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Look through the walkthrough then do the practice problem under it.

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Boyle's Law states that when temperature is constant: P1V1=P2V2.

Boyle's Law also states that pressure is inversely related to volume. This means that when pressure is increased, volume is decreased (and vice versa).

Boyle's Law also states: P⋅V=k (k = the proportionality constant).

Example of Boyle's Law

The example above shows how at a constant temperature P1V1=P2V2.

The example above also shows the inversely proportional relationship between volume and pressure. In the first beaker, the pressure is at 400 mm Hg while the volume is at 50 milli liters. When the pressure decreased to 200 mm Hg, the volume increased to 100 milliliters.

Boyle's Law Practice Problem Walkthrough!

In one chamber, the pressure is 100 mm Hg, with a volume of 80 mL. If the volume decreases to 20 mL, what is the new pressure of the chamber? Assume the temperature is constant.
Solving this problem is simple, just plug the numbers into the Boyle's Law equation, and solve for the missing variable.
1. (100 mm Hg)(80 mL) = P2 (20 mL)

2. (100 mm Hg)(80 mL)(20 mL) = P2

The new pressure is 400 mm Hg when the volume is decreased to 20 mL!

Now try a practice problem!

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Boyle's Law - Overview & Formula - Expii

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Boyle's law, expressed as V ∝ 1/P, states that the volume occupied by a gas is inversely proportional to its pressure.

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Watch this video to see how to use the Combined Gas Law.

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                PV/T = k
(P₁V₁)/T₁ = (P₂V₂)/T₂ or P₁V₁T₂ = P₂V₂T₁
               °C+273 = K

k = Constant
P₁ = Pressure of First Gas
P₂ = Pressure of Second Gas
V₁ = Volume of First Gas
V₂ = Volume of Second Gas
T₁ = Temperature of First Gas
T₂ = Temperature of Second Gas
K = Kelvin

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The Combined Gas Law combines all three gas laws into one formula. This means that memorizing all three of the the formulas is not needed as long as you know this one.

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Look through the walkthrough then do the practice problem under it.

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What is Gay-Lussac's Law?

It is a law describing the properties of gases. It is also sometimes referred to as Amonton's law or the pressure-temperature law. The law states that:

An amount of gas in a closed container (at a constant volume) has a pressure that will vary proportionally to the absolute temperature.

The mathematical representation for this law is:

PT = k or P∝T

Where, P= pressure, T=temperature, and k= constant.

Importance of Gay-Lussac's Law

Let's think about the gas molecules in a closed system. If the temperature increases, the molecules of gas will have more energy. They will move around more and expand. This causes an increase in pressure. If the temperature decreases, the molecules lose energy and are closer together. So, the pressure decrease.

A great example of Gay-Lussac's law is the tires on your vehicle. If the tire has no punctures and a good seal, it is a closed container. There is a specific amount of gas or mass of gas in that container. In the winter, the pressure in tires often drops due to cold temperatures. The amount of gas did not change, but as the temperature drops so does the pressure.

History of Gay-Lussac's Law

The Gay-Lussac law has an intriguing history. It is named after the french physical chemist Joseph-Louis Gay-Lussac. But he was actually the first person to publish Charles' Law. So, why did we call Charles' Law after Jacques Charles? It turns out Charles discovered his law but never published his work. Gay-Lussac found the unpublished work and credited Charles. Interestingly, at the same time, John Dalton had determined Charles Law on his own.

So, what about the Gay-Lussac law? It had already been discovered over 100 years earlier by Guillaume Amontons. But, because of the technology at the time, Amontons could only work with air. Gay-Lussac had the opportunity to confirm Amontons' work with pure elements. He used hydrogen, oxygen, and nitrogen gases. Each of these is an ideal gas at STP. So, he confirmed the relationship between temperature and pressure. Sadly, Amontons seems to be a forgotten figure in the origins of chemistry. His law is often named after Gay-Lussac. Some modern textbooks and papers are trying to correct the mistake. So, you'll sometimes see it called Amontons' law.

Most of Gay-Lussac's work was dedicated to the relationship between gases and volume. He actually developed the law of combined volumes. It states, "gases react and produce products in simple whole number ratios." He discovered this by observing that two liters of hydrogen reacted with one liter of oxygen. What was the result? They formed one liter of water. He had essentially created the mole ratio. But, at the time, we didn't know about the mole. In fact, Amedeo Avagadro created Avagardo's Law based on Gay-Lussac's work. Unfortunately, it would take another 50 years for Avagardo's work to be accepted. We honor him today with Avagadro's number.

So, where do we end up? At this point in history, we had three gas laws. The first was Boyle's law which connected volume and pressure. Next, Amontons developed the relationship between temperature and volume. Finally, we get Charles' law. It explained the relationship between pressure and temperature. The three laws were integrated into the combined gas law. At the time, Avagadro's law wasn't accepted. But, once it was, we had four gas laws. The combination of the four produced the ideal gas law.

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Gay-Lussac's Law - Overview & Formula - Expii

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Gay-Lussac's law states that the pressure of a gas is directly proportional to its temperature in Kelvin, given that the volume stays constant.

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Watch this video to see how temperature affects the pressure of a gas and to learn how to use the formula for Gay-Lussac's Gas Law.

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           P/T = k
P₁/T₁ = P₂/T₂ or P₁T₂ = P₂T₁
            °C+273 = K

k = constant
P₁ = Pressure of First Gas
P₂ = Pressure of Second Gas
T₁ = Temperature of Second Gas
T₂ = Temperature of Second Gas
K = Kelvin

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Gat-Lussac's Law shows the relationship between temperature and pressure: As temperature increases, pressure increases and as temperature decreases, pressure decreases.

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Look through the walkthrough then do the practice problem under it.

