Chemistry Gas Laws: Study with Video Lessons, Practice Problems & Examples

The chemistry gas laws describe the relationships between pressure, volume, and temperature of gases. Boyle's law states that volume and pressure are inversely proportional, while Gay Lussac's law indicates that pressure and temperature are directly proportional. Avogadro's law connects volume and moles directly, and Charles's law shows that volume and temperature are also directly proportional. Key equations include p1⁢v1=p2⁢v2 for Boyle's law and p1/t1=p2/t2 for Gay Lussac's law.

Chemistry Gas Laws

The chemistry gas laws are laws that relate 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 4 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-Lussac's law. It relates pressure and temperature. A is for Avogadro's law. Avogadro's law looks at volume and moles. And then finally C stands for Charles's law, which relates volume and temperature. Now that we have the chemistry gas laws connected to these pairings, let's take a look at the series of videos where we go into 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. It's named after Robert Boyle and illustrates how the volume of a container is greatly affected by pressure changes. Now, how do we depict this relationship? When we say they're inversely proportional, we can describe it as volume being inversely proportional to pressure, which means that \( V \propto \frac{1}{P} \). This shows our inverse relationship between volume and pressure. Think of it as volume being the numerator and pressure being the denominator. They're on different levels, so they are different from one another. If one goes up, the other one has to go down.

In this example, if we look at two containers with movable pistons, volume represents the space within the container. If we observe the initial state, the volume is high, indicating that the pressure, represented by the downward force on the piston, is low — which is why the piston hasn't slid down lower. Now, let's say that we gather enough force from the pressure to push down on this piston. We can see that the volume now is smaller, which is a direct result of the pressure being higher.

To depict this inverse relationship graphically, you can show a graph where volume decreases over time, and as a result, the pressure increases over time, demonstrating the inverse relationship between the two variables.

To express Boyle's law formula in a processed form, we write it as \( P_1V_1 = P_2V_2 \). This represents not only our adjusted formula but also the Boyle's law formula where \( P_1 \) is the initial pressure, \( V_1 \) is the initial volume, \( P_2 \) is the final pressure, and \( V_2 \) is the final volume. If you're unsure how these formulas derive from the ideal gas laws, I recommend revisiting those sections in our course or instructional videos. Remember, Boyle's law illustrates that pressure and volume are inversely proportional, meaning if one is high, the other would be low.

Chemistry Gas Laws

Now, Gay Lussac's law, also known as Amatons law, says that pressure and temperature are directly proportional at constant moles \( n \) and volume \( v \). As temperature increases, our gas particles collide with the walls more rapidly. That's because they're absorbing the thermal energy and using it to propel themselves faster inside the container. This will cause an increase in my pressure. 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 is staying the same; this causes my pressure to increase. Okay? So that's why pressure and temperature are directly proportional.

We must remember that with all gas law calculations, we must use the SI units for temperature in Kelvin. So our units for temperature here are in Kelvin. What is the pressure-temperature relationship? They're directly proportional, so you just say that \( p \) is directly proportional to \( t \), and that happens when moles and volume are 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, our 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 this heat, allowing them to move more rapidly and with greater force. So temperature is 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 Lussac's formula? It would just be \( \frac{p_1}{t_1} = \frac{p_2}{t_2} \). Again, take a look at my ideal gas law applications section on how we could derive this formula. Now we know that it's connected to the Gay Lussac's or Amatons law.

Remember, with these variables we'd say the initial pressure is \( p_1 \), initial temperature is \( t_1 \), final pressure will be \( p_2 \), and final temperature will be \( t_2 \). So, remember when we're talking about Gay Lussac's law or Amatons law that pressure and temperature are directly proportional when our moles, \( n \), 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 Amedeo 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 it happens when p and 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 gases 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 line of V and n would show it increasing over time. Where you could start out at 0liters 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 moles 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

Charles' 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 temperature. Here, to show this direct proportionality between volume and temperature, we just say V is directly proportional to T when our moles n 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, I mean, so the temperature would be low. Here, I'm applying a flame to this. This is going to cause a higher temperature. And what's happening here is because the 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 upward, and that's what causes the volume to also expand. So our volume is high. How do we illustrate this direct proportionality between volume and temperature? Well, we'd say here that they're both increasing or decreasing together. 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. So 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 n and our pressure p are held constant or fixed.

Chemistry Gas Laws Example 1

Here we're told that a 10 liter 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? Alright. 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 and 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

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

A sealed container with a movable piston contains a gas with a pressure of 1380 torr, a volume of 820 mL and a temperature of 31°C. What would the volume be if the new pressure is now 2.83 atm, while the temperature decreased to 25°C?

• A. 0.0253 L
• B. 0.167 L
• C. 0.326 L
• D. 0.516 L
• E. 1.46 L

Here’s what students ask on this topic:

What is Boyle's Law and how is it represented mathematically?

Boyle's Law states that the volume of a gas is inversely proportional to its pressure when the temperature and the number of moles are held constant. This means that if the pressure increases, the volume decreases, and vice versa. Mathematically, Boyle's Law is represented as:

P1V1 = P2V2

Here, P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. This relationship is crucial in understanding how gases behave under different pressure conditions.

How does Gay Lussac's Law relate pressure and temperature?

Gay Lussac's Law, also known as Amontons' Law, states that the pressure of a gas is directly proportional to its temperature when the volume and the number of moles are held constant. This means that as the temperature increases, the pressure also increases. Mathematically, it is represented as:

P1T1 = P2T2

Here, P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature. Remember, temperature must be in Kelvin for these calculations.

What is Avogadro's Law and how does it relate volume and moles?

Avogadro's Law states that the volume of a gas is directly proportional to the number of moles of the gas when the pressure and temperature are held constant. This means that if the number of moles increases, the volume also increases. Mathematically, Avogadro's Law is represented as:

V1n1 = V2n2

Here, V1 and n1 are the initial volume and number of moles, and V2 and n2 are the final volume and number of moles. This law helps in understanding how the amount of gas affects its volume.

How does Charles's Law describe the relationship between volume and temperature?

Charles's Law states that the volume of a gas is directly proportional to its temperature when the pressure and the number of moles are held constant. This means that as the temperature increases, the volume also increases. Mathematically, Charles's Law is represented as:

V1T1 = V2T2

Here, V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature. Remember, temperature must be in Kelvin for these calculations.

What is the Ideal Gas Law and how is it used?

The Ideal Gas Law is a fundamental equation that relates the pressure, volume, temperature, and number of moles of a gas. It is represented as:

PV = nRT

Here, P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. The Ideal Gas Law is used to calculate any one of these variables if the others are known. It is a combination of Boyle's Law, Charles's Law, and Avogadro's Law, and it provides a comprehensive description of the behavior of ideal gases.