The kinetic molecular theory of gases | AP Chemistry | Khan Academy

Summary

This video explores the kinetic molecular theory, which simplifies the understanding of gases by considering them as small particles in constant motion. It explains how macroscopic measurements like pressure, volume, and temperature relate to the microscopic behavior of gas molecules. The theory posits that gas pressure arises from particles bouncing off container walls, and temperature correlates with their average kinetic energy. Despite being an idealized model, it offers valuable insights into gas behavior.

Takeaways

• 🔬 The kinetic molecular theory provides a model to understand the behavior of gases at a molecular level.
• 📏 Macroscopic properties of gases such as pressure, volume, and temperature can be measured without direct observation of molecules.
• 🔍 Pressure in a gas is a result of the force exerted by gas particles colliding with the container walls.
• 🌡️ Temperature is directly related to the average kinetic energy of the gas particles, with higher temperatures corresponding to greater kinetic energy.
• 🧪 The concept of a mole predates the understanding of the exact number of particles it contains, representing an amount of substance.
• 📐 The ideal gas equation (PV=nRT) connects macroscopic measurements and provides a framework for understanding gas behavior.
• 🔄 Gas particles are assumed to be in constant random motion, which is a fundamental assumption of the kinetic molecular theory.
• 💨 The volume occupied by gas particles is considered negligible compared to the container volume, simplifying the theory for ideal gases.
• ⚖️ Elastic collisions between gas particles are assumed, meaning that kinetic energy is conserved during collisions.
• 🔗 The number of moles (N) is directly proportional to the number of particles, with each mole containing Avogadro's number of particles.
• 📉 Real-world gases may deviate from ideal behavior, especially when particle volume and intermolecular forces become significant.

Q & A

What is the kinetic molecular theory?

The kinetic molecular theory is a model that explains the behavior of gases by considering them as composed of small particles in constant random motion, which exert pressure on their container walls due to collisions.

How does the kinetic molecular theory help in understanding gases?

It provides an approximation of what's happening at the molecular level by considering the gas as small particles with negligible volume compared to the container, moving randomly and causing pressure through collisions with the container walls.

What are the macroscopic properties of a gas that can be measured?

Macroscopic properties of a gas that can be measured include pressure, volume, temperature, and the amount of substance (number of moles).

How is pressure defined in the context of gases?

Pressure is defined as force per unit area, and it can be measured using various devices. In the context of gases, it's the force exerted by gas particles colliding with the walls of their container.

What is the ideal gas equation?

The ideal gas equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.

How does the kinetic molecular theory relate to the ideal gas equation?

The kinetic molecular theory provides a microscopic explanation for the macroscopic relationships in the ideal gas equation, linking the behavior of gas particles to measurable properties like pressure, volume, and temperature.

What is the significance of temperature in the kinetic molecular theory?

Temperature, measured in Kelvin, is directly proportional to the average kinetic energy of the gas particles. Higher temperatures correspond to higher average kinetic energies.

What are the assumptions of the kinetic molecular theory?

The assumptions include: gas particles are in constant random motion, their volume is negligible compared to the container volume, particles exert no attractive or repulsive forces on each other, collisions are elastic, and the average kinetic energy is proportional to the Kelvin temperature.

Why is the volume of gas particles considered negligible in the kinetic molecular theory?

The volume of gas particles is considered negligible because the space between particles is much larger than the particles themselves, which allows for the simplification that the container volume is the primary factor in determining the gas volume.

How does the kinetic molecular theory explain the concept of moles in relation to gases?

The theory implies that the number of moles (N) of a gas is directly related to the number of particles, with each mole containing Avogadro's number of particles, thus connecting the macroscopic concept of moles to the microscopic reality of gas particles.

What is the role of elastic collisions in the kinetic molecular theory?

Elastic collisions between gas particles and the container walls are crucial as they preserve kinetic energy, ensuring that the pressure exerted by the gas is consistent with the kinetic energy of the particles.

Outlines

00:00

🌌 Introduction to Kinetic Molecular Theory

The video introduces the kinetic molecular theory, which provides a framework to understand the behavior of gases at a molecular level. It explains that macroscopic properties like pressure, volume, and temperature can be measured without direct observation of molecules. The ideal gas equation is mentioned as a macroscopic tool that connects these properties, with pressure times volume equating to the number of moles of gas, adjusted by the ideal gas constant and temperature in Kelvin. The theory posits that gases are composed of small particles that occupy a negligible volume compared to the container, and the pressure is a result of these particles' elastic collisions with the container walls.

05:03

🔍 Axioms of Kinetic Molecular Theory

This section delves into the fundamental assumptions of kinetic molecular theory, which are essential for understanding gas behavior. The theory assumes that gas particles are in constant random motion, their collective volume is insignificant compared to the container, and they do not exert attractive or repulsive forces on each other. It also assumes that collisions between particles are elastic, preserving both kinetic energy and momentum. A key point is that the average kinetic energy of the particles is directly proportional to the Kelvin temperature, linking macroscopic temperature measurements to the microscopic motion of gas particles.

