I. So just what is a real gas?
In your lifetime, you will probably never encounter a gas that was not behaving in an ideal manner. Nevertheless, not all gases are ideal. To be an ideal gas, the following two assumptions must be valid. If one or both of these assumptions is invalid, the gas ceases to be an ideal gas.
1. The space the gas molecules occupy is insignificant when compared with the space in between the gas molecules.
Think of it this way. Imagine a gymnasium that is empty, except for one marble that is lying discarded in one corner. Someone asks you to calculate the volume of air inside the gymnasium. You measure the height, width, and length of the walls, multiply them together, and come up with a good approximation for the volume of air in the room. Technically, you should now subtract the volume of the marble, but who really cares since the marble is so small compared to the gym? The same principle is true of gases. Yes, the gas molecules, themselves, have volume, but that volume is SO tiny compared to the volume in between gas molecules that it really doesn't matter.
2. Intermolecular forces between gas molecules are negligible. On the face of it, this assumption seems rather problematic, since all compounds are capable of attracting other compounds (see intermolecular forces for details). Nevertheless, gas molecules are moving so rapidly that they generally zip past each other before having time to be either attracted or repelled by other nearby gas molecules. Therefore, in general, even if gas molecules are theoretically very attractive/repulsive to each other, it doesn't matter because they move past ecah other too quickly to feel it, and thus the assumption is almost always valid.
II. When is a gas not an ideal gas?
If either (or both) of the above asusmptions are invalid, a gas is not ideal. In general this occurs in two situations:
1. Extremely high pressures
2. Extremely low temperatures
At extremely high pressures, the first assumption of ideal gases fall apart. If you pack gases under enormous pressure, the space between them becomes fairly small. It's like filling the gymnasium up with several million marbles. Now you can no longer afford the luxury of ignoring them.
At extremly low temperatures, gas are moving (relatively) much slower. So slow, in fact, that they no longer zip past each other too rapidly to notice any attractions or repulsions that might exist. Now they feel them. And thus assumption number two falls apart.
III. So if a gas isn't ideal, what is it?
A gas which is not ideal is called a Real Gas. Real gases behave slightly differently than ideal gases. For our purposes, the main drawback of a real gas is that you can NOT use the ideal gas equation. This equation only holds true for ideal gases. There is a separate equation for real gases (actually, there are several), but they are much more complicated, and involve calculus, which typically frightens most students off. General chemistry will therefore stick to ideal gases.
IV. What is the ideal gas equation?
Put simply, its PV=nRT. This equation, although deceptively simply, is enormously important in its ability to link together all the fundamental properties of gases. T stands for Temperature, and must always be measured in Kelvin (take note! It is a very common mistake to get an incorrect answer because the temperature was plugged into the equation in degrees C instead of K). n stands for "number of moles," and not surprisingly, is measured in moles. V is the volume, and is usually measured in liters (L). P is pressure, and is often measured in atmospheres (atm), but can also be measured in Pascals. R is the ideal gas constant. It is not a variable, and never changes.
Note: A thorough understanding of moles is required to effectively use the ideal gas equation.
V. If R is a constant, how come my textbook gives two different values for it?
Although R is always the same number, it is sometimes convenient to express it in a different untis. For example a person can be six feet tall or 72 inches tall--it is the same number, just expressed differently in different units. R is usually expressed in one of two ways, and is dependent on which set of units you use for pressure. If you used Pascals for your pressure units, R becomes 8.3145 J/K mol. If you used atmospheres (the more common approach), R is 0.08026 L atm/K mol.
VI. I used the ideal gas equation, but got an incorrect answer. Where did I go wrong?
There's a lot of potential mistakes you could have made, but here are the common ones that you should always check for if you have time.
1. Using the wrong R value.
2. Using Celsius instead of Kelvin for the Temperature.
3. Using the number of grams instead of the number of moles for n.
4. Using torr (or mm Hg) for the pressure instead of atm or Pascals.
VII. Where does the ideal gas equation come from?
The idela gas equation is actaully a combination of several different gas laws. Robert Boyle, in the seventeenth century, observed that pressue was inversely related to volume. This, when you think about it, makes perfect sense. If you compact a balloon down to a smaller volume, the pressure on the inside of the balloon increases. In other words, PV= constant. This became known as Boyle's Law.
