Name: molecular speed curves and vapor pressure
Uploaded: 2023-04-30T12:30:48.000Z
Duration: 1 min 27 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.12

SC.912.P.12.10

Distribution of Molecular Speeds

Consider a gas in a container, where all gas molecules have kinetic energy, a function of the molecule&#39;s mass and its velocity.
The motion of the gas molecules is random in magnitude and direction; however, the average kinetic energy remains the same.
Recall from the kinetic molecular theory that the average translational kinetic energy per molecule depends only on the temperature.
Comparing the kinetic energy equations, rearranging the terms, and taking the square root on both sides relates the square root of the mean-square speed, also known as the root-mean-square or RMS speed.
With every collision, the velocity of individual gas particles change. Therefore, a collection of gas molecules has a slightly asymmetric velocity distribution curve known as the Maxwell-Boltzmann distribution. The peak of the curve corresponds to the most probable velocity, which is less than the RMS speed.
A plot of the velocity distribution for any gas at different temperatures displays an increase in the RMS speed and a broadening of the speed distribution at higher temperatures.

distribution of molecular speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a speed equal to or more than at va to escape from the surface of a liquid into the adjacent vapor, as shown in Figure 1.
<img alt="Maxwell-Boltzmann distribution graph comparing particle speeds at different temperatures T1, T2, T3." src="/files/ftp_upload/13672/13672_PT_figure.jpg" style="text-align: center; height: 300px;" data-altupdatedat="1761830439000" data-alt="Figure1" />
The number of similar molecules, represented by the area under the curve, increases swiftly with temperature. Thus, the rate at which molecules can escape is highly temperature-dependent. To counter this process, the molecules in the vapor phase collide inelastically with the surface and get trapped back in the liquid phase. The number of molecules that experience this situation per unit time is related to the vapor phase pressure. When these two processes proceed at the same rate, phase equilibrium is established between liquid and gas. So, if the molecular speed distributions are known for various temperatures, we can make a theoretical prediction of vapor pressure as a function of temperature. Rates of chemical reactions are often strongly temperature-dependent, and the reason for this is contained in the Maxwell-Boltzmann distribution.

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution ...

Education

JoVE Core

Physics

Unit 1

The Kinetic Theory of Gases

KEY TERMS AND CONCEPTS

molecular speed curves and vapor pressure

Molecular speed curves show how the speeds of gas particles are spread out at a given temperature. For a gas with many molecules, this spread is predictable even though each molecule moves randomly in direction and speed. The pattern is called the Maxwell-Boltzmann distribution.

Liquids have a similar speed distribution, but it is not exactly the same as in gases. This difference helps explain boiling and vapor pressure. A molecule must reach at least a certain speed, v a, to escape from the liquid surface into the nearby vapor.

As temperature rises, the area under the speed curve beyond v a increases quickly. That means more molecules can escape from the liquid, so the escape rate depends strongly on temperature. In the vapor, molecules can also collide inelastically with the surface and become trapped again in the liquid.

The number of vapor molecules that return to the liquid each unit time is related to vapor pressure. When the escape rate and the return rate are equal, liquid and gas are in phase equilibrium. Knowing the speed distribution at different temperatures lets scientists predict how vapor pressure changes with temperature.

This same idea also helps explain why many chemical reaction rates change with temperature. The Maxwell-Boltzmann distribution shows how the number of fast molecules grows as temperature increases. That is one reason reaction rates are often strongly temperature-dependent.

Molecular Speed Curves and Vapor Pressure

molecular-speed-curves-and-vapor-pressure

equation of state

Gas Behavior in the Equation of State

The equation of state describes how a gas’s pressure, volume, temperature, and number of moles are related. These macroscopic properties help define the condition, or state, of the matter in a thermodynamics system. The relationship between these quantities can be written as a simple mathematical expression. In some cases, it is too complex to express in a formula. Even then, the link between the quantities still exists. When an equation of state cannot be written mathematically, scientists...

