Safety matches work by combining two parts: the match head and the rough surface on the matchbox. The match head contains an oxidising agent, while the rough surface has red phosphorous. When you strike the match head against the rough surface, it creates enough energy to turn some of the red phosphorous into white phosphorous vapour. The white phosphorous vapour ignites in the air, causing heat that starts breaking down the potassium chlorate inside the match head, releasing oxygen that fuels the flame.

But how does the energy from striking the match head cause the reaction? Well, it's all thanks to the Maxwell-Boltzmann distribution graph. This handy graph shows how the energy is distributed among the particles of an ideal gas. It helps us understand how many particles meet or exceed the activation energy needed for a reaction to occur. In this article, we'll explore the Maxwell-Boltzmann distribution graph in chemistry. We'll explain how to read the graph, including the average and most probable energy points. We'll also look at how the graph changes under different conditions, like when you increase the temperature or add a catalyst. So, if you've ever wondered about the science behind safety matches or how energy affects chemical reactions, keep reading!

The Maxwell-Boltzmann distribution curve

The Maxwell-Boltzmann distribution helps us understand how energy is distributed among particles in a gas. It's a probability function that shows the energy distribution in an ideal gas, which is a hypothetical gas made up of non-interacting particles. Although ideal gases aren't common, we can still use the Maxwell-Boltzmann curve to understand the behaviour of any gas or solution.

In simpler terms, the graph shows how the energy of gas particles varies in a system. We use the word 'particles' because the distribution applies to all types of gaseous species, from atoms to ions to molecules. So, whether you're studying chemistry or just curious about how gases behave, the Maxwell-Boltzmann distribution is an important concept to understand. (Check out Chemical Kinetics for more on this subject.)

Axes

Here's a typical example of a Maxwell-Boltzmann distribution graph.

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The Maxwell-Boltzmann distribution graph has energy on the x-axis and the number of particles on the y-axis. Sometimes speed is used instead of energy on the x-axis, but they are interchangeable because particles with high energy move at high speeds. The y-axis can also show the probability of a gas particle having a certain energy, but we can generalize it to the number of particles with each energy value.

Particles don't have a fixed amount of energy, and their energy levels change as they move and collide with each other. The graph shows the different energies we can expect to see at any given moment.

The y-axis shows the number of particles with each energy value. The higher the value, the more particles have that energy. The total number of particles is equal to the area under the graph.

The graph tells us that no particles have negative or zero energy, and there is no upper limit to the energy a particle can have. A few particles have a very high amount of energy, while most have an intermediate amount of energy, shown by the large peak in the middle of the curve. Understanding the Maxwell-Boltzmann distribution is essential to understanding the behaviour of gases and solutions in chemistry.

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Points on the graph

Let's look at our graph again. This time, we're going to mark certain points on it.

The highest point on the peak of the graph represents the most probable energy of the particles, where the greatest number of particles have this particular energy. The line to the right of the peak shows the median energy value, where half of the particles have more energy and half have less energy than this value.

The activation energy is located on the right-hand side of the graph and represents the minimum energy required to start a chemical reaction. Particles to the right of this point have enough energy to potentially react, while particles to the left do not have enough energy.

There are factors that can affect the Maxwell-Boltzmann distribution, including:

1. Temperature: Increasing the temperature of a gas increases the average kinetic energy of its particles, which in turn shifts the graph to the right and causes a broader curve.
2. Mass: The mass of gas particles affects their speed and energy. Heavier particles have lower speeds and energies compared to lighter particles, resulting in a lower and narrower peak on the graph.
3. Concentration: Increasing the concentration of gas particles in a system causes the graph to shift upwards, showing higher numbers of particles at all energy levels.
4. Presence of a catalyst: A catalyst lowers the activation energy required for a chemical reaction to occur, which shifts the graph to the left and causes a higher number of particles to meet the activation energy requirements.

