Bimolecular Collision Theory

Question 1

What is the Arrhenius equation?

Answer 1

k= Ae ^ -Ea/RT

Any theory of bimolecular reactions must behave like the Arrhenius equation

Question 2

Why does the bimolecular collision theory state?

Answer 2

For any reaction to occur we must bring the two molecules into contact with each other
The molecules need to be able to collide and they must have enough energy for them to be able to react

Question 3

How does bimolecular collision theory tackle problems for

A + B -> products

Answer 3

1) calculate the rate of collisions between A and B

2) calculate the proportion of these collisions that have sufficient energy to react

Question 4

What is the rate of collision dependent on?

Answer 4

The likelihood of collision is going to be dependent on the size of the molecule and how rapidly they move

Question 5

How do you work out collision cross section?

Answer 5

The combination of two colliding radio defines the collision cross section

= pi d^2 = sigma

Question 6

What is the use of bimolecular theory?

Answer 6

This uses the kinetic theory of gases to find an expression for the A factor in the Arrhenius equation

Question 7

What is the expression for the A factor?

Answer 7

A= sigma v
(V is the average speed of collision)

A= sigma(8KBT/pi x RM)^ 1/2 x Na

Question 8

What does A factor depend on?

Answer 8

It depends on the collision cross section (sigma) which is related to the size of the molecule and their average speed

Question 9

What is reduced mass?

Answer 9

mA x mB/ mA + mB

Question 10

How do you find the rate constant?

Answer 10

Not all collisions react and so A needs to be multiplied by the fraction of collisions that have enough energy to overcome the energy barrier 
k=sigma(8KBT/pi x RM)^ 1/2 x Na x 
e^-Ea/RT
(Sub A into the Arrhenius equation)
K= sigma v e^Ea/RT

Question 11

What is an expression for the fraction of collisions that have enough energy to overcome the energy barrier Ea?

Answer 11

e^-Ea/RT

From the Arrhenius equation

Question 12

Why is the calculated rate constant too large for most reactions?

Answer 12

This is because not all collisions with enough energy to overcome the barrier will actually go on to form products

Question 13

How do you solve the problem of the calculated rate constant being too high?

Answer 13

Introduce P which is a steric factor

k= P sigma(8KBT/pi xRM)^ 1/2 x Na x e^-Ea/RT

Question 14

Comparing k= P sigma(8KBT/pi xRM)^ 1/2 x Na x e^-Ea/RT to the Arrhenius equation, what is A?

Answer 14

A=P sigma(8KBT/pi xRM)^ 1/2 x Na

Question 15

What is a steric factor?

Answer 15

The reactants need to collide in a specific orientation to react

Question 16

What is the frequency of collisions?

Answer 16

This is the number of collisions in a unit period of time

Question 17

What is molecular density?

Answer 17

The number of molecules per unit volume

Question 18

What will the frequency of collision be if A is travelling at an average speed Va through a number of B molecules (assumed stationary)

Answer 18

Frequency is proportional to [B]sigma Va

Question 19

What will the frequency of collision be if there is more than one A is travelling at an average speed Va through a number of B molecules (assumed stationary)

Answer 19

Frequency is proportional to [A][B]sigma Va

Va is the average speed of A

Question 20

What will the frequency of collision be if there is more than one A is travelling at an average speed Va through a number of B molecules that are not stationary?

Answer 20

Frequency is proportional to [A][B]sigma V

V is the average speed to collisions of A and B
Sigma= pid^2 = pi(rA + rB)^2

Question 21

If all collisions reacted, what would the rate of change be?

Answer 21

Frequency is proportional to [A][B]sigma V

d[A]/dt= -[A][B] sigma v

This is negative as [A] decreases as it reacts

Question 22

What are the units of frequency?

Answer 22

Equivalent to collisions per unit volume per unit time (same as rate)

Question 23

What is the equation for the proportion of collisions with sufficient energy?

Answer 23

e^-Ea/RT

Question 24

What does the rate of change reaction become when you take into account that not collisions are successful?

d[A]/dt= -[A][B] sigma v

Answer 24

Predicted rate of reaction:

d[A]/dt= -k[A][B]= sigma v e^-Ea/RT[A][B]

Compare this to the Arrhenius equation and you can see which parts are A and which parts are k

Question 25

How do you calculate the average speed of collisions?

Answer 25

V = (8kBT/ pi x RM)^1/2

Question 26

What is A and what is K in simplified expression terms?

Answer 26

A= sigma v

K= sigma v e^-Ea/RT

Question 27

What do you need to do differently if you use molar masses for A and B in the calculation of V?

Answer 27

You would need to use R instead of Kb

Question 28

What are the units of sigma and v?

Answer 28

Sigma= m2
V= ms-1

Question 29

How do you calculate steric factor P?

Answer 29

P= A(experimental)/ A(bimolecular theory)

Question 30

What assumptions bimolecular theory?

Answer 30

It assumes that molecules have to collide to react?

Question 31

What does bimolecular theory rely on?

Answer 31

It relies on the prediction of cross section, steric factor and activation energy (impossible to calculate with this theory)