Jacques Charles related temperature and volume. He noticed that as the temperature of a gas increased, the volume increased (this is assuming pressure is kept constant). This also makes senses, since you have probably observed in every day life that hot things tend to expand. In other words, V= constant x T.
Avogadro made, perhaps, the most obvious correlation by linking n with V. He showed that as the number of moles increased, the volume they occupied increased. Again, this makes perfect sense. The more of anything you have, the more space it will require. In other words, V= constant x n.
The ideal gas law is simply an amalgamation of these three observed principles.
VIII. Where does the identity of the gas figure into the ideal gas equation?
Actually, it doesn't. Notice that of the four variables, P, T, V, and n, none of them depend whasoever on the identity of the gas. We could be talking about hydrogen or helium of radon or whatever, and it doesn't matter. One manifestation of this is that one mole of any gas--no matter what that gas is--will occupy the same amount of space. It doesn't matter if we're talking about a big gas (like radon) or a small one (like hydrogen) because the first assumption of an ideal gas is that its volume doesn't matter. Furthermore, it doesn't matter if we're talking about a polar or non-polar gas, because the second assumption dictates that attractions/repulsions are neglible anyway. So the identity of the gas is irrelevant as far as the ideal gas equation is concered.
IX. What's a molar volume?
It's the amount of volume that one mole of a gas occupies. For all ideal gases, this is the same number, no matter what gas you are talking about: 22.4L. A real gas would behave somewhat differently, and--if the awful truth is known--even some ideal gases deviate a little bit (cardon dioxide, for example, bucks the law and occupies 22.3L just to be different), but if such differences exist, they are small and can be safely ignored by a general chemistry student.
1. Calculations where one variable is missing.
These are arguably the easiest of the ideal gas equations, and are usually phrased as follows: "A gas cylinder of volume __ contains __ moles of an ideal gas at __ temperature. What is the pressure inside the cylinder." Alternatively, they may give you T, P, and n, and ask for V, or any combination thereof. For this type of question, you have three of the four variables, and simply need to solve for the fourth. It's a simple plug-and-chug situation. Write down "PV=nRT" and fill in the things that you know (R, mercifully, will always be soemthing you know) and then solve for the one that's still missing. I strongly recommend keeping track of units as you do this, since this is the most common student mistake.
Example: 1.12 moles of neon gas are placed in a 5.0L vessel, and the pressure is measured to be 749 torr. What is the temperature of the gas inside the cylinder?
Answer: We know n, P, and V from the question, and simply need to solve for T. The only trick is getting the units right. The pressure was given to you in torr. It is generally a good idea to convert this to atm straight away (760 torr= 1 atm). In this case, 749 torr is 0.986 atm. Also, be sure to use the correct R value (in this case, use 0.8206 since we are working with atmospheres) So . . .
PV=nRT
(0.986 atm)(5.0L) = (1.12 moles) (0.08206 L atm/K mol) (T)
58.64 K= T
In the correct number of sig figs, this becomes merely 59 K.
2. Calculations where two variables are changed.
In this scenario, there is a "before" and "after" situation. Two of the varibles are kept constant, and two are changed. The best way to solve these problems is to "group" the things that change on one side of the equation, and the things that don't change on the other side.
Example: A box containing a sample of gas at 1.00 atm is heated from 270K to 300K. What happens to the pressure inside the box?
Answer: the volume of the box (V) and the number of moles inside the box have not changed. The temperature and the pressure have changed. So re-write PV=nRT rearranged such that these two sets are grouped on either side . . . P/T = nR/V. Now, since the entire expression nR/V does not change, P/T for the "before" situation must equal P/T for the "after" situation. So . . .
(1.00 atm)/(270K) = (P)/(300K)
1.11atm = P
Pause to consider this. Does this answer make sense. You have raised the temperature, and as a result the pressure has gone up? A quick glance at the ideal gas equation vindicates this. A rise in temperature must correspond with a rise in pressure (if everything else is kept the same).