The Ideal Gas Law: Crash Course Chemistry #12

Summary

This Crash Course Chemistry episode delves into the pervasive nature of gases and their fundamental behaviors. It introduces Boyle's Law, which describes the relationship between pressure and volume in a gas, and its historical misattribution to Robert Boyle. The episode also explores the Ideal Gas Law, PV=nRT, and its derivation by scientists like Jacques Charles and Amedeo Avogadro. It explains the significance of each variable in the equation and demonstrates how deviations from ideal behavior occur under certain conditions. The video concludes with a practical demonstration of the law's application and a brief discussion on standard temperature and pressure, absolute zero, and the concept of moles.

Takeaways

• 🌌 Gases are ubiquitous, present in space, on Mars, in our blood, and even in soda.
• 🧪 Boyle's Law, despite its name, was not solely developed by Robert Boyle; it was a collaborative effort involving Richard Towneley and Henry Power.
• 🔬 The Ideal Gas Law, PV=nRT, is a fundamental equation in chemistry that relates pressure, volume, temperature, and the amount of gas.
• 🌡 Temperature, at the atomic level, is a measure of kinetic energy, which affects the pressure of a gas as particles move faster or slower.
• 📉 Boyle's Law is a special case of the Ideal Gas Law, where the relationship between pressure and volume is constant when temperature and the amount of gas are unchanged.
• 🔍 The Ideal Gas Law is a theoretical framework that unifies the work of several scientists, including Charles, Avogadro, and those incorrectly attributed to Boyle.
• 🌟 The Universal Gas Constant (R) in the Ideal Gas Law is approximately 8.3145 L·kPa/K·mol, a value that appears constant but is derived from experimental data.
• 🌬️ The behavior of gases can be predicted using the Ideal Gas Law, allowing chemists to calculate unknown variables when three of the four are known.
• 🧊 At low temperatures or high pressures, real gases may deviate from the Ideal Gas Law, indicating the law's limitations under extreme conditions.
• 🏷️ STP (Standard Temperature and Pressure) and absolute zero are key reference points in chemistry, with one mole of an ideal gas occupying 22.4 liters at STP.

Q & A

What is the significance of gases in our everyday environment?

Gases are ubiquitous, existing in space, on Mars, dissolved in our blood, and even in sodas. They are all around us, and understanding their behavior is crucial in various scientific contexts.

What is Boyle's Law and what does it describe?

Boyle's Law states that for a given amount of gas at a constant temperature, the product of pressure and volume is a constant value. Mathematically, it is expressed as PV = k, where k is the constant.

Who is often misattributed as the discoverer of Boyle's Law?

Robert Boyle is often misattributed as the discoverer of Boyle's Law, but the law was actually based on work done by Henry Power, a working-class scientist.

What is the Ideal Gas Law and how does it expand upon Boyle's Law?

The Ideal Gas Law is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the Universal Gas Constant, and T is temperature in Kelvin. It expands upon Boyle's Law by incorporating the number of moles and temperature into the equation.

Who were the scientists responsible for contributing to the development of the Ideal Gas Law?

The Ideal Gas Law was developed through the contributions of multiple scientists, including Jacques Charles and Amedeo Avogadro, whose work built upon the earlier findings that were mistakenly attributed to Robert Boyle.

What does the term 'STP' stand for in the context of the Ideal Gas Law?

STP stands for Standard Temperature and Pressure, which is defined as 0 degrees Celsius and 100,000 pascals or 100 kilopascals.

How much volume does one mole of an ideal gas occupy at STP?

At STP, one mole of any ideal gas occupies 22.4 liters of space.

What is absolute zero and how does it relate to the behavior of gases?

Absolute zero is the theoretical temperature at which all molecular motion ceases, equivalent to zero kelvins or -273.15 degrees Celsius. At this temperature, gases would deviate significantly from ideal behavior.

What is the significance of the Universal Gas Constant (R) in the Ideal Gas Law?

The Universal Gas Constant (R) in the Ideal Gas Law represents the proportionality constant that relates the pressure, volume, and temperature of a given amount of gas. It is approximately 8.3145 J/(mol·K).

How does the behavior of gases change when they deviate from ideal behavior?

When gases deviate from ideal behavior, typically at low temperatures or high pressures, the assumptions of the Ideal Gas Law no longer hold true, and the relationship between pressure, volume, temperature, and the number of moles becomes more complex.

What is the practical application of understanding the Ideal Gas Law?

Understanding the Ideal Gas Law is crucial in various fields such as chemistry, physics, and engineering, where it helps in predicting and controlling the behavior of gases in different conditions, such as in chemical reactions, gas storage, and pressure vessel design.

