Chemistry Gas Laws - Online Tutor, Practice Problems & Exam Prep

Understanding the behavior of gases is crucial in chemistry, and this is where the gas laws come into play, connecting pressure, volume, and temperature of a gas. These laws are derived from the ideal gas law, represented by the equation:

$PV=nRT$

The four primary gas laws are Boyle's Law, Gay-Lussac's Law, Avogadro's Law, and Charles's Law.

Boyle's Law states that for a given amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure, which can be mathematically expressed as:

$P_1{V}_1=P_2{V}_2$

This means that if the pressure increases, the volume decreases, and vice versa, maintaining a constant product of pressure and volume.

Gay-Lussac's Law, also known as Amontons's Law, establishes that at a constant volume, the pressure of a gas is directly proportional to its temperature in Kelvin. This is reflected in the formula:

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

indicating that an increase in temperature will result in an increase in pressure if the volume is held steady.

Avogadro's Law highlights the direct proportionality between the volume of a gas and the number of moles of gas present, assuming constant pressure and temperature.

Chemistry Gas Laws

The chemistry gas laws are laws that relate together the pressure, volume and temperature of a gas. Now we're going to say here that they can be derived from the ideal gas law. Remember, your ideal gas law is PV=nRT. And to remember your four chemistry gas laws, just remember be great at chemistry.

The first chemistry gas law B is Boyle's law. Boyle's Law looks at the relationship between volume and pressure. G stands for the gay loose Axel Law. It relates together pressure and temperature. A A is for Avogadro's law. Avogadro's Law looks at volume and moles, and then finally CC stands for Charles Law, which relates together volume and temperature.

Now that we have chemistry gas laws connected to these pairings, let's take a look at the series of videos where we go in greater depths with each one of these chemistry gas laws.

Chemistry Gas Laws

Boyle's Law states that volume and pressure are inversely proportional at constant moles and temperature. Now it's named after Robert Boyle and it illustrates how the volume of a container is greatly affected by pressure changes. Now here, how do we depict this relationship? When we say they're inversely proportional, we can say that they're on different levels. So we're going to say volume is inversely proportional to one over inversely proportional pressure, which means that V∝1P. This shows us our inverse relationship between volume and pressure.

Think of it as volume being a numerator, pressure being a denominator. They're on different levels, so they are different from one another. If one goes up, the other one has to go down. Now this is illustrated if we take a look at variables here. If we take a look, we have two containers with movable pistons. Volume is just the space within my container. So if we look at this image, we can say that the volume is pretty high. Pressure represents the downward force that we have on the piston. Now the downward force on the piston must be pretty low, which is why the piston hasn't slid down lower. OK, and here we can see volume is high, pressure is low.

Now let's say that we garnered enough force from the pressure we're able to push down on this piston. We can see that the volume now is smaller. So the volume now is low and that's a direct result of the pressure being higher. Now how do we depict this inverse relationship graphically? Well here to show an inverse relationship between 2 variables you would show it like this. So this graph is showing me that my volume is decreasing over time and as a result, pressure is increasing over time. This is how we depict an inverse relationship between 2 variables.

Now how do we show Boyle's Law formula in form of a digestive formula? Here we'd say that it becomes P1V1=P2V2. This represents our adjusted formula, also our Boyle's Law formula, where P1 is our initial pressure, V1 is our initial volume, P2 is our final pressure, and V2 is our final volume. Now remember we went over how we derived these different types of formulas under the Ideal gas laws application section. If you don't know what that is, or if you haven't seen those videos yet, I suggest you go back and take a look at how we can derive this formula.

Now we just know that it's connected to Boyle's Law and therefore called the Boyle's Law formula. OK, so keep this in mind. Boyle's Law says that pressure and volume are inversely proportional, meaning if one is high, the other one would be low.

Chemistry Gas Laws

Now Gay Lusak's law, also known as Amazon's law, says that pressure and temperature are directly proportional at constant moles N and volume V. Now, as temperature increases, our gas particles collide with the walls more rapidly. That's because they're absorbing the thermal energy and they're using it to propel themselves faster inside the container. And this will cause an increase in my pressure.

Now remember, pressure itself equals force over area. We said that the volume is constant, so your area would be constant. It's staying the same. If I'm increasing my temperature again, my gas will move faster inside the container. They're going to hit the walls more rapidly, but also with more force. So my force is increasing, my area staying the same. This causes my pressure to increase. OK, so that's why pressure and temperature are directly proportional.

