Reaction Kinetics

Question 1

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.

Answer 1

• rB = 4 CB^0.5 CB

rC = 6 CA^0.5 CB

Question 2

Define ‘conversion’ of a reaction

Answer 2

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

Question 3

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

Answer 3

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

Question 4

What is the reaction rate dependent upon?

Answer 4

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

Question 5

What affects the rate constant, k?

Answer 5

1. Temperature

2. Catalyst

Question 6

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

Answer 6

k = A e^(-E/RT)

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

Question 7

Define each of the components in the Arrhenius equation

Answer 7

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

Question 8

Write the Arrhenius equation for comparing 2 different temperatures

Answer 8

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

Question 9

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

Answer 9

False

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

Question 10

Define ‘reaction order’

Answer 10

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

Question 11

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

Answer 11

False

There is no relationship between these two factors

Question 12

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

Answer 12

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

Question 13

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

Answer 13

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

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

k2/k1 = Fraction

Question 14

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

Answer 14

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

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

k cat/k1 = Fraction

Question 15

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

Answer 15

r = k pA

Question 16

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

Answer 16

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

Question 17

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

Answer 17

Homogenous = mol/ L min
Heterogeneous = mol/ m^2 min

Question 18

What is an elementary reaction?

Answer 18

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

Question 19

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

Answer 19

False

It can just be a coincidence

Question 20

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

B + 2D –> 3T

Answer 20

• 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

Question 21

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

Answer 21

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

Question 22

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

Answer 22

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

Question 23

Derive the two integrated rate laws for a first order reaction

Answer 23

ln (CA/CA0) = - kt

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

CA/CA0 = e^(- kt)

CA = CA0 e^(-kt)

Question 24

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

Answer 24

ln (CA/CA0) = - k t

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

gradient = -k

Question 25

Derive the two integrated rate laws for a second order reaction

Answer 25

1/CA - 1/CA0 = kt

CA = CA0/(1 + k t CA0)

Question 26

What is half life?

Answer 26

The time taken for the concentration of the reactant to reduce to half of that concentration

Question 27

Derive the equation for the half life of a first order reaction

Answer 27

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

Question 28

True or false: For a first order reaction, the half life is independent of initial concentration

Answer 28

True

Question 29

Derive the equation for the half life of a second order reaction

Answer 29

1/CA - 1/CA0 = kt

t 1/2 = 1/kCA0

Question 30

True or false: For a second order reaction, the half life is independent of initial concentration

Answer 30

False

Question 31

Write the equation for the number of half lives

Answer 31

No. half lives = total time elapsed/half-lives

Question 32

Write the equation for the fraction of molecules remaining after a given number of half lives

Answer 32

(Amount remaining/Initial amount) = (0.5)^(No. half lives)

Amount remaining/Initial amount) = (0.5)^(Total time elapsed/Half-lives

Question 33

Outline the method for calculating the integrated rate law for bimolecular reactions

A + B –> P

Answer 33

• 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

Question 34

Derive the integrated rate law for a reversible reaction

A B

Answer 34

CA = [(k’+ke^(k+k’)t)/(k+k’)] CA0

Question 35

Write the rate equations for each of the components in the following reversible and concurrent reactions:
A B
A —> C

Answer 35

• 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

Question 36

Write the equation for the equilibrium constant for a reversible reaction

A B

Answer 36

K = CB,eq/CA,eq
K = [kCA0/(k+k')] / [k'/(k+k')] CA0
K = k/k'

Question 37

What happens to the integrated rate law for a reversible reaction as t –> infinity?

A B

Answer 37

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')