The Ideal Gas Law: Study with Video Lessons, Practice Problems & Examples

The ideal gas law, expressed as:

$PV=nRT$

is a fundamental equation in chemistry that relates pressure (P), volume (V), moles of gas (n), and temperature (T) to describe the behavior of ideal gases. The gas constant (R) can take two values: 0.08206 when using the ideal gas law, with pressure in atmospheres and volume in liters, and temperature in Kelvin. However, for calculations involving speed, velocity, or energy, R is 8.314 J/(mol·K). It's essential to use the correct R value based on the context of the problem. The conversion factor between these R values is 1 L·atm = 101.325 J, which helps in converting units when necessary. Understanding and applying the ideal gas law is crucial for various chemical calculations and concepts.

The Ideal Gas Law

In our exploration to describe the behavior of gases, we come upon the ideal gas law. Now, the ideal gas law formula relates the behavior of gas under varying conditions of pressure, volume, moles, and temperature. So our ideal gas law formula is PV=NRT. We see that it's in a purple box, which means that you need to memorize it. Your professor is going to expect you to know this formula. It's going to be involved in so many different types of ideas and calculations within this chapter.

Now if we take a closer look at it, we said that P equals pressure. Here the units for pressure will be in atmospheres, volume will be in liters. N equals the amount of gas in moles. R is a gas constant and here when it comes to the ideal gas law, we tend to see it as 0.08206. In the next section we'll talk about the units involved with this gas constant and then temperature. Here temperature will be in kelvins.

So just remember to talk about the ideal behavior of gases, we use the ideal gas law. So I'll click on the next video and let's take a look at an example question.

The Ideal Gas Law Example 1

Here we're told that a 500 milliliter container at a pressure of 600 milliliters of mercury possesses 29.3g nitrogen gas at 50�C. Here we need to determine the correct units needed for the ideal gas law. So remember the ideal gas law is PV=nRT, so P stands for pressure. Remember, pressure needs to be in units of atmospheres. So here we're going to do a conversion. We're going to go from 600mm of mercury into atmospheres. Millimeters of mercury go here on the bottom and then atmosphere go here on top. Remember the relationship is that for everyone atmosphere it's 760mm of mercury. So when we do that we're going to get a pressure of 0.789 atmospheres.

Although 600 has one sick figs, let's just go with three sig figs here just so that we don't have just .8 as atmospheres. Next volume volume needs to be in liters, so we have 500 milliliters. And remember 11 milli equals 10 to the -3. So this would just come out as oh point 500 liters. Next we need moles. So moles is N Remember nitrogen gas, nitrogen. It's natural or a standard state is N2. It's one of our diatomic molecules, so we're told that we have 2029 .3G of N2. We got to convert that into moles SO1 mole of N2.

So there's two nitrogens. According to the periodic table, each one is 14.01g, so multiplying that by two gives me 28.2g for the combined weight in north 2. So grams here cancel out and I'll have my moles here. We'll put it as 1.05 moles of N2 and then finally we need our temperature, ours our constant, so we don't have to worry about giving the correct units. It's 08206 like we said earlier, so temperature here needs to be in Kelvin. So remember to go from Celsius to Kelvin you're supposed to add 273.15. Sometimes professors will just say plus 273, but if you want to be as accurate as possible you want to put 273.15. So when you add that, that's three 23.15 Kelvin.

So here we have all of the units that we need in the correct forms. So just remember ideal gas law and what are the correct units that we need to utilize for each one of these variables?

The Ideal Gas Law

As we said, the ideal gas law uses R, which is our gas constant. But realize that the gas constant R can have two different values depending on the situation. Now, the two terms you'll tend to see when it comes to the R constant is the first one we talked about earlier, R being equal to 0.08206. We utilize this value when dealing with the ideal gas law, but R can also equal 8.314.

This happens when we're dealing with speed, velocity or energy. If a question is dealing with the speed of an object or a subatomic particle, or dealing with the energy of a reaction or solution, the R converts to 8.314. Now the conversion factor between the R groups is that one liter times atmospheres equals 101.325 joules. So we have our 0.08206. Here we use the conversion factor.

So remember we want to get rid of liters times atmospheres, so we put them on the bottom. So one liters times atmosphere on the bottom is 101.325 Joules. Here on top, liters times atmospheres cancel out and that's how we end up with joules at the end. When you plug this in you get a long string of numbers as 8.3147295 joules over moles times K, but we just focus on the 8.314 portion.

I know there's a seven there when you work it out completely, but to keep it simple, books were just listed as 8.314. So just keep in mind the gas constant can be two different numbers. And remember, with the ideal gas law we use this value and when dealing with speed, velocity or energy we use this value of 8.314.

The Ideal Gas Law Example 2

Here in this example question, it says how many moles of ammonia are contained in a 25 liter tank at 190�C and 5.20 atmospheres. All right, so they're asking me to find moles of ammonia, so that would be my N variable. They're giving me liters, so that would be volume. They're giving me degrees Celsius, which is temperature, and they're giving me atmospheres, which is a unit for pressure.

We can see that we have PV and NT, so we have the ideal gas law to deal with. And the variable that's missing, the one that we're looking for is moles. So all we have to do here is isolate moles, so divide both sides here by RT and then we're going to say here that moles equals PVRT. Pressure is already in atmosphere, so no need to convert. Then we're going to have here volume which is already in liters, so no need to convert.

Then we have our R constant, remember is 0.08206. And now that we know that we're using the ideal gas law, we have to use the units of liters times atmospheres over moles times K. Temperature, remember, has to be in Kelvin, so there is a little bit of converting here necessary. So we have 190�C, so add 273.15 to that and that'll give us 463.15 Kelvin.