Now we're going to say, remember that with all gas law calculations, we must use the SI units for temperature in Kelvin. Our units for temperature here are in Kelvin. Now what is the pressure temperature relationship? They're directly proportional. So you just say that P∝T. And that happens when moles and volume are the same or fixed. Not the same, but fixed.

How do we show this? Well, here we have two images of Pistons containers with Pistons that are movable. In the first image, I haven't applied a heat source, so we're going to say that our temperature here would be low. The temperature is low, so our molecules don't have extra outside energy to absorb, so they're not moving as vigorously and as rapidly. They're not hitting the container with as much force and therefore pressure would be low.

But all of a sudden I add a flame. The container absorbs the heat, which eventually transitions to the molecules, absorbing the heat, allowing them to move more rapidly and with greater force. So temperature's high, which eventually leads to greater force, which leads to greater pressure. So pressure would be high. How would I depict this in a plot? They're both directly proportional, so we'd say that they both would be increasing together. So you'd have a line that's increasing over time.

What would their adjusted formula be? Or the Gay Lusak's formula? It would just be P1T1=P2T2. Again, take a look at my ideal gas law applications section on how we could derive this form. Now we know that it's connected to the Gay Lusak's or Amazon's law. Now remember, with these variables we'd say initial pressure is P1. Initial temperature is T1, final pressure will be P2 and final temperature would be T2. So remember when we're talking about Gay Lusak's law or Amazon's law that pressure and temperature are directly proportional when our moles and our volume V are constant or fixed.

Chemistry Gas Laws

Avogadro's law states that our volume V and our moles N are directly proportional at constant pressure P and temperature T. Now it's named after Amadeo Avogadro and it shows that the volumes of gases are connected to their number of molecules. Here we're going to say that the relationship between volume and moles is that V is directly proportional to moles and again that happens when P & T are constant or fixed.

The way we depict this with our mobile Pistons is if we take a look here at this image, we're going to say this container has a lot of dots, so it has a lot of moles or number of molecules. So moles would be high to house all of these molecules. We'd want our volume to be high because gas is like it when there's an optimal amount of distance between them. But what happens if I take some of these molecules of gases out? Well, our moles of gas would be low and I no longer need as much space for them, so my volume would be low. They both are high together or low together when pressure and temperature are constant or fixed.

Now, how do we depict this in a plot? Since they're directly proportional, you'd say this linear of V & N which showed increasing overtime where you could start out at 0 liters and it increases over time as our moles increase. Now what would our adjusted formula or our Avogadro's law formula be? That would just be V1N1 = V2N2. So our initial variables here initial modes would be N1, initial volume V1, final moles would be N2 final volume would be V2.

So just remember, our volume and moles are directly proportional, meaning they're both high together or low together when our pressure and temperature are constant or fixed.

Chemistry Gas Laws

Troll's law states that volume and temperature are directly proportional at constant moles N and pressure P. It's named after Jacques Charles, and it illustrates how the volume of a container is greatly affected by volume. Here, to show this direct proportionality between volume and temperature, we just say V is directly proportional to T when our moles end and pressure P are constant or fixed.

If we were to illustrate this with movable Pistons, if we take a look here, we'd say that in this first image our volume is low and we haven't applied any temperature or heat to this container amine, so the temperature would be low. Here I'm applying a flame to this. This is going to Causeway higher temperature. And what's happening here is because a piston is movable and the pressure is constant, our gas particles are gaining enough outside energy to basically hit all corners of this container, including the movable piston up. And that's what caused the volume to also expand. So our volume is high.

How do we illustrate this direct proportionality between volume and temperature? What we'd say here that they're both increasing or decreasing together. So you can illustrate this by a line that's going up over time as they both increase. The adjusted formula or Charles law formula would just become

V 1 T 1 = V 2 T 2

Here we'd say that our initial volume is V₁, our initial temperature is T₁, final volume is V₂, and our final temperature is T₂.

Remember, when it comes to Charles law, we say that volume and temperature are directly proportional, which means they both can increase or decrease together if our moles end and our pressure P are held constant or fixed.

Chemistry Gas Laws Example 1

Here we're told that a 10-litre cylinder with a movable piston contains 10 grams of xenon gas. When an additional 10 grams of xenon gas are added, the volume increases. Which chemistry gas law can be used to justify this result?

All right, so within this question, what are we talking about? We're talking about the volume of a container. And they tell me when I add grams, it increases. So they could be asking me to determine what the new volume is. So V₂, they're giving me 10 grams of a gas. If I know the grams of a gas, I can use that to find the moles of the gas and then by adding additional grams of the gas that changes the moles, right.

