An ideal gas is defined as a gas in which the molecules can be considered as "point masses" thereby taking up negligible volume compared to the volume of the container. No significant forces, intermolecular interactions, exist between the molecules except during collisions which are considered to be perfectly elastic. All real gases that are far removed from conditions at which they condense, low temperatures or high pressures, display nearly ideal behavior.
Avagadro's Number: NA = 6.022 x 1023
The number of carbon atoms in 12 grams of a sample of carbon-12 is called
Avogadro's number, NA,
which equals
6.022 x 1023 molecules. A mole of any substance contains Avagadro's number of particles.
Ideal Gas Law:
PV = nRT
where
- P is the pressure measured in Pa = N/m2 (1 atm = 1.013 x 105 Pa)
- V is the volume measured in m3
- n is the amount of gas present measured in moles
- T is the temperature measured in K
- R is the ideal gas law constant: 8.314 J/mole K (0.0821 atm L/mole K)
Combined Gas Law:
where
- P1, V1, n1 and T1 are the initial values
- P2, V2, n2 and T2 are the final values
When selected quantities are held constant then this law can be restated as three others.
|
Boyle's Law
|
temperature and the amount of gas present
held constant
|
|
|
|
Charles' Law
|
pressure and the amount of gas present
held constant
|
|
|
|
Guy-Lussac's Law
|
volume and the amount of gas present
held constant
|
|
|
Some fundamental relationships
Often in determining the amount of gas present in moles (n), you need be familiar with the following relationships between Avogadro's number (N A), the amount of mass present (m), molecular mass (N), and the mass of a single molecule (  ). The relationship between N, n, and NA is N = nNA
- n is measured in moles
- N equals the number of molecules present in the sample
This relationship let's us rewrite the ideal gas law as:
PV = (N/NA) RT
PV = N (R/NA) T
PV = NkBT where kB is Boltzmann's constant, 1.38 x 10-23 J/K. The relationship between m, n and M is m = nM
- m is the mass present in the sample in grams or kilograms
- M is the molar mass in grams or kilograms
- n is the number of moles
The relationship between m, N and  is
m =  N
- m is the mass present in the sample in grams or kilograms
- N is the total number of molecules present in the sample
-
 is the mass of a single molecule in grams or kilograms
The relationship between M, N A and  is
M =  NA
- M is the molar mass in grams or kilograms
- NA is Avagadro's number of molecules present a mole
-
 is the mass of a single molecule in grams or kilograms
Now let's take some time and practice several problems that will allow you to become familiar with these formulas. |