So take those and plug it in. 463.15 Kelvin. So what cancels out? Atmospheres cancel out, liters cancel out, Kelvin cancels out, and you'll see that the only unit left are the moles that we need to find. So we're going to get initially 3.42050 moles. If we look back on the question, this has three sig figs, 2 sig figs, 3 sig figs. We go with the least number of sig figs, so we're going to put our answer as 3.4 moles of ammonia.

So this would be our final answer. So just realize what variables are you being given, what's the missing variable? Just use your algebra skills to isolate that one variable and you'll get your answer at the end.

How many grams of carbon dioxide, CO₂, are present in a 0.150 L flask recorded at 525 mmHg and 32 ºC?

• A. 1.77 g
• B. 0.93 g
• C. 0.66 g
• D. 0.18 g
• E. 0.052 g

How many liters of HNO₃ gas, measured at 28.0 ºC and 780 torr, are required to prepare 2.30 L of 4.15 M solution of nitric acid?

• A. 56 L
• B. 62 L
• C. 189 L
• D. 230 L
• E. 262 L

When 0.670 g argon is added to a 500 cm³ container with a sample of oxygen gas, the total pressure of the gases is found to be 1.52 atm at a temperature of 340 K. What is the mass of the oxygen gas in the bulb?

• A. 0.266 g
• B. 0.335 g
• C. 0.621 g
• D. 0.715 g
• E. 1.72 g

Here’s what students ask on this topic:

What is the ideal gas law?

The ideal gas law is a fundamental equation in chemistry and physics that describes the relationship between pressure, volume, temperature, and the number of moles of an ideal gas. It is usually expressed as:

P V = n R T

where P represents the pressure of the gas, V is the volume it occupies, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature of the gas in Kelvin.

This law combines several simpler gas laws, such as Boyle's law, Charles's law, and Avogadro's law, into one comprehensive equation. The ideal gas law assumes that the gas particles are point masses with no volume and that there are no intermolecular forces between them. While no real gas perfectly fits these assumptions, the ideal gas law provides a good approximation for the behavior of gases under many conditions, particularly at high temperatures and low pressures. It's a crucial tool for scientists and engineers in predicting and understanding the behavior of gases in various scenarios.

What is "R" in the ideal gas law?

In the Ideal Gas Law, represented by the equation PV=nRT, "R" is known as the gas constant or the ideal gas constant. It is a proportionality constant that relates the energy scale in physics to the temperature scale. The value of "R" depends on the units used for pressure, volume, and temperature. When using the SI unit system, where pressure is in pascals (Pa), volume is in cubic meters (m³), and temperature is in kelvin (K), the value of "R" is approximately 8.314 J/(mol·K). This means that for every mole of an ideal gas, there are 8.314 joules of energy per kelvin of temperature. The gas constant is derived from the combination of several fundamental constants and plays a crucial role in thermodynamics and physical chemistry.

When is the ideal gas law valid?

The ideal gas law, which is expressed as:

P V = n R T

where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, is most valid under conditions where the gas molecules do not interact significantly with each other, and the volume of the gas particles is much less than the volume of the container. This typically occurs at high temperatures and low pressures, where the gas molecules have enough kinetic energy to overcome intermolecular forces and behave independently.

At very high pressures or low temperatures, gases deviate from ideal behavior because the particles are closer together and intermolecular forces become significant. Additionally, at these conditions, the actual volume of the gas molecules is no longer negligible compared to the container's volume. Real gases under these conditions are better described by other equations of state, like the van der Waals equation, which take into account the size of molecules and the attraction between them.

What does the ideal gas law assume?

The ideal gas law assumes several key points about the gases it describes:

1. Gas Particles are Point Particles: The volume of the gas particles themselves is negligible compared to the volume of the container. This means that the particles are considered to have no volume.
2. Elastic Collisions: When gas particles collide with each other or with the walls of the container, the collisions are perfectly elastic. This means that there is no net loss of kinetic energy from these collisions.
3. No Intermolecular Forces: The particles do not exert any forces on each other except during collisions. That is, there are no attractive or repulsive forces between particles, which is a significant simplification compared to real gases.
4. Random Motion: The particles are in constant, random motion, and their velocities follow a distribution that depends on the temperature of the gas.
5. Uniform Distribution: The gas particles are uniformly distributed throughout the container, meaning the density of the gas is the same throughout.
6. Kinetic Energy and Temperature Relationship: The average kinetic energy of the gas particles is directly proportional to the absolute temperature of the gas.

The ideal gas law is a good approximation for many gases under a range of conditions, but it becomes less accurate at high pressures, low temperatures, or when the gas particles are very large or have strong intermolecular forces.

How can the ideal gas law be used?

The ideal gas law, expressed as PV=nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature, is a fundamental equation in chemistry and physics that describes the behavior of an ideal gas under various conditions. It can be used in several practical ways:

1. Calculating the Amount of Gas: If you know the pressure, volume, and temperature of a gas, you can use the ideal gas law to calculate the number of moles of the gas present.
2. Predicting Gas Behavior: By manipulating the equation, you can predict how a gas will respond to changes in pressure, volume, or temperature. For example, if you increase the temperature, you can predict either an increase in volume or pressure if the other is held constant.
3. Stoichiometry in Chemical Reactions: In reactions involving gases, the ideal gas law helps in determining the volumes of gases consumed or produced at a given pressure and temperature.
4. Molar Mass Determination: The ideal gas law can be rearranged to find the molar mass of a gas by measuring the gas's pressure, volume, and temperature.
5. Real Gas Behavior Estimation: Although real gases do not always follow the ideal gas law perfectly, the law can be used as