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Boltzmann distribution

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Intros
Lessons
  1. The Boltzmann kinetic energy distribution
  2. Introduction to the Boltzmann distribution.
  3. Changes in the Boltzmann distribution.
  4. Explaining curve changes in the Boltzmann distribution.
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Examples
Lessons
  1. Recall the shape and features of the Boltzmann distribution.
    1. Sketch the Boltzmann distribution for a reaction proceeding slowly at room temperature. Include the axis titles and the labels Ea and average energy of molecules.
    2. The reaction vessel has its temperature raised by 10°C. On the same axes, sketch another Boltzmann curve showing the new distribution of the kinetic energy possessed by the reactant molecules.
    3. A catalyst is added to change the rate of reaction. Sketch the change this catalyst has on the reaction onto your Boltzmann distribution and explain the effect on the rate of reaction.
Topic Notes
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Introduction to the Boltzmann Distribution

Welcome to our exploration of the Boltzmann distribution, a fundamental concept in chemistry that's as fascinating as it is important! This distribution describes how molecules in a system are distributed across different energy levels, particularly focusing on their kinetic energy. It's named after Ludwig Boltzmann, a brilliant physicist who laid the groundwork for statistical mechanics. The Boltzmann distribution is crucial for understanding how temperature affects molecular behavior. As we increase the temperature, we see a shift in the distribution, with more molecules occupying higher energy states. This concept is key to explaining various chemical and physical phenomena. To kick off our learning journey, I've prepared an introductory video that visually demonstrates these principles. This video will help you grasp the core ideas behind the Boltzmann distribution, making our subsequent discussions much more intuitive. So, let's dive in and unravel the mysteries of molecular energy distributions together!

Understanding the Boltzmann Curve

The Boltzmann curve, also known as the Maxwell-Boltzmann distribution, is a fundamental concept in statistical mechanics and thermodynamics. This curve provides a visual representation of the distribution of kinetic energy among molecules in a gas at a given temperature. Understanding the Boltzmann curve is crucial for grasping various chemical and physical phenomena, including reaction rates and gas behavior.

Let's break down the basic structure of the Boltzmann curve. The x-axis represents the kinetic energy of the molecules, typically measured in joules (J) or kilojoules per mole (kJ/mol). As we move from left to right along this axis, we're looking at molecules with increasing amounts of kinetic energy. The y-axis, on the other hand, represents the number or fraction of molecules possessing a particular energy level. This can be thought of as the probability of finding a molecule with a specific kinetic energy.

The shape of the Boltzmann curve is distinctive and informative. It starts at zero, rises quickly to a peak, and then gradually tails off towards infinity. This shape is not symmetrical, which is a key characteristic of the distribution. The peak of the curve corresponds to the most probable energy the energy level at which you're most likely to find molecules in the system. This point is not at the average energy, but slightly below it, due to the curve's asymmetry.

To visualize this, imagine a classroom of students jumping. The height each student reaches represents their kinetic energy. Most students will jump to an average height (the peak of the curve), while fewer will reach very low or very high heights (the tails of the distribution). The Boltzmann curve would show this distribution of jump heights across the class.

The asymmetry of the curve is a result of two competing factors. On one hand, as energy increases, there are more ways for molecules to possess that energy (considering translational, rotational, and vibrational modes). This tends to push the curve upward at higher energies. On the other hand, the probability of a molecule having very high energy decreases exponentially, which pulls the curve down at higher energies. The balance between these factors creates the characteristic shape.

A crucial aspect of the Boltzmann curve is the area under the curve. This area represents the total number of molecules in the system. In other words, if you were to add up the number of molecules at each energy level (integrating the curve), you'd get the total number of molecules. This concept is vital for calculations involving reaction rates and equilibrium constants.

