Chemistry 103A; Sections 5, 6, 7, 8; Lecture 34, 15 Nov 00

Recall:

We were talking about:

The Ideal Gas Law

Going back to the combined gas law

it was easily seen from experiments that the constant in this equation depended on the quantity of gas. In fact, the constant is proportional to the number of moles, n, of gas. If we call the proportionality constant R, we get
The latter of these two equations is known as the ideal gas law. (There are logical reasons why this equation should be called the "perfect gas law," and it was called this for a while, but the name "perfect gas law" has lost favor in recent times. We will call it simply the ideal gas law or the ideal gas equation of state.)

("The ideal gas equation of state" is a more accurate name for this equation because the equation provides a relationship between the state variables p, V, T, and n. We can't pick arbitrary values for these four variables. If we select the values of any three variables the fourth is fixed by the equation. Solids and liquids have, in principle, an equation of state. One of the goals of a theory of liquids would be to provide the equation of state for the liquid.)

It is easy to see that the ideal gas law contains all of the gas laws we have already discussed. It also contains some that we have not discussed.

For example:

In Boyle's law temperature is held constant. If take the ideal gas law and keep all the constant quantities (n, R, and T) on the right-hand side and all the variable quantities (p and V) on the left-hand side we get Boyle's law,  


To get the combined gas law, leave the constants (n and R) on the right-hand side and move T to the left-hand side with the other variables, p and V, to get

 
which is the combined gas law.

The constant R is called the "gas constant," or sometimes the "universal gas constant." It is expressed is several different set of units.

R = 0.0820578 Latm/Kmol

= 0.0831451 Lbar/Kmol

= 8.31451 J/Kmol.

(It may seem surprising that Latm has the same units as J, namely energy. 1 Latm = 101.325 J It is an instructive exercise for you to convince yourself that a volume times a pressure has the same units as energy.)

In this course we will mostly use R = 0.082578 Latm/Kmol. If you go on to take Physical Chemistry you will use mostly R = 8.31451 J/Kmol.
 
 

Gas Density

The ideal gas law can be written in terms of the density of the gas. Recall that the number of moles of a substance is given by (writing the mass of the gas as m)

Then the ideal gas law becomes,
which rearranges to give,
From this equation we see that the density of a gas is proportional to the pressure and to the formula weight of the gas and inversely proportional to the absolute temperature.
 

The ideal gas law provides a method for measuring the formula weight of a gas. This can be done in two (related) ways. If we rearrange the above equation for density we can solve it directly for the formula weight,

Or we can go back to a previous equation,
and rearrange it to get the formula weight in terms of m, V, p, and T,
Example:
0.107 g of a compound of C, Cl, and F gives a pressure of 21.3 Torr at 25.0oC when placed in a flask of volume of 458 mL. What is the formula weight of the compound?

If the empirical formula is CCl2F, what is the molecular formula of the compound?


Standard Temperature and Pressure (STP)

It is very common to define 0oC and 1 atm pressure as standard temperature and pressure, abbreviated "STP."

The reason for this is that it doesn't make any sense to compare volumes of gases unless the gases being compared are at the same temperature and pressure.

The volume of 1.00 mol of an ideal gas at STP is easy to calculate to be 22.4 L.
 

Stoichiometry of Gases

We can do stoichiometry with gases. We use the same "road map" as in our previous stoichiometry problems. We just have to add our method for going from volumes to moles, namely,

The rest of the stoichiometric calculation is the same as before. For example, we use the same "reaction fraction."
 
 

Gas Mixtures, Partial Pressures, and Dalton's Law

In a mixture of gases we speak of the total pressure of the gas mixture and the "partial pressures" of the individual gases in the mixture.

The partial pressure of a gas in a mixture is defined as the pressure the gas would have (at the same temperature and in the same volume) if all the other component gases were removed leaving only the one gas. For example, consider a sealed box containing air. Air is a mixture of gases containing mostly N2 and O2, with a little bit of Ar, CO2, some water vapor, and traces of other gases like He, Ne, H2S, etc.

Imagine that we have some kind of very special pump that allows us to pump selected gases out of the box, leaving unselected gases alone.

Now pump out the N2, then the Ar, then the CO2, then the water vapor and then all the other trace gases like He, Ne, and etc. The only gas remaining in our box is the O2. The pressure in the box after all the gases except O2 are pumped out is, by definition the partial pressure of O2.

Dalton's law of partial pressures says that the total pressure of a gas mixture is the sum of all the partial pressures of all the gases in the mixture. If we number the gases as gas 1, gas 2, gas 3, and so on then,

p = p1 + p2 + p3 + . . . .
We can derive Dalton's law from the ideal g as law. Note that the n in
doesn't have any information about the identity of the gas and the equation is the same regardless of the identity of the gas. There is no reason why n couldn't be the sum of the number moles of each component in a gas mixture.

That is,

n = n1 + n2 + n3 + . . . .
If we place this n into the ideal gas law we get,
which is Dalton's law.

Example,

What is the total pressure of a mixture of He and O2 where the partial pressures are 0.800 atm and 0.198 atm respectively?