Keywords

💡Kinetic Molecular Theory

Kinetic Molecular Theory is a model that explains the behavior of gases by considering them as composed of small particles in constant random motion. This theory is fundamental to the video's theme as it provides a framework for understanding the macroscopic properties of gases, such as pressure, volume, and temperature, in terms of the microscopic behavior of gas molecules. The video script discusses how this theory helps build intuition about what is happening at the molecular level within a gas.

💡Macro Level

The term 'macro level' refers to observations and measurements made at a scale that is much larger than the scale of individual atoms or molecules. In the context of the video, macroscopic properties like pressure, volume, and temperature of a gas can be measured without directly observing the gas molecules. The script explains how these macroscopic measurements are connected to the microscopic behavior of gas molecules through the kinetic molecular theory.

💡Pressure

Pressure is defined as the force exerted per unit area. In the video, pressure is a key macroscopic property of a gas that can be measured using various devices. The script explains that pressure in a gas arises from the collisions of gas molecules with the walls of their container, which is a direct application of the kinetic molecular theory where the force due to these collisions is measured as pressure.

💡Volume

Volume, in the context of the video, refers to the amount of space occupied by a container that holds the gas. The script mentions that volume is a measurable macroscopic property, and it is straightforward to calculate the volume of different shapes, such as rectangular prisms or spheres. The volume is significant in the kinetic molecular theory as it provides the space within which gas molecules move.

💡Temperature

Temperature is a measure of the average kinetic energy of the particles in a substance. The video script explains that temperature can be measured using thermometers and is expressed in Kelvin, an absolute temperature scale. According to the kinetic molecular theory, temperature is directly related to the average kinetic energy of gas molecules, which is a central concept in understanding gas behavior.

💡Ideal Gas Equation

The Ideal Gas Equation, represented as PV = nRT, is a fundamental equation in thermodynamics that relates the pressure (P), volume (V), and temperature (T) of an ideal gas to the amount of substance (n) and the ideal gas constant (R). The video script uses this equation to illustrate the relationship between macroscopic measurements and the properties of an ideal gas, which is a key concept in understanding the behavior of gases.

💡Elastic Collisions

Elastic collisions are collisions in which both momentum and kinetic energy are conserved. In the video, it is mentioned that the collisions between gas molecules and the walls of their container are elastic, meaning that the molecules retain their kinetic energy after the collision. This concept is crucial for understanding how pressure is generated in a gas.

💡Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated as one half times the mass of the object times the velocity squared (KE = 0.5 * m * v^2). The video script discusses how the kinetic energy of gas molecules is related to their velocity and how it is preserved in elastic collisions, which is a key aspect of the kinetic molecular theory.

💡Moles

A mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as the number of particles (atoms, molecules, ions, etc.) in 12 grams of carbon-12, which is Avogadro's number (approximately 6.022 × 10^23 particles). The video script explains that moles can be used to measure the amount of a gas, which is important for understanding the relationship between the number of particles and the macroscopic properties of the gas.

💡Avogadro's Number

Avogadro's number is the number of constituent particles (usually atoms or molecules) in one mole of a substance, which is approximately 6.022 × 10^23. The video script mentions Avogadro's number in the context of calculating the total number of particles in a given amount of gas, which is essential for understanding the connection between the macroscopic and microscopic properties of gases.

💡Random Motion

Random motion, as discussed in the video, refers to the unpredictable and disordered movement of gas molecules within their container. This concept is central to the kinetic molecular theory, as it explains how gas molecules continuously collide with the walls of their container, leading to the development of pressure and other macroscopic properties.

Highlights

Introduction to kinetic molecular theory as a way to understand gas behavior.

Macroscopic measurements of gas: pressure, volume, and temperature.

Definition of pressure as force per unit area and methods to measure it.

Volume measurement of containers and its relevance to gas study.

Temperature measurement in Kelvin and its significance in gas properties.

Concept of moles and its historical context before atomic theory.

The ideal gas equation and its macroscopic variables.

Historical context of ideal gas law before atomic theory.

Kinetic molecular theory's explanation of gas pressure through particle collisions.

Assumption of elastic collisions in gases preserving kinetic energy.

Relationship between temperature and average kinetic energy of gas particles.

Importance of considering average kinetic energy due to particle velocity variations.

Explanation of how the number of moles relates to the number of particles in a gas.

Visualizing gases using kinetic molecular theory by chemists and physicists.

Axioms of kinetic molecular theory and their assumptions for ideal gas behavior.

Gas particles are in constant random motion according to kinetic molecular theory.

Negligible volume of gas particles compared to the container volume.

Absence of attractive or repulsive forces between gas particles in ideal conditions.

Completely elastic collisions between gas particles.

Proportionality of average kinetic energy to Kelvin temperature in gases.

Transcripts

- [Instructor] In this video,

we're gonna talk about something called

kinetic molecular theory, which sounds very fancy.

