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Physical chemistry (3.1)›Kinetics (3.1.5)

Kinetics (3.1.5)

Collision theory, the Maxwell-Boltzmann distribution and the impact of different factors on reaction rate.

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Collision theory states that for a chemical reaction to take place, particles must collide in the correct orientation and with sufficient energy.

Activation energy, is the energy barrier that must be overcome for the reaction to proceed. It is typically measured as the energy difference between the reactants and the transition state.

A graph illustrating the energy changes during a chemical reaction. The vertical axis represents energy, while the horizontal axis shows the progress of the reaction. It depicts reactants at a higher energy level, a transition state peak, and products at a lower energy level, indicating a negative change in enthalpy (ΔH).

This means that for a successful collision to occur, the reactant particles must collide with energy equal to or above the activation energy.

If reactant particles collide with sufficient energy (equal to at least the activation energy, ) and in the correct orientation they will react, leading to an effective collision.

If reactant particles collide with insufficient energy, they bounce off of each other and it will be an ineffective collision.

Diagram illustrating a chemical reaction, showing reactants (O2 and N2) on the left with labels indicating they are energetic and oriented correctly, and products (N2 and CO2) on the right with a label indicating a chemical reaction has occurred.

If reactant particles collide in the incorrect orientation, they will bounce off each other resulting in an ineffective collision.

There are several factors which can increase the frequency of collisions such as:

increasing concentration
increasing pressure
increasing surface area
increasing temperature.

Frequency of collisions is defined as the number of collisions per unit time.

If the frequency of collisions increases, the frequency of effective collisions will also increase. This will cause an increase in the rate of the chemical reaction.

The Maxwell-Boltzmann distribution curve is a graphical representation showing the distribution of energies of molecules at a particular temperature.

The Maxwell-Boltzmann distribution curve plots the number of molecules on the axis and energy of the molecules on the axis.

A graph depicting the relationship between the number of molecules and energy, showing a peak at a certain energy level before declining.

The area under the curve in the Boltzmann distribution is equal to the number of molecules in the substance.

Upon changing conditions, the total area under the curve does not change.

The peak of the curve represents the most probable energy, ; the mode.

The curve is asymptotic (does not reach the axis), as molecules have no maximum kinetic energy, and starts at the origin , as molecules must have a non-zero energy.

A graph depicting the relationship between the number of molecules and energy. The y-axis represents the number of molecules, while the x-axis represents energy. The curve peaks at a certain energy level, labeled 'Emp', indicating the maximum number of molecules at that energy. The graph shows a decrease in the number of molecules as energy increases beyond this point.

The curve becomes useful in explaining reaction kinetics, as only molecules with energy equal to or greater than the activation energy will result in effective collisions. This is the area under the curve to the right of the line.

Increasing the temperature shifts the Maxwell-Boltzmann distribution curve to the right and down.

The total area under the curve remains unchanged, meaning a shift to the right must be accompanied by a lower peak height.

A graph showing the relationship between the number of molecules and energy at two different temperatures, T1 (blue curve) and T2 (green curve). The blue curve represents the distribution of molecules at a lower temperature, while the green curve indicates an increased temperature, showing a shift in the energy distribution.

For decreasing temperature, the curve shifts to the left and the peak height increases.

The rate of a chemical reaction measures the change in concentration in reactants or products over time.

This is expressed as:

where:

concentration has units of
time has units of
rate has units of .

Increasing temperature causes an exponential increase in reaction rate due to the increase in both the frequency of collisions and the proportion of collisions which are successful.

A diagram illustrating the effect of temperature on particle energy and collision frequency. The left side shows particles with less energy, resulting in fewer and less successful collisions. The right side depicts particles with higher energy, leading to more frequent and successful collisions, with an arrow indicating the increase in temperature.

If the temperature of a chemical reaction is increased, the reacting particles gain more kinetic energy and therefore move faster.

This will increase the frequency of collisions and the energy of the collisions, leading to a greater proportion of collisions exceeding the activation energy.

The Maxwell-Boltzmann distribution shows how a small increase in temperature, from to , results in a larger proportion of molecules having sufficient energy to overcome the activation energy barrier and react.

Graph illustrating the relationship between temperature and the number of molecules capable of reacting. The blue curve represents the number of molecules at a lower temperature (T1), while the green curve shows an increased temperature (T2). The graph indicates that more molecules at T2 have sufficient activation energy (Ea) to react.

Since more molecules are able to collide with sufficient energy to, the frequency of successful collisions increases, leading to a faster reaction rate at higher temperatures.

If the concentration of solutions is increased there are more particles per unit volume.

This will increase the frequency of collisions, and therefore the frequency of effective collisions will also increase.

A diagram illustrating the concept of increasing concentration. On the left, a sparse arrangement of blue and red circles represents low concentration. An arrow labeled 'Increase concentration' points to the right, where a denser arrangement of the same circles indicates higher concentration.

In the diagram above, the concentrations of the reactant particles have increased. This would increase the frequency of effective collisions , and therefore increase the rate of reaction.

If the pressure of gaseous reactants is increased it has a similar effect to increasing the concentration.

Although the number of particles remains the same, the volume is decreased, and therefore the gaseous particles are more tightly packed. There are more gaseous particles per unit volume.

A diagram illustrating the effect of increased pressure on gas particles. The left side shows a scattered arrangement of blue and red circles representing gas molecules. An arrow labeled 'Increase pressure' points to the right side, which depicts a denser arrangement of the same molecules, indicating a change in their distribution due to pressure.

Increasing the number of particles per unit volume will increase the frequency of effective collisions, leading to an increase in the rate of reaction between the gaseous reactants.

Catalysts increase the rate of a chemical reaction but are not used up by the overall reaction.

Catalysts increase the rate of a chemical reaction by providing an alternative reaction pathway with a lower activation energy.

This can be shown on enthalpy profiles.

Although catalysts increase the rate of a chemical reaction they do not impact the total frequency of collisions. However, they do increase the proportion of successful collisions and therefore the frequency of successful collisions.

The use of a catalyst has no effect on the energy distribution or the shape of the Maxwell-Boltzmann distribution curve.

Catalysts lower activation energy so the position of the activation energy is shifted to the left.

A graph illustrating the effect of a catalyst on activation energy in a chemical reaction. The vertical axis represents the number of molecules, while the horizontal axis represents energy. The graph shows a peak indicating the activation energy without a catalyst, and a lower peak with a catalyst, highlighting that more molecules can reach the required activation energy and react.

This means that a greater proportion of molecules have an energy exceeding the activation energy and are able to react; a greater number of collisions per unit time are effective, and there is a faster rate of reaction.