Temperature The presence of a catalyst

We can then apply this to rate of reaction.

Temperature

When a system is heated, the Maxwell-Boltzmann distribution graph shifts to the right, indicating an increase in the average kinetic energy of the particles. The peak on the graph also broadens, indicating a wider range of energies present in the system.

As the temperature increases, more particles have energies equal to or greater than the activation energy, resulting in a higher probability of a successful collision and increased reaction rate. This is shown by the area under the curve to the right of the activation energy increasing as the temperature is raised.

Overall, heating a system increases the energy of the particles, causing an upward shift in the entire graph and a higher number of particles to have energies equal to or greater than the activation energy. This leads to an increased rate of reaction, as shown by the area under the curve to the right of the activation energy increasing.

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When the temperature is decreased, the Maxwell-Boltzmann distribution graph shifts to the left, indicating a decrease in the average kinetic energy of the particles. The peak on the graph also narrows, indicating a smaller range of energies present in the system.

As the temperature decreases, fewer particles have energies equal to or greater than the activation energy, resulting in a lower probability of a successful collision and decreased reaction rate. This is shown by the area under the curve to the right of the activation energy decreasing as the temperature is lowered.

Overall, decreasing the temperature decreases the energy of the particles, causing a downward shift in the entire graph and a lower number of particles to have energies equal to or greater than the activation energy. This leads to a decreased rate of reaction, as shown by the area under the curve to the right of the activation energy decreasing.

Therefore, temperature is a critical factor affecting the Maxwell-Boltzmann distribution graph and the rate of reaction. A higher temperature increases the kinetic energy of the particles, allowing more particles to meet the activation energy, and thus increasing the reaction rate. In contrast, a lower temperature decreases the kinetic energy of the particles, leading to fewer particles having enough energy to react, and thus decreasing the reaction rate.

The presence of a catalyst

Adding a catalyst doesn't change the energy of any of the particles. Instead, it reduces the activation energy of the reaction. This means that a greater number of particles now meet or exceed the activation energy. This increases the rate of reaction.

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In contrast, concentration does not affect the Maxwell-Boltzmann distribution graph, as it only measures the number of particles in a given volume, without changing their energy distribution. However, increasing the concentration of a species in a system by reducing the volume or adding more particles can increase the rate of reaction. This is because the particles are closer together, and there are more collisions per second, leading to a faster rate of reaction.

Overall, the Maxwell-Boltzmann distribution is a useful tool to understand the energy distribution of particles in a system, and how changes in temperature and the addition of a catalyst can affect the rate of reaction. While concentration does not directly affect the distribution graph, it can impact the rate of reaction by changing the number of particles in a given volume and increasing the frequency of collisions.

Maxwell-Boltzmann Distribution

What is the Maxwell-Boltzmann distribution law?

The Maxwell-Boltzmann distribution is a probability function that shows the distribution of energy amongst the particles of an ideal gas. It predicts how many particles within a system have a particular energy.

What is the Maxwell-Boltzmann distribution?

The Maxwell-Boltzmann distribution is a probability function that shows the distribution of energy amongst the particles of an ideal gas. Put simply, a Maxwell-Boltzmann distribution graph shows how the energy of gas particles varies within a system. 

Does concentration affect a Maxwell-Boltzmann distribution?

Concentration doesn't affect a Maxwell-Boltzmann distribution. Increasing the concentration doesn't change the energy of the particles in a system, so the distribution stays the same.

What is a Maxwell-Boltzmann distribution of molecular speeds? 

The Maxwell-Boltzmann distribution is a probability function that shows the distribution of energy amongst the particles of an ideal gas. Put simply, a Maxwell-Boltzmann distribution graph shows how the energy of gas particles varies within a system. Kinetic energy is directly related to speed, so this is just a measure of the speeds of particles.

Does the presence of a catalyst affect the rate of reaction?

Yes, the presence of a catalyst increases the rate of reaction.

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