One of the most practical applications of the Boltzmann curve is in understanding chemical reactions through the concept of activation energy. Activation energy is the minimum energy required for a chemical reaction to occur. On a Boltzmann curve, this can be represented by a vertical line. The area under the curve to the right of this line represents the fraction of molecules that have enough energy to overcome the activation barrier and potentially react.

This visualization helps explain why increasing temperature speeds up reactions. As temperature rises, the entire curve shifts to the right and broadens, meaning more molecules have higher energies. Consequently, a larger area of the curve falls beyond the activation energy line, indicating more molecules can participate in the reaction.

To make this concept more tangible, think of activation energy as a hill that molecules need to climb to react. The Boltzmann curve shows how many molecules have enough "oomph" to get over the hill. Heating the system is like giving all the molecules a boost, helping more of them clear the hill.

The Boltzmann curve is not just a theoretical construct; it has practical implications in various fields. In atmospheric science, it helps explain the escape of light gases from planetary atmospheres. In materials science, it aids in understanding diffusion processes. Even in biology, the principles behind the Boltzmann distribution play a role in explaining enzyme kinetics and membrane transport.

In conclusion, the Boltzmann curve is a powerful tool for visualizing and understanding the distribution of kinetic energy among molecules. Its asymmetrical shape, the significance of the area under the curve, and its application in concepts like activation energy make it an essential concept in chemistry and physics. By providing a clear picture of molecular energy distributions, the Boltzmann curve helps bridge the gap between the microscopic world of molecules and the macrosc

Effects of Temperature on the Boltzmann Distribution

The Boltzmann distribution is a fundamental concept in statistical mechanics that describes the distribution of energy among particles in a system at thermal equilibrium. Temperature plays a crucial role in shaping this distribution, and understanding how temperature changes affect the Boltzmann distribution is essential for comprehending various physical and chemical processes. This article explores the impact of temperature on the Boltzmann distribution, focusing on curve shifts, average kinetic energy changes, and their implications for reaction rates.

When temperature increases, the Boltzmann distribution curve undergoes a significant transformation. The curve becomes wider and flatter, stretching out towards higher energy levels. This shift can be visualized as the curve "spreading its wings," with the peak of the distribution moving to the right on the energy axis. Conversely, when temperature decreases, the curve becomes narrower and taller, with the peak shifting towards lower energy levels. This change can be likened to the curve "huddling together" at lower energies.

The impact of these temperature-induced changes on the average kinetic energy of molecules is substantial. As temperature rises, the average kinetic energy of the particles in the system increases. This is reflected in the rightward shift of the distribution curve's peak. In practical terms, this means that at higher temperatures, molecules move faster and collide more frequently. For instance, in a pot of boiling water, the water molecules have higher average kinetic energy compared to room temperature water, resulting in more vigorous molecular motion.

One of the most significant consequences of temperature changes on the Boltzmann distribution is its effect on the proportion of molecules with energy above the activation energy. The activation energy is the minimum energy required for a chemical reaction to occur. As temperature increases and the distribution curve shifts to the right, a larger fraction of molecules possess energy exceeding the activation energy. This phenomenon has profound implications for reaction rates.

In chemical reactions, the rate at which reactions occur is directly related to the number of molecules with sufficient energy to overcome the activation barrier. As temperature rises and more molecules surpass this energy threshold, reaction rates increase. This principle explains why many chemical reactions proceed faster at higher temperatures. For example, food spoils more quickly when left out in warm conditions because the higher temperature accelerates the chemical reactions responsible for decomposition.

The visual description of the Boltzmann distribution curve changes can be further elaborated. At higher temperatures, imagine the curve as a stretched-out bell shape, with a lower peak but extended tails reaching into higher energy regions. This stretched shape represents a broader range of energies among the particles. In contrast, at lower temperatures, picture the curve as a tall, narrow bell, with a higher peak concentrated around lower energies. This compressed shape indicates that most particles have similar, lower energies.

