Ideal Gas Law

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.

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: + =

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.

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.

Boltzmann’s Constant The constant k applies to all gases. It’s called Boltzmann’s constant. k = 1.38 x 10-23 J/K Dimension links temperature and energy

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 12.00 g Amount of molecules equal to Avogadro’s number NA = 6.022 x 1023

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 = 8.314 J / mol-K

Mole Size Standard temperature and pressure (STP) is 0 C and 1 atm = 1.013 x 105 Pa. What is volume of one mole? Convert temperature to K. T = 0 + 273.15 = 273.15 K Use the molar form of the ideal gas law. V = nRT/P Substitute values: V = (1.000 mol)(8.314 J/mol-K)(273.15 K) / (1.013 x 105 Pa) V = 2.242 x 10-2 m3 = 22.42 L next