Learn how pressure, volume, temperature, and the amount of a gas are related to each other.
What is an ideal gas?
Gases are complicated. They're full of billions and billions of energetic gas molecules that can collide and possibly interact with each other. Since it's hard to exactly describe a real gas, people created the concept of an Ideal gas as an approximation that helps us model and predict the behavior of real gases. The term ideal gas refers to a hypothetical gas composed of molecules which follow a few rules:
Ideal gas molecules do not attract or repel each other. The only interaction between ideal gas molecules would be an elastic collision upon impact with each other or an elastic collision with the walls of the container.
The phrase elastic collision refers to a collision wherein no kinetic energy is converted to other forms of energy during the collision. In other words, kinetic energy can be exchanged between the colliding objects (e.g. molecules), but the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
A car crash where kinetic energy gets converted into heat energy and sound energy yielding two crumpled bumpers would not be elastic.
Ideal gas molecules themselves take up no volume. The gas takes up volume since the molecules expand into a large region of space, but the Ideal gas molecules are approximated as point particles that have no volume in and of themselves.
If this sounds too ideal to be true, you're right. There are no gases that are exactly ideal, but there are plenty of gases that are close enough that the concept of an ideal gas is an extremely useful approximation for many situations. In fact, for temperatures near room temperature and pressures near atmospheric pressure, many of the gases we care about are very nearly ideal.
If the pressure of the gas is too large (e.g. hundreds of times larger than atmospheric pressure), or the temperature is too low (e.g. ) there can be significant deviations from the ideal gas law. For more on non-ideal gases read this article.
What is the molar form of the ideal gas law?
The pressure, , volume , and temperature of an ideal gas are related by a simple formula called the ideal gas law. The simplicity of this relationship is a big reason why we typically treat gases as ideal, unless there is a good reason to do otherwise.
Where is the pressure of the gas, is the volume taken up by the gas, is the temperature of the gas, is the gas constant, and is the number of moles of the gas.
are a way to describe how many molecules are in a gas.
is equal to . This number is called Avogadro's constant and it's a way to convert from to or vice versa.
For a typical room there is likely to be at least of gas molecules. That's an almost unthinkably high number of molecules since,
This is far larger than the estimated number of stars in the Milky Way galaxy, and is even larger than most estimates of the number of stars in the observable universe.
Perhaps the most confusing thing about using the ideal gas law is making sure we use the right units when plugging in numbers. If you use the gas constant then you must plug in the pressure in units of , volume in units of , and temperature in units of .
If you use the gas constant then you must plug in the pressure in units of , volume in units of , and temperature in units of .
This information is summarized for convenience in the chart below.
Units to use for | |
---|
Pressure in | Pressure in | |
Volume in | volume in | |
Temperature in | Temperature in | |
Here is some useful information relating the different types of units.
To convert into we can use the formula .
Also, the term STP refers to "standard temperature and pressure" which are defined to be and respectively.
What is the molecular form of the ideal gas law?
If we want to use instead of , we can write the ideal gas law as,
Where is the pressure of the gas, is the volume taken up by the gas, is the temperature of the gas, is the number of molecules in the gas, and is Boltzmann's constant,
When using this form of the ideal gas law with Boltzmann's constant, we have to plug in pressure in units of , volume in , and temperature in . This information is summarized for convenience in the chart below.
Units to use for | |
---|
Pressure in | |
Volume in | |
Temperature in | |
What is the proportional form of the ideal gas law?
There's another really useful way to write the ideal gas law. If the number of moles (i.e. molecules ) of the gas doesn't change, then the quantity and are constant for a gas. This happens frequently since the gas under consideration is often in a sealed container. So, if we move the pressure, volume and temperature onto the same side of the ideal gas law we get,
This shows that, as long as the number of moles (i.e. molecules) of a gas remains the same, the quantity is constant for a gas regardless of the process through which the gas is taken. In other words, if a gas starts in state (with some value of pressure , volume , and temperature ) and is altered to a state (with , volume , and temperature ), then regardless of the details of the process we know the following relationship holds.
This formula is particularly useful when describing an ideal gas that changes from one state to another. Since this formula does not use any gas constants, we can use whichever units we want, but we must be consistent between the two sides (e.g. if we use for , we'll have to use for ). [Temperature, however, must be in Kelvins]
What do solved examples involving the ideal gas law look like?
Example 1: How many moles in an NBA basketball?
The air in a regulation NBA basketball has a pressure of and the ball has a radius of . Assume the temperature of the air inside the basketball is (i.e. near room temperature).
a. Determine the number of moles of air inside an NBA basketball.
b. Determine the number of molecules of air inside an NBA basketball.
