Collision theory requires that particles collide. However, not all collisions lead to successful reaction even if they have enough energy to overcome the activation energy barrier. The Arrhenius factor takes this into account.
Syllabus reference R2.2.13
Reactivity 2.2.13 - The Arrhenius factor, A, takes into account the frequency of collisions with proper orientations. (HL)
- Determine the activation energy and the Arrhenius factor from experimental data.
Arrhenius Factor
The Arrhenius factor, also known as the pre-exponential factor (A), is a crucial component in the Arrhenius equation. It helps describe the rate of a chemical reaction.
Arrhenius Equation
The Arrhenius equation is given by:
- k: Rate constant of the reaction
- A: Pre-exponential factor or Arrhenius factor
- Ea: Activation energy
- R: Universal gas constant (8.314 J/mol·K)
- T: Temperature in Kelvin
Understanding the Arrhenius Factor (A)
The Arrhenius factor is a measure of the frequency of collisions and the orientation of reacting molecules. It represents the number of times reactants collide with the proper orientation to form products.
- High value of A indicates a large number of effective collisions.
- Depends on factors like the nature of the reactants and the complexity of the reaction mechanism.
Factors Influencing the Arrhenius Factor
- Nature of reactants
- Simple molecules generally have higher A values.
- Complex molecules may have lower A values due to steric factors.
- Reaction Mechanism
- Elementary reactions usually have higher A values.
- Multi-step reactions might have lower A values.
Significance of the Arrhenius Factor
The Arrhenius factor is essential for understanding the kinetics of a reaction:
- Helps in calculating the rate constant (k) of a reaction.
- Provides insight into the reaction mechanism.
- Assists in predicting how reaction rates change with temperature.
Practical Applications
- In industrial chemistry for optimizing reaction conditions.
- In pharmaceuticals for understanding drug stability and reaction rates.
- In environmental science for studying pollutant degradation rates.
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Worked examples
Q642-01 For irreversible reactions,
the rate will be affected by changes in all of these factors except
- temperature.
- concentration of reactants.
- presence of a catalyst.
- concentration of products.
Answer
|
The concentration of products cannot
affect the rate of the forward reaction if it is irreversible. In
reality there are no irreversible reactions, rather they are irreversible
under the chosen conditions.
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Q642-02 The rate of the reaction:
2NO + Cl
2 → 2NOCl is
given by the rate equation, rate = k[NO]
2[Cl
2]. The value
of the rate constant can be increased by:
- increasing the concentration of the NO.
- increasing the concentration of the Cl1.
- increasing the temperature.
- doing all of these.
Answer
|
The rate constant is independent of concentrations, but does depend
on the temperature.
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Q642-03 A small increase in
temperature often causes a large increase in the rate of a chemical reaction.
This effect is best attributed to
- a decrease in the activation energy of the reaction
- more frequent collisions at the higher temperature
- the occurrence of more collisions with the needed energy
- different reaction pathways at the higher temperature
Answer
|
Activation energy cannot be affected except by providing an alternative
pathway (mechanism) using a catalyst
There are more collisions as the temperature rises, but this is not
as important as the success of the collisions.
The increase in temperature means that more
particles will have the required energy to make their collisions
successful
There is no reason to suppose that higher temperatures lead to different
mechanisms
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Q642-04 Zinc metal reacts
with excess HCl according to the equation:
Zn(s) + 2H+(aq) + 2Cl-(aq) → Zn2+(aq) + 2Cl-(aq) + H2(g)
Which of the following change will increase the rate of evolution of H2?
- I. using zinc dust in place of chunks
- II. using 2 M HCl in place of 1 M HCl
- III. using 200 mL of 1 M HCl in place of 100 mL
- I only
- I and II only
- II and III only
- I, II, and III
Answer
|
Using dust in place of lumps increases the available surface area
for reaction. Increasing the concentration increases the rate as seen
by the rate expression (this would not apply for 0th order components),
however increasing the volume has no effect on the rate. I
and II only
|
Q642-05 Ingold was awarded
a Nobel Prize for his investigations into the kinetics of the hydrolysis of
bromoalkanes in alkaline aqueous ethanol.