But as we'll see in the next few seconds,

or the next few minutes,

it actually helps build our intuition

for what is actually going on with the gas

or at least an approximation

of what's going on with the gas.

So first, let's think about the types of things

that we know we can measure about a gas

at a macro level.

Now, what do I mean at a macro?

I'm saying at a large scale, at a scale that's much larger

than the scale of atoms or molecules.

And we know the types of things that we can measure.

We can measure pressure.

How do we do you do that?

Well, pressure is just force per unit area.

So, you can do this.

There's various contraptions you can use to measure pressure

depending what you're using it for.

Force, you can measure with springs

and you can apply a certain forces to certain square areas.

But these are all ways that you can measure pressure

and we can measure the pressure of a gas in a container.

You can measure volume of a container.

That's actually pretty straightforward.

You can imagine a container

that looks something like this, it's volume.

We know how to find the volume

of a rectangular prism like this,

or even if it was sphere or some other type of figure.

There's many ways of measuring the volume

without even being able to observe

or even know that things like molecules exist.

We know how to measure temperature,

and we can do that in different scales.

Kelvin is what we use 'cause it's more of an absolute scale,

but you can use literally thermometers

to measure temperature.

And once again, you can measure temperature

without knowing anything about atoms or molecules

or whether they even exist.

And you can also measure an amount of a substance.

And in particular, we could say,

you can measure the number of moles.

Now you might say don't moles involve a certain number

of a molecule or an atom.

Well, they do, but the notion of a mole actually existed

even before we knew exactly how many molecules,

how many particles made up a mole.

It was just viewed as an amount

where people knew it must be some number of particles,

but they didn't know exactly.

So all of these things, we can measure at a macro level.

And we know that we can connect them all

with the ideal gas equation

that tells us that pressure times volume

is equal to the amount of the gas we're dealing with.

And this is, of course, we're talking about an ideal gas

and in future videos,

we'll talk about how some gases approach being an ideal gas

while some are less than ideal.

But the amount we have measures the number of moles.

You have your ideal gas constant

that just helps us make all the units work out

depending on our units for everything else.

And then you have your temperature measured in Kelvin.

And, scientists long before we were actually able

to know about things like atoms or even observe atoms

or molecules directly, or even indirectly,

they were able to establish this relationship

using these macro measurements.

But how do these macro measurements and this relationship

actually make sense at a molecular level?

And that's what kinetic molecular theory provides us.

It says, imagine the gas is being made up

of a bunch of really, really the small particles.

Those are really the gas molecules.

And their collective volume is very small

compared to the volume of the container.

So, it's mostly empty space between those particles.

Now, the pressure is caused by these particles

bouncing into the sides of the container.

Because at any given moment,

you have enough particles bouncing off the side

of any unit area that it's providing a force per unit area.

It's providing a pressure.

It assumes that those collisions

are what's known as elastic,

which we'll study in much more detail in a physics course,

but it really says that your kinetic energy is preserved.

You might already be familiar with the notion

that kinetic energy is equal to one half

times mass times velocity squared.

And so the kinetic energy of these particles,

when they bounce off, their mass doesn't change.

The mass of the particles still there.

And we're saying that the velocity is going to be preserved.

So you have all of these really small particles,

even their collective volume is small

compared to the volume of the container.

They're providing the pressure

by having these elastic collisions

with the side of the container.

And temperature is related to the average kinetic energy

of these particles.

It would be proportional.

The higher the temperature,

the higher average kinetic energy.

Now average kinetic energy is really important

because some of these particles

might be moving faster than others.

And of course, N, the number of moles,

tells us how many particles we're dealing with.

We know that each mole has Avogadro's number of particles.

So, if you just multiply the most times Avogadro's number,

you have the number of particles.

And what's cool about kinetic molecular theory,

I know it's built as a theory,

but this is fundamentally what chemists

and physicists visualize

when they imagine a gas in a container of some kind.

And just to make it a little bit more clear,

the axioms you could say of kinetic molecular theory,

the assumptions of it, I'll give them here.

And it's important to realize that these are assumptions

and the real world, we have slight variation from it,

but these assumptions get us a long way

to explaining the behaviors of gases.

So, we've already talked about it.

Gas consists of particles in constant random motion.

We've already talked about that.

They're bouncing off the side of the container.

The combined volume of the particles is negligible

compared to the total volume in which the gas is contained.

And that also matters

when you talk about things like ideal gases,

because if it stops becoming negligible,

then you have to start thinking about the repulsive

and attractive interactions, a little bit more.

The particles exert no attractive

or repulsive forces on each other.

And that kind of builds into the last point I just made,

which is if they did,

then we're getting closer to being a less than ideal gas.

And we'll talk about that in other videos.

The collisions between the particles are completely elastic.

So, they preserve kinetic energy

and it's actually, they would also preserve momentum.

And that the average kinetic energy of the particles

is proportional to the Kelvin temperature.

And we already talked about that,

that the macro variable,

the macro measurement of temperature

is giving us an indication,

it's proportional to the average kinetic energy

of the particles.