Question

I need help please: Reaction Mechanisms and Catalysis

1. The rate constant in an elementary reaction's rate equation can be modeled by the Arrhenius equation: & Ae a. The coefficient A is the frequency factor. What are the units of A for a first-order reaction? Justify your answer mathematically. (2 points) b. Describe how the value of A is affected by molecular collisions. (1 point)

Answer 1

1a)

The expression of rate constant (K) according to Arrhenius equation is given by:

............ (1)

k= Ae-E/RT

Where K is the rate constant, A is the frequency factor or pre-exponential factor, E_a is the activation energy, T is the temperature.

In order to find out the unit of 'A' for the first-order reaction, we have to incorporate the rate equation for the first-order reaction.

We know the expression of the rate constant for the first-order reaction is-

............. (2)

k = -In I-D

Where t is the time and a is the initial amount of the reactant and x is the amount of product formed after time t.

Now form equations (1) and (2), we will have

Ae-Ea/RT – In a ta - r

A = -In- ta - r /e-Ea/RT

Now we know the term has no unit because both 'a' and 'a-x' are representing the same thing.

1 - D -u1

Hence, the unit of A will be

A = Unit of energy / unit of R * unit of temperature * unit of time

Unit of A = liter mol^-1 sec-¹

b)

Now we already have:

k= Ae-E/RT

A = k/e-E./RT

or

A = keE/RT

Hence, A is directly related to Ea which is the activation energy. Now we know the greater the collision between the molecules greater will be the activation energy and the value of Ea will be greater as well. Hence as the collision between molecules increases, the value of A should increase and vice-versa.

c)

A = keE/RT

From the previous equation, we have already got that A is now inversely related to reaction temperature 'T'.

Thus T or reaction temperature has a high effect on the value of A and the value of A decreases as the value of T increases.

d)

Since the term
e-E./RT
does involve the term T or the reaction temperature, it (T) will have a high impact on the term
e-E./RT
.

2a)

From the four diagrams, it is clearly visible that the fruitful collisions are only those collisions where the atoms or molecules collide head-on and the atoms or molecules should touch each other. So we can derive the two most important aspects of effective collisions:

1. While getting bombarded, two atoms or molecules must maintain proper orientation.

2. The reactive centers should be as close as possible ( in picture 4, two reactive centers are almost touching one another).

b)

The Arrhenius equation with the probability factor is given by:

k = Pze-E/RT

Where 'P' is the probability factor

This term 'P', also known as the steric factor, depends on the orientation of the two atoms colliding. The more proper the orientation, higher the value of P will be. Hence, if individual atoms are colliding with proper orientation instead of a molecule, then the value of 'P' should be higher.