Real-world examples abound that demonstrate the effects of temperature on molecular energy distributions. In cooking, higher temperatures not only speed up chemical reactions but also enable different types of reactions to occur. For instance, the Maillard reaction, responsible for the browning of foods, requires higher temperatures to proceed efficiently. This is why foods brown more quickly in a hot oven compared to a cooler one.

In industrial processes, temperature control is often crucial for optimizing reaction rates and product yields. Catalytic converters in automobiles, for example, operate most effectively within a specific temperature range. If the temperature is too low, the reactions that convert harmful emissions into less harmful substances occur too slowly. Conversely, if the temperature is too high, the catalyst may become damaged or less efficient.

The relationship between temperature and the Boltzmann distribution also has implications for energy storage and transfer. In solar thermal energy systems, higher temperatures lead to more efficient energy collection and storage. The increased average kinetic energy of particles at higher temperatures allows for more effective heat transfer and storage in thermal fluids or materials.

Understanding the temperature effects on the Boltzmann distribution is not only important for chemistry and physics but also for biology. Enzyme activity, which is crucial for life processes, is highly temperature-dependent. The optimal temperature for enzyme function corresponds to a Boltzmann distribution that provides enough high-energy molecules for reactions to occur efficiently without causing protein denaturation.

In conclusion, temperature changes significantly affect the Boltzmann distribution, causing shifts in the curve shape and position. These changes directly impact the average kinetic energy of molecules and the proportion of molecules with energy above the activation energy. The visual

Catalysts and the Boltzmann Distribution

Catalysts play a crucial role in chemical reactions, and their effects can be understood through the lens of the Boltzmann distribution. To comprehend this relationship, it's essential to first grasp how catalysts function and how they interact with the energy landscape of a reaction. Catalysts are substances that increase the rate of a chemical reaction without being consumed in the process. They achieve this by providing an alternative reaction pathway with a lower activation energy in reactions, which is the energy barrier that reactants must overcome to form products.

The Boltzmann distribution describes the distribution of molecular energies in a system at thermal equilibrium. When we consider how catalysts affect this distribution, it's important to note that catalysts do not change the overall energy of the molecules involved in the reaction. Instead, they lower the activation energy in reactions required for the reaction to proceed. This distinction is crucial for understanding the catalyst's impact on the Boltzmann curve and, consequently, on the reaction rate.

On a Boltzmann distribution curve, the x-axis represents the energy of molecules, while the y-axis shows the number of molecules with that energy. The activation energy is typically represented as a vertical line on this curve. Without a catalyst, only molecules with energies exceeding this activation energy line can participate in the reaction. When a catalyst is introduced, it effectively lowers this activation energy line on the graph. As a result, a larger portion of the molecular population now has sufficient energy to overcome the reduced energy barrier and participate in the reaction.

This shift in the activation energy threshold has a significant impact on the reaction rate. With more molecules able to overcome the lower energy barrier, the frequency of successful collisions leading to product formation increases dramatically. Consequently, the overall reaction rate accelerates, often by orders of magnitude, without altering the thermodynamics of the reaction. It's important to emphasize that while catalysts increase the rate at which equilibrium is reached, they do not affect the position of the equilibrium itself.

To further illustrate the effect of catalysts, we can compare their impact to that of temperature changes on the Boltzmann distribution. Increasing temperature shifts the entire Boltzmann curve to higher energies, resulting in more molecules with sufficient energy to overcome the activation barrier. This also leads to an increase in reaction rate. However, the mechanism is fundamentally different from that of catalysts. Temperature changes affect the energy distribution of all molecules, while catalysts specifically target the activation energy barrier.

In practical applications, the use of catalysts often provides significant advantages over simply increasing temperature to speed up reactions. Catalysts allow reactions to proceed more quickly at lower temperatures, which can be beneficial for energy efficiency, reducing unwanted side reactions, and preserving heat-sensitive compounds. This is particularly important in industrial processes where energy costs and product quality are critical factors.