So basically using this information, it could help me find my second set of moles. So this question is really highlighting the fact that it's your volume and your moles that are changing. And based on the chemistry gas law that we know, we know that when we're dealing with volume in moles, it has to be Avogadro's law. So option B would be the correct choice. It is the only chemistry gas law that's talking about changes between volume and moles.

A 10.0 L cylinder with a movable piston exerts 3.00 atm of pressure. What will happen to the pressure if the volume of the container increases to 20.0 L?

• A. It will double
• B. It will decrease by half
• C. It will increase slightly
• D. No change

Here’s what students ask on this topic:

What is Boyle's law?

Boyle's Law is a fundamental principle in the field of chemistry and physics that describes the relationship between the pressure and volume of a gas at constant temperature. Formulated by the chemist and physicist Robert Boyle in 1662, the law states that for a given mass of an ideal gas that's kept at a constant temperature, the pressure of the gas is inversely proportional to its volume. This means that if you increase the volume of the gas by expanding the container it's in, the pressure will decrease proportionally, and vice versa. Mathematically, Boyle's Law can be expressed as:

P 1 V 1 = P 2 V 2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the pressure and volume after a change has occurred, assuming temperature remains constant. This relationship is crucial for understanding how gases behave under different conditions and is widely applied in various scientific and engineering disciplines.

What is Gay-Lussac's law?

Gay-Lussac's law, named after the French chemist Joseph Louis Gay-Lussac, is a gas law that describes the relationship between the pressure and temperature of a gas when its volume is held constant. The law states that the pressure of a fixed amount of gas held at a constant volume is directly proportional to its temperature in kelvins. In other words, if you increase the temperature of a gas, its pressure will also increase, as long as the volume doesn't change.

Mathematically, Gay-Lussac's law can be expressed as:

P 1 T 1 = P 2 T 2

Here, P1 is the initial pressure, T1 is the initial temperature (measured in kelvins), P2 is the final pressure, and T2 is the final temperature. This equation shows that the ratio of the initial pressure to the initial temperature is equal to the ratio of the final pressure to the final temperature. This relationship is useful for predicting how a gas will behave under different thermal conditions when confined to a constant volume.

What is Avogadro's law?

Avogadro's Law is a principle within chemistry that establishes a relationship between the volume of a gas and the number of gas particles, assuming the temperature and pressure are constant. Named after the Italian scientist Amedeo Avogadro, this law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. In other words, the volume of a gas is directly proportional to the number of moles of gas present when the temperature and pressure are held constant.

Mathematically, Avogadro's Law can be expressed as:

V n = k

where V is the volume of the gas, n is the number of moles of gas, and k is a constant. This means that if you have a gas at a certain volume and you double the number of moles while keeping temperature and pressure constant, the volume will also double. Avogadro's Law is fundamental in understanding gas behavior and is one of the gas laws used to derive the ideal gas law.

What is Charles' Law?

Charles' Law, also known as the law of volumes, is a fundamental principle in gas laws that describes how gases tend to expand when heated. It was named after the French scientist Jacques Charles, who formulated the original law in the 1780s. Charles' Law states that at constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in Kelvin) increases or decreases.

In mathematical terms, Charles' Law is expressed as:

V 1 T 1 = V 2 T 2

where V1 is the initial volume, T1 is the initial temperature (in Kelvin), V2 is the final volume, and T2 is the final temperature. This relationship means that if you increase the temperature of a gas, its volume will increase, provided the pressure remains constant, and vice versa. It's important to note that this law only applies to ideal gases under constant pressure, and real gases may deviate from this behavior under certain conditions.

What are the gas laws?

The gas laws are a set of fundamental principles that describe the behavior of gases under various conditions of pressure, volume, and temperature. They are essential for understanding how gases react and interact in different situations, which is crucial in fields such as chemistry, physics, and engineering. The main gas laws include:

1. Boyle's Law: This law states that the pressure of a given mass of gas is inversely proportional to its volume when the temperature is kept constant. Mathematically, it's expressed as P 1 V 1 = P 2 V 2 , where P is pressure and V is volume.
2. Charles's Law: It describes how gases tend to expand when heated. The law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure is held constant. The formula is V 1 T 1 = V 2 T 2 .
3. Gay-Lussac's Law: This law focuses on the pressure-temperature relationship, stating that the pressure of a gas is directly proportional to its temperature (in Kelvin) when the volume remains constant. It can be represented as P 1 T 1 = P 2 T 2 .
4. Avogadro's Law: Avogadro's Law posits that the volume of a gas at a constant temperature and pressure is directly proportional to the number of moles (or molecules).