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Liquid-Gas Changes on pV Curves

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molecular kinetic energy

Gas Pressure and Molecular Motion

Gas pressure comes from the motion of molecules in a container. The word gas came from a Flemish word meaning “chaos,” and J. B. van Helmont first used it to describe vapors. In a gas, molecules move in a continuous and random way. When a molecule hits a container wall, its velocity changes. The part of the velocity parallel to the wall stays the same. The part perpendicular to the wall reverses direction, but its size does not change. If the molecule’s velocity changes in the x-direction, its...

Molecular speed curves show how the speeds of gas particles are spread out at a given temperature. For a gas with many molecules, this spread is predictable even though each molecule moves randomly in direction and speed. The pattern is called the Maxwell-Boltzmann distribution. Liquids have a similar speed distribution, but it is not exactly the same as in gases. This difference helps explain boiling and vapor pressure. A molecule must reach at least a certain speed, v a, to escape from the...

maxwell-boltzmann distribution: problem solving

maxwell-boltzmann-distribution-problem-solving

Maxwell-Boltzmann Gas Speed Ratio

The Maxwell-Boltzmann distribution describes how molecular speeds are spread in a gas. Even though individual molecules move in random directions, the whole gas has a predictable speed pattern. This distribution is written as f(v), where v is molecular speed. The distribution function is used to find the expected number of particles with speeds between v1 and v2. Because N is dimensionless, f(v) has units of seconds per meter. The relationship can also be written in differential form for speed...

phase diagram

Water Phase Changes on a Pressure Chart

Water phase changes can be mapped on a pressure and temperature chart called a phase diagram. These plots show which phase a substance is in at different conditions. They also reveal where phase transitions happen, because the boundary lines mark the temperatures and pressures where two phases coexist. The water phase diagram shows how pressure affects boiling. As pressure rises, the boiling temperature increases gradually until it reaches 374 °C at 218 atm. A pressure cooker works this way.

mean free path and mean free time

Gas collisions: path length and time

Gas collisions in a cylinder help explain the mean free path and mean free time. Gas molecules move in random motion. They collide with each other and change speed and direction. The mean free path is the average path length between collisions. The mean free path depends on how many molecules are packed into a volume. It varies inversely with density. When more molecules are present, collisions happen more often, so the mean free path becomes shorter. It also depends on molecule size. Larger...

heat capacity: problem-solving

Heat Capacity of Gases by Degrees of Freedom

Heat capacity of gases depends on the gas type and the motion of its molecules. It is the amount of heat energy needed to raise the temperature of a unit mass of gas by one degree Celsius. This thermodynamic property is important in science and industry. To solve heat capacity problems, first identify the gas. A gas's molecular structure affects its heat capacity because the molecules have different degrees of freedom. These values can be found from tables or from empirical equations. Next,...

dalton's law of partial pressure

Gas Mixtures and Their Partial Pressures

Gas mixtures have a total pressure that comes from the partial pressures of each gas. A partial pressure is the pressure one gas would make if it filled the whole container by itself. This idea helps explain how gases behave when they are mixed together. When two or more gases share a container, their molecules move randomly and collide with one another. If the gases are at the same temperature, they reach thermal equilibrium. Their molecules then have the same average kinetic energy. In that...

escape velocities of gases

Why Lighter Gases Escape Earth First

Earth’s escape velocity is the speed an object needs to leave gravity behind. Near the top of the atmosphere, about 100 km above Earth, that speed is 11.1 km/s. Gas molecules can escape only if their speeds become high enough to reach that limit. The chance of escape depends on gas temperature and molecular speed. According to kinetic theory, the average kinetic energy of gas molecules is proportional to temperature. As temperature rises, the rms speed, or root-mean-square speed, also rises.

key terms and concepts

Learn how the Maxwell-Boltzmann distribution shapes molecular speeds, explains vapor pressure, and helps predict boiling and temperature effects in gases and liquids.

Molecular Speed Curves and Vapor Pressure | JoVE K12

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SC.912.P.12.5

A. Motion can be measured and described qualitatively and quantitatively. Net forces create a change in motion. When objects travel at speeds comparable to the speed of light, Einstein's special theory of relativity applies.

B. Momentum is conserved under well-defined conditions. A change in momentum occurs when a net force is applied to an object over a time interval.

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Molecular Speed Curves and Vapor Pressure

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