Understanding the relationship between catalysts and the Boltzmann distribution is crucial for chemists and chemical engineers. It provides insights into reaction kinetics and helps in the design of more efficient chemical processes. By manipulating activation energies through catalysis, researchers can develop new pathways for challenging reactions, improve yields, and create more sustainable chemical transformations. The interplay between catalysts, activation energy, and the Boltzmann curve continues to be a fundamental concept in the study of reaction rates and the development of innovative chemical technologies.

Interpreting Changes in the Boltzmann Distribution

Understanding how to interpret changes in the Boltzmann distribution is crucial for analyzing reaction rates and kinetic energy distributions in chemical systems. This guide will walk you through the process of interpreting Boltzmann curves, focusing on how shifts in the curve and changes in the area under the curve past the activation energy affect reaction rates.

Step 1: Familiarize Yourself with the Boltzmann Distribution

The Boltzmann distribution represents the distribution of kinetic energies among particles in a system. It's typically shown as a curve with kinetic energy on the x-axis and the number of particles on the y-axis. The activation energy is often marked on this curve.

Step 2: Analyze Shifts in the Curve

When interpreting Boltzmann curves, pay attention to shifts in the overall shape:

  • A shift to the right indicates an increase in average kinetic energy, often due to higher temperature.
  • A shift to the left suggests a decrease in average kinetic energy, typically from lower temperature.

Step 3: Examine Changes in the Peak

The peak of the Boltzmann distribution represents the most probable kinetic energy:

  • A higher, narrower peak indicates a more uniform distribution of energies.
  • A lower, broader peak suggests a wider range of energies among particles.

Step 4: Assess the Area Under the Curve Past Activation Energy

The area under the curve to the right of the activation energy is crucial for reaction rates:

  • A larger area indicates more particles have sufficient energy to react.
  • A smaller area suggests fewer particles can overcome the activation energy barrier.

Step 5: Relate Changes to Reaction Rates

Connect your observations to reaction rates:

  • An increase in the area past the activation energy correlates with faster reaction rates.
  • A decrease in this area suggests slower reaction rates.

Step 6: Draw and Explain Changes

To illustrate changes in the Boltzmann distribution:

  1. Draw two overlapping Boltzmann curves on the same axes.
  2. Label one curve as the initial state and the other as the changed state.
  3. Clearly mark the activation energy on both curves.
  4. Shade the areas under both curves past the activation energy.
  5. Use arrows to indicate shifts in the curve's position or changes in its shape.

Step 7: Provide a Detailed Explanation

When explaining your drawing:

  • Describe the overall shift of the curve (left or right).
  • Discuss changes in the peak's height and width.
  • Compare the shaded areas past the activation energy.
  • Explain how these changes affect the number of particles with sufficient energy to react.
  • Conclude with the impact on reaction rates.

Example Interpretation

Let's consider a scenario where temperature increases:

  1. The Boltzmann curve shifts to the right, indicating higher average kinetic energy.
  2. The peak becomes slightly lower and broader, showing a wider distribution of energies.
  3. The area under the curve past the activation energy increases significantly.
  4. This larger area means more particles have sufficient energy to overcome the activation barrier.
  5. Consequently, the reaction rate increases due to more frequent successful collisions.

Applications of the Boltzmann Distribution in Chemistry

The Boltzmann distribution is a fundamental concept in statistical mechanics that finds numerous practical applications in chemistry. This powerful tool helps scientists understand and predict the behavior of particles in chemical systems, making it invaluable for various chemical processes and industrial applications. In this section, we'll explore how the Boltzmann distribution is applied to predict reaction rates, understand temperature effects on chemical processes, and optimize reaction conditions in real-world scenarios.

