Рівняння ідеального газу: $PV=nRT$

Ideal Gas Law

• A gas law created by Benoît Paul Émile Clapeyron.

• He was a French physical chemist. He made huge contributions to thermodynamics. He is also known for the Clausius-Clapeyron equation and for formulating the second law of thermodynamics.

• A gas law that combines Charles’s Law, Boyle’s Law, Gay-Lussac’s Law, Avogadro's Law, and the Combined Gas Law.

What is an Ideal Gas?

• An Ideal gas, obeys the assumptions of the kinetic molecular theory.

• In an ideal gas, we assume the particles have no volume. The volume of the system is much larger than the volume of the atoms or molecules. So, we assume the gas volume is negligible. The gas fills the container and has empty space between gas molecules. That means they are expandable and compressible.

• The gases do not experience any intermolecular forces. The gas particles move and collide, but do not interact/affect each other in any way.

• The gas particles always move in a straight line. They only change direction when they collide with their container or another particle.

• Collisions between gas particles are perfectly elastic. So, the kinetic energy is conserved.

• The average kinetic energy corresponds to the temperature in Kelvin. Absolute zero is the temperature where molecular motion stops.

What is the Ideal Gas Law?

• 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 equation is: $PV=nRT$

• The ideal gas law states that all gases contain the same number of gas molecules when under equal temperature, volume, and pressure. That's why one mole of any gas fills a volume of 22.4 liters at STP. (Note: This does not mean that the gases have equal masses!)

Ideal Gas Law Units Cheat Sheet:

Ideal Gas Law Practice Problem Walkthrough:

At what pressure would 3.5 moles of hydrogen gas have a temperature of 700K and a volume of 100L?

1) Identify the variables.

• Pressure = ?

• Temperature = 700 K

• Volume = 100L

• Number of moles of gas = 3.5 moles

2) Identify the correct R-value.

• In this case, we have liters for the volume, so we should use the corresponding R-value. That's $R =0.082\frac{L\cdot atm}{K\cdot mol}$

3) Plug values into the Ideal Gas Law equation and solve for the missing variable.

• PV = nRT

• $P\left(100\right)=\left(3.5\right)\left(0.082\right)\left(700\right)$

• $P=\frac{\left(3.5\right)\left(0.082\right)\left(700\right)}{100}$

• P = 2.009 atm

Now try a practice problem!

(Video) The Ideal Gas Law: Crash Course Chemistry #12

by CrashCourse

In this video, Hank Green goes over the ideal gas law. This law can be proven experimentally, mathematically, and theoretically. If you've already learned the other gas laws, you'll see that they can all be derived from the same equation, $PV = nRT$.

Ideal Gas Law