Reaction Kinetics Flashcards

1
Q

For the reaction:
A + 2B –> 3P

Where the rate expression is defined as:
- rA = 2 CA^0.5 CB

Write the rate expression for each of the components.

A
  • rB = 4 CB^0.5 CB

rC = 6 CA^0.5 CB

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2
Q

Define ‘conversion’ of a reaction

A

The ratio between the amount of A reacted and the initial amount of A

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3
Q

Write the general rate expression and derive the expression for a constant volume system

A
  • rA = k CA^a
  • rA = dCA/dt
  • rA = - 1/V dnA/dt
  • rA = nA0/V dXA/dt
    OR
  • rA = CA0 dXA/dt
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4
Q

What is the reaction rate dependent upon?

A
  1. Concentration of reactants
  2. Rate constant, k
  3. Temperature
  4. Catalyst
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5
Q

What affects the rate constant, k?

A
  1. Temperature

2. Catalyst

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6
Q

Write the Arrhenius equation and write the equation if this was plotted on a graph

A

k = A e^(-E/RT)

ln k = ln A - (E/R)*(1/T)

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7
Q

Define each of the components in the Arrhenius equation

A

E = activation energy, the minimum kinetic energy that reactants must have in order to form products

exp = exponential factor, the fraction of collusions that have enough kinetic energy to lead that reaction

A = pre-exponential factor or frequency factor, a measure of the rate at which collisions occurred, irrespective of their energy

k = rate constant, the rate of successful collisions

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8
Q

Write the Arrhenius equation for comparing 2 different temperatures

A

ln k2/k1 = E/R (1/T1 - 1/T2)

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9
Q

True or false; reactions with a lower activation energy are more sensitive temperature

A

False

Higher activation energies are more sensitive to temperature changes. This is shown by a steeper gradient on the Arrhenius plot.

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10
Q

Define ‘reaction order’

A

The index, or exponent, to which its concentration term in the rate equation is raised.

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11
Q

True or false; the stoichiometric coefficients of a reactant influence the order of the reaction

A

False

There is no relationship between these two factors

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12
Q

In what case will a temperature increase cause the rate of reaction to decrease?

A

When the reactant degrades at a certain temperature, the rate of reaction will decrease above this temperature

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13
Q

Show how to calculate and compare the fraction of molecules able to react at 2 different temperatures

A
k1 = A e^(-E/RT1)
k1 = \_\_\_\_ A
k2 = A e^(-E/RT2)
k2 = \_\_\_\_ A

k2/k1 = Fraction

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14
Q

Show how to calculate and compare the fraction of molecules able to react at when a catalyst is present at a given temperature

A
k1 = A e^(-E/RT)
k1 = \_\_\_\_ A

k cat = A e^(-E/RT)
k cat = ____ A

k cat/k1 = Fraction

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15
Q

Write the general rate equation for a first order, homogenous, gas phase reaction

A

r = k pA

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16
Q

Show how the rate equation for a homogenous, first-order reaction can be written in terms of:

  1. Catalyst weight
  2. Surface of catalyst
  3. Volume of fluid
  4. Volume of reactor
  5. Volume of solid
A
  1. rA = 1/W dNA/dt
  2. rA = 1/S dNA/dt
  3. rA = 1/V dNA/dt
  4. rA = 1/Vr dNA/dt
  5. rA = 1/Vs dNA/dt
17
Q

Define the difference between the units for rate of reaction for a homogenous reaction vs. heterogeneous

A
Homogenous = mol/ L min
Heterogeneous = mol/ m^2 min
18
Q

What is an elementary reaction?

A

A reaction where the orders of the reactants match the stoichiometry of the reaction

19
Q

True or false: A rate equation that has reaction orders corresponding to the reaction stoichiometry are always elementary reactions

A

False

It can just be a coincidence

20
Q

Write the rate equations and the equivalent rate constants for each of the components of the following elementary reaction:

B + 2D –> 3T

A
  • rB = kB CB CD^2
  • rD = kD CB CD^2

rT = kT CB CD^2

rB = 1/2 rD = 1/3 rT
kB = 1/2 kD = 1/3 kT
21
Q

Use the initial rates method to determine the rate law using the following data:

A + 2B –> 3C where r = k CA^a CB^b

1 - r = 2.73 - CA = 0.1 - CB = 0.1
2 - r = 6.14 - CA = 0.15 - CB = 0.1
3 - r = 2.73 - CA = 0.1 - CB = 0.2

A

ln r = a ln CA + b ln CB + ln k

  1. ln 2.73 = a ln 0.1 + b ln 0.1 + ln k
  2. ln 6.14 = a ln 0.15 + b ln 0.1 + ln k
  3. ln 2.73 = a ln 0.1 + b ln 0.2 + ln k