We'll solve by using the ideal gas law. To solve for the number of moles we'll use the molar form of the ideal gas law.
Given this choice of gas constant, we need to make sure we use the correct units for pressure (), volume (), and temperature ().
Yes, we could have used the gas constant . We would have just had to be careful to plug in pressure in terms of and volume in terms of .
We can convert the pressure as follows,
.
And we can use the formula for the volume of a sphere to find the volume of the gas in the basketball.
The temperature can be converted with,
. .
Now we can plug these variables into our solved version of the molar ideal gas law to get,
Now to determine the number of air molecules in the basketball we can convert into .
Alternatively, we could have solved this problems by using the molecular version of the ideal gas law with Boltzmann's constant to find the number of molecules first, and then converted to find the number of moles.
Example 2: Gas takes an ice bath
A gas in a sealed rigid canister starts at room temperature and atmospheric pressure. The canister is then placed in an ice bath and allowed to cool to a temperature of .
Determine the pressure of the gas after reaching a temperature of
Since we know the temperature and pressure at one point, and are trying to relate it to the pressure at another point we'll use the proportional version of the ideal gas law. We can do this since the number of molecules in the sealed container is constant.
Notice that we plugged in the pressure in terms of and ended up with our pressure in terms of . If we wanted our answer in terms of we could have plugged in our pressure in terms of , or we can simply convert our answer to as follows,
FAQs
The ideal gas law states that PV = NkT, where P is the absolute pressure of a gas, V is the volume it occupies, N is the number of atoms and molecules in the gas, and T is its absolute temperature.
What is ideal gas law in your own words? ›
This empirical relation, formulated by the physicist Robert Boyle in 1662, states that the pressure (p) of a given quantity of gas varies inversely with its volume (v) at constant temperature; i.e., in equation form, pv = k, a constant.
What is the ideal gas law quizlet? ›
The Ideal Gas Law. PV=nRT. The Ideal Gas Law. The product of the pressure and volume of an ideal gas is proportional to the number of moles of the gas and its absolute temperature.
What is the ideal gas law summary? ›
The ideal gas law states that for a specific amount of gas, the product of pressure and volume is directly proportional to the absolute temperature. The ideal gas law states that all gases contain the same number of gas molecules when under equal temperature, volume, and pressure.
What is an ideal gas answer? ›
An ideal gas is a theoretical gas with zero inter-molecular force between many randomly moving point particles. Point particles are point mass with negligible volume.
What does the ideal gas law best describe? ›
The ideal gas law is an equation demonstrating the relationship between temperature, pressure, and volume for gases (see Graph. The Ideal Gas Law). These specific relationships stem from Charles's, Boyle's, and Gay-Lussac's laws.
What best summarizes the ideal gas law? ›
The ideal gas law is summarized by the equation PV = nRT, which relates the pressure, volume, temperature, and amount of a gas under ideal conditions.
What is ideal gas law in real? ›
According to the ideal gas law, if the temperature and amount of gas are held constant, an increase in volume will cause a decrease in pressure, and vice versa. This is because the molecules have more (or less) space to move, impacting the frequency of collisions with container walls, which defines pressure.
What is ideal gas equation in brief? ›
The ideal gas equation is formulated as: PV = nRT. In this equation, P refers to the pressure of the ideal gas, V is the volume of the ideal gas, n is the total amount of ideal gas that is measured in terms of moles, R is the universal gas constant, and T is the temperature.
When gas acts as ideal gas? ›
A real gas behaves like an ideal gas at higher temperature and lower pressure, as the potential energy due to inter-molecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them.
The molecules of an ideal gas behave as rigid spheres. All the collisions are elastic. The temperature of the gas is directly proportional to the average kinetic energy of the molecules. Pressure occurs due to the collision between the molecules with the walls of the container.
What is the ideal gas law in words? ›
noun. , Physics. the law that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the absolute temperature of the gas and the universal gas constant.
Why is the ideal gas law important? ›
The ideal gas equation is a valuable tool that provides a decent approximation of gases at high temperatures and low pressures.
What does ideal gas law teach? ›
Ideal Gas Law Role-Play: Students can role-play as atoms. Create a “gas container” with tape on the floor and ask students to move within the space. As you change the volume (size of the container), pressure (number of students), or temperature (speed of the students) changes.
What is the real gas ideal gas law? ›
An ideal gas is a theoretical gas composed of many randomly moving particles that are not subject to interparticle interactions. A real gas is simply the opposite; it occupies space and the molecules have interactions. This results in PV always equaling nRT.
How to solve PV nRT for N? ›
Simply use cross-multiplication to solve for n. Since the equation is PV = nRT, divide both sides by the R & T and you end up with n = PV/RT, which is actually none of the 4 choices.