RBr + OH- → ROH + Br-
He obtained the following rate constants for the hydrolysis of bromoalkanes.
| - |
CH3Br
|
C2H5Br
|
CH3CHBrCH3
|
(CH3)3CBr
|
| First order |
-
|
-
|
1.4 x 104
|
1.0 x 102
|
| Second order |
1.1 x 102
|
7.1 x 103
|
4.7 x 105
|
-
|
Deduce the initial rate of hydrolysis of bromoethane, if 50 cm3
of a 0.1 mol dm-3 ethanolic solution of bromoethane is completely
mixed with 50 cm3 of alkaline aqueous ethanol, which has a concentration
of 0.05 mol dm-3 with respect to hydroxide ions.
Answer
|
Bromoethane, C2H5Br, in the table undergoes
hydrolysis via a second order process.
Therefore the rate expression is:
Rate = k[C2H5Br]1[OH-]1
Moles of bromoethane in the mixture = 0.1 x 0.05 = 0.005 moles
This is in 50 + 50 = 100 cm3 therefore the initial concentration
of bromoethane = 0.005/0.1 = 0.05 mol dm-3
Concentration of hydroxide ions initially = 0.05 x 0.05/0.1 = 0.025
mol dm-3
Substituting the values in the rate equation: Rate = k[C2H5Br]1[OH-]1
Rate = 7.1 x 103 x 0.05 x 0.025
Therefore initial rate = 8.875
mol dm-3 s-1
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Q642-06 A small increase in
temperature often produces a large increases in the rate of a chemical reaction
because it:
- decreases the activation energy of the reaction.
- increases the effectiveness of the collisions between the reactant molecules
- decreases the number of collisions per second between the reactant molecules
- decreases the volume of the solution, altering the concentrations of the
reactants.
Answer
|
Increasing the temperature gives more energy to the particles and
increases the effectiveness of the collisions.
|
Q642-07 The reaction between
nitrogen and oxygen in the atmosphere under normal conditions is extremely slow.
Which statement best explains this?
- The concentration of oxygen is much lower than that of nitrogen
- The molar mass of nitrogen is less than that of oxygen
- The frequency of collisions between nitrogen and oxygen molecules is lower
that that between nitrogen molecules themselves
- Very few nitrogen and oxygen molecules have sufficient energy to react
Answer
|
Nitrogen is an unreactive gas due to its strong triple bond that
must be broken for reaction to occur. Very
few nitrogen and oxygen molecules have sufficient energy to react
|
Q642-08 The rate of the reaction
of a strip of magnesium ribbon and 50cm
3 of 1.0 mol dm
-3
HCl is determined at 25ºC. In which case would both new conditions contribute
to an increase in rate?
- Mg powder and 100cm3 of 1 mol dm-3 HCl
- Mg powder and 100cm3 of 0.8 mol dm-3 HCl
- 100cm3 of 1 mol dm-3 HCl at 30ºC
- 50cm3 of 1.2 mol dm-3 HCl at 30ºC
Answer
|
decreasing particle size to powder increases the rate. Increasing
the concentration of the acid increases the rate. Increasing the temperature
increases the rate. The only choice that has two rate increasing factors
is D, 50cm3 of 1.2 mol dm-3
HCl at 30ºC.
|
Q642-09 Doubling which of
the following will double the rate of a first order reaction?
- Concentration of the reactant
- Size of the solid particles
- Volume of the solution in which the reaction is carried out
- Activation energy
Answer
|
First order reactions have the form rate = k[A], therefore doubling
the concentration of the reactant
doubles the rate.
|
Q642-10 The curve in the diagram
is obtained for the reaction of an excess of CaCO
3 with hydrochloric
acid. How and why does the rate of reaction change with time?
|
|
Rate of reaction
|
Reason
|
|
A.
|
decreases
|
HCl becomes more dilute |
|
B.
|
decreases
|
The pieces of CaCO3 become smaller |
|
C.
|
increases
|
The temperature increases |
|
D.
|
increases
|
The CO2 produced acts as a catalyst |
Answer
|
The rate decreases over time as
the reactants get used up. In this case the HCl is becoming
more dilute.
|
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