Outlines

00:00

🌌 Introduction to Gases and Boyle's Law

This paragraph introduces the ubiquity of gases, highlighting their presence in space, on Mars, in our blood, and even in soda. It emphasizes the difficulty in perceiving gases due to their intangible nature, yet their constant presence. The narrator discusses the behavior of gases, noting that while they are theoretically easy to describe, they often do not behave as expected. The historical context of Boyle's Law is explored, explaining its significance in the 1600s. However, the paragraph also delves into the misattribution of the law to Robert Boyle, when it was actually the work of Henry Power, a working-class scientist whose contributions were overshadowed by Boyle's social standing.

05:00

🔬 The Ideal Gas Law and Its Components

The second paragraph delves into the Ideal Gas Law, which is a fundamental principle in chemistry that relates the pressure, volume, temperature, and amount of gas in a system. It explains how the law evolved from the works of Jacques Charles and Amedeo Avogadro, who each contributed to understanding the relationships between these variables. The Ideal Gas Law is expressed as PV=nRT, where P stands for pressure, V for volume, n for the number of moles, R for the Universal Gas Constant, and T for temperature. The paragraph also discusses the practical application of the law, using a demonstration with a soda can to illustrate how changes in temperature and the number of moles affect pressure and volume. It concludes with a brief overview of terms like STP (Standard Temperature and Pressure), and absolute zero, providing a foundation for further discussions on the behavior of gases.

Keywords

💡Gas

Gas is a state of matter that is characterized by its ability to expand and fill its container. In the video, gas is discussed as being ubiquitous, existing in space, on Mars, and even dissolved in our blood and soda. It is a fundamental concept as the video delves into the behavior of gases and how they can be described theoretically and mathematically.

💡Boyle's Law

Boyle's Law states that for a given amount of gas at a constant temperature, the product of pressure and volume is a constant value. This law is significant in the video as it introduces one of the foundational principles in the study of gases. The video humorously discusses the historical misattribution of the law to Robert Boyle, instead of its actual contributors, Towneley and Power.

💡Pressure

Pressure, in the context of the video, refers to the force exerted by gas molecules colliding with the walls of their container. It is measured in units like pascals or atmospheres. The video explains how pressure changes with volume, as illustrated by the balloon example, and is a key variable in Boyle's Law.

💡Volume

Volume is the amount of space that a gas occupies. The video explains the relationship between volume and pressure through Boyle's Law, where a decrease in volume leads to an increase in pressure, and vice versa, assuming the temperature and amount of gas remain constant.

💡Ideal Gas Law

The Ideal Gas Law is a scientific equation that describes the behavior of an ideal gas in terms of its pressure, volume, temperature, and the number of moles of the gas. The equation PV = nRT is highlighted in the video as a unifying principle that encompasses Boyle's Law, Charles's Law, and Avogadro's Law. It is central to the video's theme of understanding gas behavior.

💡Moles

In the video, moles refer to the amount of a substance, measured in units called moles, which is a fundamental concept in chemistry. The number of moles (n) is one of the variables in the Ideal Gas Law, indicating the quantity of gas present and its role in determining the gas's behavior.

💡Temperature

Temperature, as discussed in the video, is a measure of the average kinetic energy of the particles in a gas. It is directly related to the pressure of a gas, as higher temperatures lead to more frequent collisions with the container walls, thus increasing pressure.

💡Universal Gas Constant (R)

The Universal Gas Constant (R) is a proportionality constant that relates the pressure, volume, and temperature of an ideal gas. In the video, it is noted that R is approximately 8.3145 liters kilopascal per kelvin mole, and it is a key component of the Ideal Gas Law equation.

💡Charles's Law

Charles's Law is mentioned in the video as the principle that states the volume of a gas is directly proportional to its temperature, provided the pressure and the amount of gas remain constant. It is one of the gas laws that contribute to the formulation of the Ideal Gas Law.

💡Avogadro's Law

Avogadro's Law, as explained in the video, states that the volume of a gas is directly proportional to the number of moles of the gas, at a constant temperature and pressure. This law is also a precursor to the Ideal Gas Law and helps to establish the relationship between the amount of gas and its volume.

💡Standard Temperature and Pressure (STP)

STP is a set of standard conditions for scientific measurements, defined as 0 degrees Celsius and 100 kilopascals of pressure. The video uses STP to illustrate that one mole of an ideal gas occupies 22.4 liters under these standard conditions, which is a useful reference for gas calculations.

💡Absolute Zero

Absolute Zero, as mentioned in the video, is the theoretical temperature at which particles have minimal kinetic energy, effectively stopping all motion. It is defined as 0 Kelvin or -273.15 degrees Celsius. The concept is used to emphasize the relationship between temperature and the motion of gas particles.

Highlights

Gas is ubiquitous, existing in space, on Mars, in the human body, and in beverages.

Gas behavior can be theoretically, experimentally, and mathematically described, despite their unpredictable nature.