One of the most significant applications of the Boltzmann distribution in chemistry is in predicting reaction rates. Chemical reactions occur when molecules with sufficient energy collide, and the Boltzmann distribution helps determine the fraction of molecules that possess this required energy. By applying this principle, chemists can calculate the rate constants for chemical reactions, which is crucial for understanding how quickly reactions proceed under different conditions. This knowledge is particularly valuable in industrial settings where precise control over reaction rates is essential for efficient production processes.

The Boltzmann distribution also plays a vital role in understanding the effects of temperature on chemical processes. As temperature increases, the distribution of molecular energies shifts, resulting in a larger fraction of molecules with higher energies. This relationship explains why many chemical reactions proceed faster at higher temperatures. In industrial applications, such as in the production of pharmaceuticals or petrochemicals, understanding these temperature effects is crucial for optimizing reaction conditions and improving yield. For instance, in the Haber process for ammonia production, the Boltzmann distribution helps engineers determine the optimal temperature range to balance reaction rate and equilibrium yield.

Optimizing reaction conditions is another area where the Boltzmann distribution proves invaluable. By analyzing the energy distribution of molecules at different temperatures and pressures, chemists can identify the ideal conditions for maximizing product yield while minimizing unwanted side reactions. This optimization is particularly important in the fine chemicals industry, where high purity and efficiency are paramount. For example, in the synthesis of complex organic compounds, such as pharmaceuticals, applying the Boltzmann distribution principles helps researchers design reaction protocols that maximize the desired product while minimizing the formation of isomers or byproducts.

In laboratory settings, the Boltzmann distribution is frequently used to interpret spectroscopic data. Techniques such as nuclear magnetic resonance (NMR) spectroscopy and infrared (IR) spectroscopy rely on the population distribution of different energy states, which is governed by the Boltzmann distribution. By analyzing these distributions, scientists can deduce structural information about molecules and study their behavior under various conditions. This application is crucial for both fundamental research and quality control in industrial processes.

The Boltzmann distribution also finds applications in understanding and designing catalytic processes. Catalysts work by lowering the activation energy of reactions, effectively altering the energy landscape described by the Boltzmann distribution. By applying this concept, researchers can develop more efficient catalysts for industrial processes, such as in the production of fuels, plastics, and other chemicals. This application has significant implications for green chemistry initiatives, as more efficient catalysts can lead to reduced energy consumption and waste production in chemical manufacturing.

In conclusion, the Boltzmann distribution is a powerful tool with wide-ranging applications in chemistry. From predicting reaction rates and understanding temperature effects to optimizing reaction conditions and interpreting spectroscopic data, this fundamental concept underpins many aspects of chemical research and industrial processes. By leveraging the insights provided by the Boltzmann distribution, chemists and chemical engineers can develop more efficient, sustainable, and cost-effective processes, driving innovation in fields ranging from pharmaceuticals to materials science and beyond.

Conclusion

The Boltzmann distribution is a fundamental concept in understanding molecular energy distributions and their impact on chemical processes. This powerful statistical tool provides insights into how kinetic energy distribution is distributed among particles in a system, directly influencing reaction kinetics and thermodynamic properties. The introduction video serves as a crucial foundation for grasping these complex ideas, offering a visual representation of the distribution's principles. By comprehending the Boltzmann distribution, chemists can predict and explain various phenomena, from gas behavior to reaction kinetics. Its applications extend across multiple fields, including atmospheric chemistry, materials science, and biochemistry. As you delve deeper into this topic, consider how the Boltzmann distribution might apply to your specific area of study or research. We encourage you to explore further resources and apply this knowledge to practical scenarios, enhancing your understanding of chemical processes at the molecular level. Remember, mastering the Boltzmann distribution is key to unlocking deeper insights into the behavior of matter and energy in chemical systems.

Boltzmann Distribution: Shape and Features

Recall the shape and features of the Boltzmann distribution. Sketch the Boltzmann distribution for a reaction proceeding slowly at room temperature. Include the axis titles and the labels Ea and average energy of molecules.

