1. Ideal Gas Law

2. Combining Relationships
Science often relies on a controlled experiment.
Hold all variables fixed except one
Measure change in another property
Gas laws were each made with all but two properties constant.
Combine those three laws into a single relationship.

3. Counting Atoms + = Adding atoms increases the volume of a gas.
Twice the air in a balloon doubles the volume
Constant pressure and temperature
Try a relationship: + =

4. Mass Independent Density is mass divided by volume.
Mass in an equation can be converted to density
PV=amT becomes P = arT
Experimentally a would vary for each type of gas
Constant is the same if the number of molecules N is counted instead of the mass m.

5. Ideal Gas Law I
The equation of state links pressure, volume, temperature, and amount of gas.
This is an ideal gas law, since real gases may vary slightly.

6. Boltzmann’s Constant The constant k applies to all gases.
It’s called Boltzmann’s constant.
k = 1.38 x J/K
Dimension links temperature and energy

7. The Mole Boltzmann’s constant has a very small value.
There are a vast number of atoms in a macroscopic system
Define a fundamental unit to count large numbers
The mole (mol) is a unit of amount.
Number of carbon-12 atoms in g
Amount of molecules equal to Avogadro’s number
NA = x 1023

8. Ideal Gas Law II The amount of gas can be measured in moles.
n = N / NA
R is the universal gas constant
R = NA k
R = J / mol-K

9. Mole Size
Standard temperature and pressure (STP) is 0 C and 1 atm = x 105 Pa.
What is volume of one mole?
Convert temperature to K.
T = = K
Use the molar form of the ideal gas law.
V = nRT/P
Substitute values:
V = (1.000 mol)(8.314 J/mol-K)( K) / (1.013 x 105 Pa)
V = x 10-2 m3 = L
next