Boyle's Law, which links pressure and volume in a closed system, was a significant scientific breakthrough in the 1600s.

The historical misattribution of Boyle's Law to Robert Boyle rather than its actual contributors.

Robert Boyle's influential idea that scientific publications should be based on experimental evidence.

The contributions of Henry Power, whose work on gas behavior was overshadowed by Boyle's publication.

The Ideal Gas Law, which relates pressure, volume, temperature, and the number of moles of a gas.

The theoretical understanding of the Ideal Gas Law, which builds on the work of Charles, Avogadro, and others.

The physical interpretation of pressure as a result of gas molecules colliding with their container.

The measurement of pressure in pascals, with one atmosphere equal to 101,325 pascals.

Volume as a measure of the space available for gas particles, influencing pressure due to particle density.

The Universal Gas Constant (R) in the Ideal Gas Law, which has a specific value in liters kilopascal per kelvin mole.

Temperature's role in the Ideal Gas Law, reflecting the kinetic energy and movement of gas particles.

Practical demonstration of the Ideal Gas Law using a soda can, illustrating changes in pressure and volume.

The concept of STP (Standard Temperature and Pressure) and its significance in gas law calculations.

Absolute zero as the theoretical limit of temperature where molecular motion ceases.

The educational value of the Ideal Gas Law in predicting gas behavior given three of four variables.

Transcripts

Gas! It's all around you. It's in space. It's on Mars.

It's dissolved in your blood, and in your soda.

It's everywhere.

And it's easy to forget that we're submerged in an ocean of gas, but it's there all the time.

You can feel it if you wave your arms around.

Can't look cool while you're feeling it but you can feel it. It's there.

Those little molecules and atoms bumping around against your hands as you wave them around.

Feel it? Are you doing this?

I've got good news and bad news about gases.

First the good news, when they're behaving themselves

it is extremely easy to describe their behavior theoretically, experimentally and mathematically.

The bad news is, they almost never behave themselves.

[Theme Music]

The first mathematical description of a behavior of a gas was a link between pressure and volume.

In a closed system like the inside of this balloon,

when we decrease the volume of the balloon the pressure inside goes up.

And if we could somehow expand the balloon, then the pressure inside the balloon would go down.

If I keep pushing on it the pressure inside might go so high that it'll break.

I hope...I can't do it. It's a very strong balloon!

The relationship here is a simple one.

When you multiply the pressure and volume together, you get a constant.

As long as the temperature and amount of gas stays the same, so does that constant.

It's called Boyle's Law, and it was a pretty big deal back in the 1600s.

It's also, one of the greatest scientific mis-attributions of all time.

Robert Boyle was a super rich Englishman, raised in Ireland.

His father was so rich that he paid another family to raise his children.

I guess because he was too busy administering lands or something.

Boyle had lots of great ideas about science and chemistry.

His most important one, and this is arguably even more important than Boyle's Law,

being that chemists should publish papers not on what they feel is correct,

but rather on theories that have been backed up by experimentation.

Richard Towneley a wealthy, but considerably less wealthy, Englishman struck up a relationship with Boyle.

Telling him about some of his work that would disprove one of those "But it feels right" kind of chemists.

Boyle published the paper mentioning that work, which he called Towneley's Hypothesis.

But which ended up, because of Boyle's superior scientific standing and possibly his wealth, being called Boyle's Law.

But here's the really messed up thing:

the experiments that led to the creation of this theory were actually done largely by

Towneley's family friend and physician, Henry Power, who's not a member of the aristocracy at all.

He was just a working class scientist.

Power was working on a publication that would have snared him the position as discover of

the relationship between the pressure and volume of a gas.

But Boyle, having discussed the ideas with Towneley privately, published his first,

attributing Towneley as the sole researcher, ensuring that Power's contributions were all but lost to history.

Henry Power's Wikipedia page didn't even mention Boyle's Law until a few weeks ago,

when I personally added a paragraph about it, with proper citations of course.

But no matter who thought it up or who it got named after, Boyle's Law is pretty cool.

For a given amount of gas at a constant temperature, pressure times volume always equals the same number.

But where is that constant coming from,

and why is it different for different amounts of gas at different temperatures?

Well it was more than a hundred years before we'd figure out the answer to those questions,

with the help of a Frenchman Jacques Charles and our old, Italian house-elf friend Amedeo Avogadro.

Charles and Avogadro created equations much like Boyle's law

with two features of a gas being linked directly together by constants.

Charles discovered that volume divided by temperature equals a constant,

as long as the pressure remains the same.

And then Avogadro figured out that volume divided by the number of moles in the container

at a constant pressure and temperature gave yet another constant.

But here's the crazy cool thing:

all of these scientists were basically dealing with a different form of the same equation.

