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Kinetics (Topics 9 and 16)›Kinetics I (Topic 9)

Kinetics I (Topic 9)

Collision theory, the Maxwell-Boltzmann distribution, and factors impacting the rate of reaction.
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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.

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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.

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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.

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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.

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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.

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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.

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Breaking a solid into smaller pieces increases the surface area, leading to a higher rate of reaction.

A diagram illustrating two different arrangements of molecules. On the left, a structured grid of blue and red circles represents one molecular arrangement, while on the right, a more scattered arrangement of blue and red circles depicts another molecular configuration.

If the surface area of a solid reactant is increased, more particles are exposed to react with other reactants.

This will increase the frequency of collisions and therefore the frequency of effective collisions

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To calculate the rate of reaction at a specific point of the chemical reaction using a concentration–time graph.

  1. Draw a tangent to the line of best fit at the specified concentration or time. Make sure you draw the tangent as large as possible to increase accuracy.
  2. Use your tangent to construct a right-angled triangle.
  3. Determine the .
  4. Determine the .
  5. To calculate the gradient, which is equal to the rate of the chemical reaction use: .

If the initial rate of reaction is required, the tangent should originate at .

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The graph below illustrates how to draw a tangent and extract the relevant data from a concentration–time graph in order to calculate reaction rate.

A graph showing the relationship between concentration (in mol dm^-3 s^-1) and time (in seconds). The blue curve represents concentration over time, with a tangent line drawn at the point t1. The graph includes annotations for changes in concentration (Δ) and time (Δ), as well as a constant k.

The x-axis for time is often in minutes. When calculating the it is important to convert the time to seconds.

The gradient will commonly have the units of .

This method can also be used if there is a change of mass, change in volume etc. If this is the case, the units for the gradient will be different.

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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.
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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.

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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.

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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.

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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.

Graph illustrating the energy profile of a chemical reaction, showing the energy (in kJ mol^-1) on the vertical axis and the extent of reaction on the horizontal axis. It compares an uncatalyzed reaction with a higher activation energy (Ea) to a catalyzed reaction with a lower activation energy (Ea(new)). The graph indicates the reactants on the left and the products on the right, highlighting the difference in energy levels between the two types of reactions.

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.

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There are two different types of catalysts.

Homogeneous catalysts are catalysts which are in the same phase as the reactants in the chemical reaction. For example gaseous chlorine free radicals in the decomposition of the gaseous ozone layer.

Heterogeneous catalysts are catalysts which are in a different phase to the reactants in the chemical reaction. For example the use of solid iron in the Haber process where the reactants – nitrogen and hydrogen – are in the gaseous phase.

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Catalysts provide an alternative reaction pathway with a lower activation energy. This allows chemical reactions in industry to be carried out at lower temperatures and pressures.

  • Lower temperature: less energy required.
  • Lower pressure: reduces the amount of electricity required to artificially increase the pressure.

Reductions in energy consumption are directly linked to a reduction of cost and lower carbon emissions.

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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.

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