Step 1: Understanding the Axes

The first step in sketching the Boltzmann distribution is to understand the axes. The x-axis represents the kinetic energy of the molecules, while the y-axis represents the number of molecules. This setup helps in visualizing how the kinetic energy is distributed among the molecules in a given system.

Step 2: Drawing the Curve

Next, we need to draw the Boltzmann distribution curve. The curve does not start at the origin (0,0) because molecules cannot have zero kinetic energy. Instead, it starts just after the y-axis. The curve rises to a peak and then gradually falls off, never touching the x-axis again. This behavior is known as an asymptote, where the curve approaches the x-axis but never actually reaches it.

Step 3: Labeling the Activation Energy (Ea)

The activation energy (Ea) is a crucial part of the Boltzmann distribution. It represents the minimum energy required for a reaction to occur. On the graph, Ea is usually marked on the far right side, indicating that only a small proportion of molecules have enough energy to overcome this barrier and react.

Step 4: Identifying the Average Energy of Molecules

The average energy of the molecules is another important feature to label. This is found at the highest point of the curve, which corresponds to the most frequently occurring energy level among the molecules. The x-value at this peak represents the average kinetic energy of the molecules in the system.

Step 5: Finalizing the Sketch

With the axes labeled and the key features marked, the final step is to ensure the sketch accurately represents the Boltzmann distribution. The curve should start just after the y-axis, rise to a peak, and then gradually fall off, never touching the x-axis again. The activation energy (Ea) should be marked on the far right, and the average energy of the molecules should be indicated at the peak of the curve.

Conclusion

By following these steps, you can accurately sketch the Boltzmann distribution for a reaction proceeding slowly at room temperature. Remember to include the axis titles and the labels for Ea and the average energy of molecules to provide a complete and informative graph.

FAQs

  1. What is the Boltzmann distribution?

    The Boltzmann distribution is a fundamental concept in statistical mechanics that describes how particles in a system are distributed across different energy states at thermal equilibrium. It relates the probability of a particle being in a particular energy state to the temperature of the system and the energy of that state.

  2. How does temperature affect the Boltzmann distribution?

    As temperature increases, the Boltzmann distribution curve becomes wider and flatter, with its peak shifting towards higher energy levels. This means that at higher temperatures, more particles have higher energies, leading to faster reaction rates and increased molecular motion.

  3. What is the relationship between the Boltzmann distribution and reaction rates?

    The Boltzmann distribution helps predict reaction rates by determining the fraction of molecules with enough energy to overcome the activation energy barrier. As temperature increases, more molecules have sufficient energy to react, leading to faster reaction rates.

  4. How do catalysts affect the Boltzmann distribution?

    Catalysts don't directly change the Boltzmann distribution, but they lower the activation energy for a reaction. This effectively increases the number of molecules with sufficient energy to react, even though the overall energy distribution remains the same.

  5. What are some practical applications of the Boltzmann distribution in chemistry?

    The Boltzmann distribution has numerous applications in chemistry, including predicting reaction rates, optimizing industrial processes, interpreting spectroscopic data, and understanding gas behavior. It's also crucial in fields like atmospheric chemistry, materials science, and biochemistry for explaining various molecular phenomena.

Prerequisite Topics

Understanding the Boltzmann distribution is crucial in various fields of science, particularly in statistical mechanics and thermodynamics. To fully grasp this concept, it's essential to have a solid foundation in several prerequisite topics. These topics provide the necessary background knowledge and context for comprehending the intricacies of the Boltzmann distribution.

One of the fundamental concepts related to the Boltzmann distribution is rotational kinetic energy and angular momentum. This topic is vital because the Boltzmann distribution describes the probability distribution of particles in a system based on their energy states. Understanding how energy is distributed in rotational systems provides a crucial foundation for grasping the broader concept of energy distribution in statistical mechanics.

