Gas Phase

What is an ideal gas?

The ``perfect gas.'' Ideal gases are characterized as having the following properties:

• Consisting of identical particles with negligible volume
• Undergoing perfectly elastic collisions
• Exhibt no intermolecular forces
• Store zero intramolecular energy

In reality though, real gases do not have any of these properties, but the assumption of ideal gases is made for day-to-day calculations.

How do real gases differ from ideal gases?

1. Qualitatively, gases change their ÒqualityÓ or nature under different conditions, e.g. the attractive forces between gas molecules lower the overall pressure of the gas, and at low temperatures, gases can change phases into liquids or sometimes even solids, resulting in even stronger forces than in ideal gases.
2. Quantitatively, gases have volume and exhibit intermolecular forces: The Van der WaalsÕ equation takes into account the ÒrealnessÓ of gases by adapting the ideal gas law to take into account (i) intermolecular forces and (ii) volume.
3. The collisions are not necessarily elastic.

What is the ideal gas law?

$$PV=nRT$$ (35.1)

Just like the date of the MCAT, this should be scored into your brain. Seriously though, the manipulations of this formula are incredibly powerful and allow you to make some important calculations.

What is Boyle's law?

$$P_{1}V_{1}=P_{2}V_{2}$$ (35.2)

One variation of the gas law which states that pressure and volume are inversely related at constant temperature. That is, at a constant temperature, pressure and volume will ``compensate'' for each. This makes sense: High pressure leads to small volume; conversely, low pressure leads to high volume.

Figure 34.1: Boyle's Law.

What is Charles' law?

$$\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}$$ (35.3)

Another variation of the ideal gas law which states that, at constant pressure, temperature and volume are directly related. This makes sense: Hotter gases will take up a large volume. Conversely, cooler gases are denser and take up less volume. Just an aside, colder air is more efficient in combustion. Because colder air is in fact denser, you get more ``bang for your buck'' because there are more O$_{2}$ molecules per unit volume. Therefore, jets taking off on winter days can create more thrust, get into the air quicker and can get away with using a shorter runway.

Figure 34.2: Charles' Law.

What is Avogadro's principle?

$$\frac{n_{1}}{V_{1}}=\frac{n_{2}}{V_{2}}$$ (35.4)

Another variation of the gas law that shows that volume is directly related to the number of moles of gas at constant pressure and temperature. Therefore, the more moles of a gas you have, the more volume the gas takes up.

Figure 34.3: Avogadro's Law.

In summary, what are the three gas laws and what is held constant in each?

Table 34.1: Side-by-side comparison of the gas laws.

	Boyle's Law	Charles' Law	Avogadro's Principle
Law:	$P_{1}V_{1}=P_{2}V_{2}$	$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$	$\frac{n_{1}}{V_{1}} = \frac{n_{2}}{V_{2}}$
Holding constant:	Temperature	Pressure	Pressure
			Temperature

What are partial pressures of gases?

The pressure exerted by a particular gas in a vessel containing more than one gas.

How does partial pressure relate to moles?

In a given vessel, the total moles present of all the gases can be correlated to the total pressure of all the gases present. Further, the mole fraction - the moles of one gas over the total moles of all gases - can be correlated to the partial pressure of the gas:

$$Mole \ fraction \ of \ Gas \ A = \frac{Moles \ of \ Gas \ A}{Total \ moles \ of \ all \ gases}$$ (35.5)

$$Partial \ pressure \ of \ Gas \ A = \frac{Pressure \ of \ Gas \ A}{Total \ pressure \ of \ all \ gases}$$ (35.6)

Therefore, since we are dealing with proportions, you can use these proportions to find the individual pressure of a gas when given only moles of the gases and the total pressure of a system:

Take the mole fraction of the gas and multiply it by the total pressure of all the gases:

$$\left(Mole \ fraction \ of \ Gas \ A\right)\left(Total \ pressure \ of \ all \ gases\right) = Pressure \ of \ Gas \ A$$ (35.7)

Again, since we are dealing with proportions, this can be interchanged to find the mole fraction of Gas A given the total moles of a gas and partial pressure of gas A.

What is Dalton's law of partial pressures?

Law 1   The total pressure of a gas mixture is the sum of the partial pressures of each gas in a given vessel.

$$P_{Total} = p_{1} + p_{2} + \ldots.. + p_{n}$$ (35.8)

Figure 34.4: Dalton's Law of Partial Pressures: In this example, there is a mixture of three gases. Each gas contributes to the overall mixture in a 4$_{Gas \ A}$:3$_{Gas \ B}$:3$_{Gas \ C}$ ratio totaling 10. The number designation is arbitrary and is used to illustrate the point of ``parts of a whole.'' When it comes to doing your own calculations, the same methodology can be applied using the appropriate units.

What main assumption is made with Dalton's law of partial pressure?

Each gas in the vessel does not react with any other gas and can be treated as an independent member of the vessel.

What is the basis of the kinetic theory of gases?

A theory that explains the macroscopic properties of gases based on their microscopic (molecular) properties.

What are four assumptions of the kinetic molecular theory?

1. Gas molecules are in constant, random motion.
2. Collisions between gas molecules are elastic, i.e. there is no loss of kinetic energy due to the collision.
3. The total volume of the gas molecules is negligible compared to the volume of the container.
4. The force of attraction between molecules is negligible.

These assumptions should seem similar to the ideal gas law. Again, memorize these or at least understand them.