first completely consumed into B)

• k1 << k2: [B] stays low

• SSA:
\frac{intermediate}{t} = 0

valid when intermediate is reactive or unstable

• Lindermann mechanism

A + M <=> A* + M A* → P

SSA \frac{[A]*}{t} = 0

• Michaelis-Menten

\frac{1}{v_{o}} = \frac{1}{v_{m}} + \frac{K_{m}}{v_{m}} \frac{1}{s_{o}}

• Inhibition
• competitive
• non-competitive

• Free radical kinetics

radicals are very reactive, thus we use SSA

In general
1. Setting up differential rate law
2. Setting up SSA
3. Identify how the reaction kinetics change if the mechanism changes (if a step didn't exist, or a step would be added)

Chapter 3

How do you actually calculate the reaction constant?

k(T) ?

Collision

• overestimates k
• limitations:
• geometry is ignored
• steric factor

We use G(\epsilon) from chapter 1 (big connection)

k = A \exp{- \frac{\epsilon^{*}}{R T}} A = \pi{} b_{max}^{2} v_{r}

A.C.T.

Chapter 5

Also about k(T), but in solution (when there are solvents; liquid phase)

Diffusion limited

k = 4 \pi{} \left(D_{A} + D_{B}\right) R

R: for neutral, related to geometry

from Chapter 1: A = \pi{} b_{max}^{2} v_{r}, b_max is geometry

• When there is charge

R → \beta{} → U(r),

where U(r) is Coulombic potential, \beta{} is ionic strength

I = \frac{1}{2} \sum_{}^{}{\left(c_{i} z_{i}^{2}\right)}

screening effect: charge makes the reaction slower

Marcus theory: chargge trans

Chapter 4

Transport phenomena

Flux equation

J_{z} = - \frac{1}{3} \lambda{} \langle{v\rangle} \left(\frac{n q^{*}}{x}\right)

\lambda: mean free path from Chapter 1 \langle{v\rangle}: from Chapter 1

• k = \frac{1}{3} \lambda{} \langle{v\rangle} \frac{C_{V}}{N_{A}}
• \eta = ( ) \cdot{} m
• D =

Fick's law

      |
      |
      | \
      |  \
      |   \
      |    \
      |     \
      |      \
      |       \
      +-------------------------

J = - D \left(\deriv{C}{x}\right)

Infinite diffusion

Infinite diffusion ~ erf(\frac{x}{2 \sqrt{D t}})

    -----------------------+
                    .....  |
                        ...|
                          ..
                           ..
                           |..
                           | ....
                           |    .....
   ------------------------------------------------> x

Random walk ~ Thin layer

gas v.s. liquid

• gas:
• mean free path (\lambda{}): large
• v: large
• liquid
• mean free path (\lambda{}): small
• v: large
• solid
D = \frac{1}{2} \Gamma{} \left(\Delta{x}\right)^{2}
• hopping mechanism
• \Gamma{}: hopping rate (similar to velocity)
• Follows Arrenhius ~ A \exp(- \frac{\Delta{G}}{R T})
• vacancies don't move as quickly
• boundary diffusion easier than bulk diffusion, but if you increase the temperature, the rate of boundary diffusion is more affected

#+BEGIN_SRC ditaa | -- | \--- | \-- | \--- | ------- \--- | \----------- | \----------- | \-- \------ | \--- | \- -+------------------------------------------

A few reminders about the midterm exam

#+END_SRC

Posted on: Friday, March 1, 2019 2:03:41 PM MST

1. The exam will be given during regular class time next Tuesday (Mar 5, 8:35 - 10:15am)

1. This is an open book exam. You may use any book or printed/hand-written materials. Electronic devices won't be allowed.

1. You will need a scientific/engineering calculator. Graphing function is not required.

1. The exam will cover Ch 1-4 of Houston text and Ch 4 of O'Hayre text. Sections 4.1-4.3 of O'Hayre overlaps with Houston, content-wise.

1. I'll hold an extra office hours on Monday (March 4) from 4:30 - 6pm at the meeting area (east end of the building) on the 2nd floor of ERB.

Review

Ch 2

• Probability distribution function (can you work with them?)
• If the probability of getting 1 is the double of another one, can you do with it
• What happens if the rate of something is doubled?
• can you get the values of other variables?
• set up steady state approximation, why? know when to use it.

A → B → C

\deriv{[B]}{t} = 0 [B] = ?

To reduce the order of the

If there is no steady state, set up the equation

Only valid when [B] (radicals are unstable)

Collision theory

Understand the theory

D + H2 → N = 3 3N - 6 They are not linear

Diffusion

Numerical