3.6 Deviation from Ideal Gas Law

Kanya Shah

Dalia Savy

AP Chemistry🧪

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In the real world, gases don’t always behave as defined by the kinetic molecular theory. Let's quickly review the five assumptions of the KMT:
1. There are no attractive or repulsive forces between gas particles.
2. The particles of an ideal gas are separated by great distances compared to their size (gas particles have negligible, or no, volume because of how small and spread apart particles are).
3. Gas particles move in random, constant, straight-line motion.
4. Collisions are elastic: when gas particles collide, they transfer energy without a net loss - no energy is lost.
5. When observing particles, their kinetic energy is directly related to their velocity (KE = 1/2mv^2). All gases have the same average kinetic energy at a given temperature.

When do gases deviate from the Ideal Gas Law?

Conditions of low temperatures and high pressures will cause gases to deviate from ideal gas behavior for the following reasons:

➡️⬅️Gas particles can become attracted to each other

When the gas particles are close together due to a large number of particles, this can cause more attractive forces. At low temperatures🌡️, gas particles move slower and spend more time around each other. This violates the first assumption of the KMT.
Polar molecules and larger molecules behave less ideally than smaller non-polar molecules. The IMFs between polar molecules and larger molecules can cause these gas molecules to exert attractive forces on one another.
🌟In other words, the pressure of real gases is usually lower than the pressure of ideal gases due to attractive forces. When particles are attracted to each other, IMFs become significant and the particles aren't hitting the walls of the container as often.

Gas particles can make up a significant portion of a gas sample's volume

At high pressure, as shown through Boyle's Law, the volume of the container decreases. When volume decreases, the volume of gas particles begins to be more significant. This can be shown visually:

🌟In other words, the volume of real gases is much higher than the volume of ideal gases.

Graphically

This graph shows how when you increase pressure, gases pretty quickly deviate from the Ideal Gas Law:

When we increase the pressure, PV/RT, should equal one (PV = nRT, and with 1 mol of ideal gas, PV = RT), but these gases deviate from one.

Correcting the Ideal Gas Law using the Van der Waals Equation

Since the traditional ideal gas law has been shown to have certain exceptions, chemists have created new equations to correct for intermolecular forces and for volumes that become significant. This is called the Van der Waals equation:
Woah! That equation looks really scary, but there are only a few things you need to know about this equation🥳:
1. You will NEVER have to use this equation on the AP exam to make calculations, you only need to know it conceptually. Don't even bother memorizing it.
2. All this does is makes corrections to the pressure and volume terms to make it so that at high pressures and/or low volumes, PV=nRT is corrected. That's why we're adding to P and subtracting from V.
1. The +a is used to correct the pressure since the pressure is lower in real gases
2. The -b is used to correct the volume since the volume is higher in real gases

Practice Question

In the last key topic, we went over the first three parts of #4 on the 2019 AP Chemistry Exam - FRQ Section. Now that we know about real gases, we can answer the 4th part:
1. The student measures the actual pressure of CO2(g) in the container at 425K and observes that it is less than the pressure predicted by the ideal gas law. Explain this observation.
This is what we just went over, and it all has to do with pressure and attractive forces!
Sample Response: The attractive forces between CO2(g) molecules result in a pressure that is lower than that predicted by the ideal gas law. Since the particles are attracted to each other, they aren't colliding with the walls of the container as often as ideal gases with no attractive forces would.

Diffusion and Effusion

Diffusion

Diffusion describes the mixing of gases. There are a few rules that you should memorize:
• As temperature increases, the rate of diffusion increases since the particles are moving faster🏃.
• The bigger the molecules, the slower the diffusion. This is because these molecules contain more mass and make slower movements.

Image Courtesy of Ideal Gas Law and the KMT

Effusion

Effusion is very similar to diffusion, but it describes the passage of gas through a tiny space into a vacuum space. Basically, the gases are flowing from a space with higher pressure to a space with lower pressure through a pinhole.

Image Courtesy of Ideal Gas Law and the KMT

Same rules for effusion: temperature increases the rate of effusion while a higher mass decreases the rate of effusion. The only difference is that the rate of effusion represents the speed at which the particles are transferred into the vacuum.

Graham's Law of Effusion

Graham's law of effusion states that the rate at which a gas effuses, or escapes, through a small pole is inversely proportional to the square root of its molecular weight:
where
• Rate1 represents the rate of effusion of the first gas
• Rate2 represents the rate of effusion of the second gas
• M2 represents the molar mass of the second gas
• M1 represents the molar mass of the first gas
Graham's law is based on part of the kinetic molecular theory: the rate at which a gas effuses is related to the average kinetic energy of its molecules. Since the molecular weight of a gas is a measure of the mass of its molecules, Graham's law states that the lighter the gas, the faster it will effuse.
It is best to put the lighter gas as gas 1 (rate 1 / m1), and then in your explanation, you could state that the rate of gas 1 is __ times as fast as gas 2.
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