Another important prerequisite is the knowledge of atomic orbitals and energy levels. The Boltzmann distribution is often applied to describe the population of different energy levels in atoms and molecules. Familiarity with atomic structure and energy levels is essential for understanding how the Boltzmann distribution relates to molecular energy states and spectroscopic observations.

The concept of activation energy is also closely tied to the Boltzmann distribution. In chemical reactions, the Boltzmann distribution helps explain the proportion of molecules that have sufficient energy to overcome the activation barrier. This connection is crucial for understanding reaction rates and the temperature dependence of chemical processes.

Speaking of reaction rates, knowledge of the factors affecting rate of reaction is another prerequisite that ties directly into the Boltzmann distribution. Temperature, one of the key factors influencing reaction rates, is intimately connected to the Boltzmann distribution through its role in determining the energy distribution of particles in a system.

Lastly, understanding reaction mechanisms is essential when applying the Boltzmann distribution to chemical kinetics. The distribution helps explain why certain reaction pathways are favored over others and how temperature affects the likelihood of different mechanistic steps occurring.

By mastering these prerequisite topics, students can develop a comprehensive understanding of the Boltzmann distribution and its wide-ranging applications in physics and chemistry. This foundational knowledge enables a deeper appreciation of how energy is distributed among particles in a system and how this distribution influences various physical and chemical phenomena. As you delve into the study of the Boltzmann distribution, remember that these prerequisite concepts serve as building blocks, allowing you to construct a robust understanding of this fundamental principle in statistical mechanics.

In this lesson, we will learn:

  • How to draw the Boltzmann kinetic energy distribution and understand its meaning.
  • How a change in reaction conditions affects the Boltzmann distribution curves.
  • How to explain changes in the Boltzmann distribution in terms of molecules and kinetic energy.
Notes:

  • The Boltzmann distribution (AKA kinetic energy distribution) is a distribution that describes the amount of kinetic energy that a proportion of gas particles have in a given sample. See below:
  • As with all graphs, read the axes carefully and think about what they mean when put together:
    • It is not possible for an atom or molecule to have absolute zero kinetic energy, so the Boltzmann curve never touches the y-axis, starting just to the right of it.
    • There is no limit to the amount of energy an atom or molecule can have, so the curve once started never touches the x axis a second time.
    • The y-axis is measuring number, or proportion of molecules. Therefore, the x-value marked with the highest y-coordinate the distribution makes is the 'Average energy of molecules' because it is the amount of energy 'most of the molecules' have.
    • The activation energy, Ea, is the energy required by a molecule to initiate reaction. Molecules lower energy than this will not react, while the portion of molecules with higher (to the right) energy than this will have energy to react.
    • Because the y axis is measuring number of molecules, you can think of the area under the curve as all of the molecules in the reaction – the greater the area under the curve at a certain point, the more molecules there are!
    • No values are ever given to the axes of the distribution. The distribution just tells us the proportion of molecules and how much energy they have!
  • The Boltzmann curve can be used to show changes in the conditions of the reaction in a number of ways:
    • An increase in temperature will increase the average kinetic energy of the molecules in the reaction – remember that for many reactions, a 10°C rise in temperature will double the reaction rate. This will change the graph in a few ways:
      • The 'average energy of molecules' will shift to the right.
      • The area of the curve beyond the 'activation energy' marker, because now that the average molecule has more energy, more molecules will now also have the required activation energy to react.
      • The area under the curve shouldn't change. The curve will look 'shorter' and 'wider' due to the shift to the right. See below:
        temperature difference change graph
    • Adding a catalyst to a reaction mixture will have an effect on the Boltzmann distribution too:
      • A catalyst reduces the activation energy of a reaction, it does not affect the actual kinetic energy of the molecules that are reacting. So a catalyst will shift the activation energy label to the left of the distribution. This will show a greater area of the curve on the right – more molecules having the required energy to react! See below:
        catalyst change graph