An equation that we must never forget, and is gonna be stuck in my head until I die, and here's how it works:

Pressure times volume is equal to the number of moles of substances times a constant times temperature.

P V equals n R T: The Ideal Gas Law, which works for all gases as long as they behave themselves.

Now here's the cool part,

using this equation we can show how all of these chemists were dealing with the same relationship.

They were just clumping various variables together in different orders.

All of the chemists we just mentioned: Charles, Avogadro and Boyle (or more properly Towneley and Power),

figured out their contribution to the Ideal Gas Law experimentally.

But more interesting to me, is that it can be understood theoretically.

First, we have to understand what each of these variables actually mean.

In that same way the atoms and molecules that make up gases

are bouncing against things, applying pressure to them.

This balloon is inflated because the molecules are bouncing around inside of it,

bumping into the inside of the balloon harder than the molecules bouncing off the outside of the balloon.

Scientists generally measure pressure with the S.I. unit of force:

Newtons per area, meters squared, which is shortened to pascals.

But since pascals are so tiny we either use kilopascals

or we use the pressure here on earth at sea level, that we call one atmosphere or one atm.

Completely by chance, one atmosphere is equal to 101325 pascals,

but that's so close that we often just say that one atmosphere is 100,000 pascals or 100 kilopascals.

Volume is the amount of space particles have to exist inside of.

So yeah, that makes sense, when the volume goes down, the pressure goes up,

because there are more particles in a smaller space, and they'll each hit the walls more often.

N is simply the amount of gas, the number of moles in the system.

Here I am decreasing the amount of gas in the system and in response the volume is decreasing. Obviously.

But so is the pressure inside the balloon.

R in the Ideal Gas Law is called the Universal Gas Constant.

Even though, as we will see in a coming episode, it is neither universal or constant.

It's 8.3145 liters kilopascal per kelvin mole.

Temperature, is experienced by you and me as hot or cold but at the atomic level it's kinetic energy.

Literally, how fast or slow the average particle is moving.

So if temperature goes up, so will the pressure as the particles are moving faster

and thus will run into the sides of the container more often.

So now we know about all of the little bits of the Ideal Gas Law, so let's take a look at it in action.

We here at Crash Course generally like to be very safe. This is a little bit of overkill here.

I put a little bit of water into this soda can and now I'm boiling it.

So instead of atmosphere gas in this can right now there's water vapor,

and it's hot and all the molecules are zipping around like crazy.

We pick it up and we plop it down inside of that -- ooh! -- and it crushes itself.

So what just happened there?

Well, let's see what the gas law can tell us.

So which of these things are changing?

Starting on the right hand side: R, is constant, so that can't change.

The temperature of the gas though, that definitely changed;

it drops like mad when it's exposed to the ice water.

N is decreasing too as water vapor is condensing into liquid water, it thus disappears from the gas phase.

So the next result on the right hand side is a decrease,

and that means that the left hand side has to have a decrease too.

So on to the left hand side.

The pressure does indeed drop because the lower temperature makes the molecules move more slowly,

thus bumping into the sides of the can a lot less than before.

And volume drops too, but not quite for the reason you might think.

It's really that the pressure inside the can goes so low, that the pressure outside the can,

the atmospheric pressure, literally crushes the can.

Now I understand that you probably don't think this is as cool as I do,

but understanding the physical reality of atoms and molecules smacking into things is

a special kind of beautiful for me.

It's also pretty cool that if you know any 3 things about a gas, you can figure out the fourth using the ideal gas law.

Of course, not all gases behave ideally,

and all gases deviate from the law at low temperatures or high pressures.

But we'll save that discussion for a later episode.

Jargon fun time.

STP means standard temperature and pressure,

which according to the lords of chemistry is 0 degrees Celsius and 100,000 pascals or 100 kilopascals.

One mole of any ideal gas takes up 22.4 liters of space at STP, which is a fact that can simplify a lot of calculations.

Absolute zero is the temperature at which all movement of all particles stops.

It is zero kelvins or -273.15 degrees Celsius.

And that's all for this episode. Thank you for watching Crash Course Chemistry.

If you were paying attention you learned about

how the work of some amazing thinkers combined to produce the Ideal Gas Law;

how none of those people were Robert Boyle,

and how the Ideal Gas Equation allows you to find out pressure, volume, temperature or number of moles,

as long as you know three of those four things.

And you learned a few jargon-y phrases to help you sound like you know what you're talking about.

This episode of Crash Course Chemistry was written by me.

The script was edited by Blake de Pastino

and our chemistry consultants were Dr. Heiko Langner and Edi Gonzalez.

It was filmed, edited and directed by Nicholas Jenkins.

Our script supervisor was Caitlin Hofmeister and our sound designer is Michael Aranda.

Our graphics team is Thought Cafe.