1 - 2 = ln 2.73/6.14 = a ln 0.1/0.15 –> a = 2
1 - 3 = ln 2.73/2.73 = b ln 0.1/0.2 –> b = 0

Sub in to any of 1, 2 or 3
k = 273 L/mol s

r = 273 CA^2 CB^0

22
Q

Use the isolation method to determine the rate law using the following data:

A + 2B –> 3C where r = k CA^a CB^b

1 - r = 2.73 - CA = 0.1 - CB = 0.1
2 - r = 6.14 - CA = 0.15 - CB = 0.1
3 - r = 2.73 - CA = 0.1 - CB = 0.2

A
r1 = k CA1^a CB1^b
r2 = k CA2^a CB2^b
r3 = k CA3^a CB3^b

r1/r2 = (k CA1^a CB1^b)/(k CA2^a CB2^b)
2.73/6.14 = (0.1/0.15)^a
log 2/3 (2.73/6.14) = a
a = 2

r1/r3 = (k CA1^a CB1^b)/(k CA3^a CB3^b)
2.73/62.73 = (0.1/0.2)^b
log 0.5 (2.73/2.73) = b
b = 0

23
Q

Derive the two integrated rate laws for a first order reaction

A

ln (CA/CA0) = - kt

e^(ln (CA/CA0)) = e^(- kt)

CA/CA0 = e^(- kt)

CA = CA0 e^(-kt)

24
Q

How do you determine the rate constant graphically for a first order reaction (hint: using the integrated rate law)

A

ln (CA/CA0) = - k t

plot t (x-axis) vs. ln (CA/CA0) (y-axis)

gradient = -k

25
Derive the two integrated rate laws for a second order reaction
1/CA - 1/CA0 = kt CA = CA0/(1 + k t CA0)
26
What is half life?
The time taken for the concentration of the reactant to reduce to half of that concentration
27
Derive the equation for the half life of a first order reaction
ln (CA/CA0) = - k t t 1/2 = 1/k ln (0.5 CA0/CA0) t 1/2 = 1/k ln (0.5) t 1/2 = ln 2/k
28
True or false: For a first order reaction, the half life is independent of initial concentration
True
29
Derive the equation for the half life of a second order reaction
1/CA - 1/CA0 = kt t 1/2 = 1/kCA0
30
True or false: For a second order reaction, the half life is independent of initial concentration
False
31
Write the equation for the number of half lives
No. half lives = total time elapsed/half-lives
32
Write the equation for the fraction of molecules remaining after a given number of half lives
(Amount remaining/Initial amount) = (0.5)^(No. half lives) | Amount remaining/Initial amount) = (0.5)^(Total time elapsed/Half-lives
33
Outline the method for calculating the integrated rate law for bimolecular reactions A + B --> P
- rA = k CA CB = - dCA/dt = - dCB/dt Let the amount of A or B reacted = m = CA0 - CA = CB0 - CB Therefore: - rA = dm/dt = k (CA0 - m) (CB0 - m) = - dCA/dt dm/dt = k (CA0 - m) (CB0 - m) k dt = 1/(CA0 - m) (CB0 - m) dm Initial conditon: m = 0 when t = 0 Use partial fraction integration to determine the integral of the RHS: 1/(AD - BC) ln ((Ax + B)/(Cx + D)) 1/(CA0 - CB0) ln ((CB0 CA)/(CB CA0)) Therefore: 1/(CA0 - CB0) ln (CB0CA/CBCA0) = kt n (CB0CA/CBCA0) = (CA0 - CB0)kt
34
Derive the integrated rate law for a reversible reaction | A B
CA = [(k'+ke^(k+k')t)/(k+k')] CA0
35
Write the rate equations for each of the components in the following reversible and concurrent reactions: A B A ---> C
- rA = k1 CA + k2 CA rA = k-1 CB rA = k-1 CB - (k1 + k2) CA - rB = k-1 CB rB = k1 CA rB = k1 CA - k-1 CB rC = k2 CA
36
Write the equation for the equilibrium constant for a reversible reaction A B
``` K = CB,eq/CA,eq K = [kCA0/(k+k')] / [k'/(k+k')] CA0 K = k/k' ```
37
What happens to the integrated rate law for a reversible reaction as t --> infinity? A B
Concentrations --> Equilibrium Hence: e^(k+k')t --> 0 ``` CA,eq = [(k'+ke^(k+k')t)/(k+k')] CA0 CA,eq = [k'/(k+k')] CA0 ``` ``` CB,eq = CA0 - CA,eq CB,eq = kCA0/(k+k') ```