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As we have studied the phases of matter, we've looked at the properties of solids, liquids, and gases. But, we have a lot to learn about gases. Scientists have studied them for hundreds of years. Robert Boyle developed the first gas law in 1662! Over one hundred years after Boyle, Jaques Charles began to study gases. He determined the relationship between volume and temperature. Unfortunately, he died before he could publish his work. Joseph Gay-Lussac discovered Charles' work and attributed it to him.

Charles' law relates a gas's volume and temperature. Charles developed his law by filling five balloons with different gases. Each balloon had the same volume. Next, he heated each balloon. He discovered that each of their volumes increased by the same amount. He realized that a gas's volume was a physical property, not a chemical property. Of course, today, we know that the gas has to be ideal. Real gases experience Van der Waal's forces. So, the [electrostatic attractions](vhttps://www.expii.com/t/electrostatic-interactions-definition-overview-8368) affect their properties.

Charles' Law Formulas

We can write Charles Law in three ways. Also, the temperature is always in kelvin. Let's explore each one.

The first way to write Charles' law is as a proportionality. It tells us that volume and temperature are directly related. So, if the volume increased, the temperature did too. If the temperature drops, the volume declines too.

The second way to write Charles' law is as a ratio. The ratio of volume and temperature is a fixed value. We denote the constant with the letter "k." Let's consider an increase in volume. The temperature is in the denominator. So, to keep the ratio the same, the temperature had to increase. The same is true for the numerator. If the temperature increases, the volume has to as well.

The final form relates the initial and final states. We just learned that the ratio is constant. So, even if we change the conditions, the proportion stays the same. Let's start with an initial temperature and volume. For ease, let's say their ratio is 1. Now we'll increase the temperature. We know the volume also rises. But, the new volume divided by the new temperature is still 1. So, if we know three of the terms, we can solve for the fourth.

Charles' Law and Kinetic Molecular Theory

Kinetic molecular theory can help us understand Charles Law. As the temperature increases, the molecules' kinetic energies increase. They are moving faster. So, they collide more often with the walls of the container. In a rigid container, the pressure would increase because of the Gay-Lussac law. But, if we have an expandable canister, it will offset the pressure by raising the volume. Of course, that's Boyle's Law.

We are seeing the interconnectedness of the gas laws. The interconnection is what led to the development of the ideal gas law. We can deduce any of the relationships from the ideal gas law.

Charles' Law and Absolute Zero

What would happen if the temperature reached absolute zero? Let's look at the second form of Charles' law. We can't divide by zero. So, let's multiply both sides by the temperature. We get V=kT. Now we can see that at absolute zero, the volume would be zero. But, that's not possible! At absolute zero, we know that, theoretically, all movement would stop. But, the gas molecules still have a volume. Simply by being matter, they must have a volume. So, Charles' law only works at normal temperatures.

As a side note, quantum mechanics teaches us that absolute zero is impossible. If we reached absolute zero, a particle would be at rest. So, we would know both its position and momentum. But, according to the uncertainty principle, that's impossible! So, absolute zero is only theoretical.

Who was Jacques Charles?

Charles' interest in gas behavior wasn't just scientific curiosity. He wanted to fly! He is the first person to launch hydrogen sourced hot air balloons. He believed hydrogen would be a good source based on his study of Boyles law. He and his partners created hydrogen gas by mixing sulfuric acid with iron. The reaction is Fe(s)+H2SO4(aq)→FeSO4(aq)+H2(g). It is a single replacement reaction.

He launched the first hydrogen balloon in 1783 from the Champ de Mars in Paris. Almost 100 years later, the Champ de Mars became the home of the Eifel tower! A lead pipe fed the gas into the balloon. But, the sulfuric acid and iron reaction is exothermic. So the gas was hot. As the gas entered the balloon, it cooled. Charles' law tells us that as the gas's temperature cools, the volume decreases. They had a difficult time filling the balloon. Eventually, they filled it enough to launch. But, it could not lift a person. They followed it on horseback. The balloon traveled about 20 kilometers (13 miles). But, it got too far ahead. When it landed, terrified local farmers attacked it with pitchforks.

Three months later, Charles' was ready to fly. We estimate that he and his copilot reached a height of 1800 meters (1.10 miles). They traveled a distance of 36 kilometers (22.3 miles). He would never fly again. But, his experience with balloons led him to try and understand gas behavior. Before his death, we would formulate Charles' law. Unfortunately, he was unable to publish his work.

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Charles's Law - Overview & Formula - Expii

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Charles's law, expressed as V ∝ T, states that the volume occupied by a gas is directly proportional to its temperature in Kelvin.

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Watch this video to see how temperature affects the volume of a gas and to learn how to use Charles' Gas Law.

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Watch this video to see how pressure affects the volume of a gas and to learn how to use the formula for Boule's Gas Law.

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         V/T = k
V₁/T₁ = V₂/T2 or V₁T₂ = V₂T₁
       °C+273 = K

k = constant
V₁ = Volume of First Gas
V₂ = Volume of Second Gas
T₁ = Temperature of First Gas
T₂ = Temperature pf Second Gas
K = Kelvin

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Charles' Law shows the relationship between temperature an pressure: As temperature increases, volume increases and as temperature decreases, volume decreases.

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        PV = k
       P₁V1 = P₂V₂

k = constant
P₁ = Pressure of First Gas
P₂ = Pressure of Second Gas
V₁ = Volume of First Gas
V₂ = Volume of Second Gas

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Boyle's Law shows the relationship between pressure and volume: As pressure increases, volume decreases and as pressure decreases, volume increases.

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There are three main gas laws – Boyle's Law, Charles's Law, and Gay-Lussac's Law – and they can all be put together in the Combined Gas Law.

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Look through the walkthrough then do the practice problem under it.