Ideal Gas

Gas Expansion For small changes in volume, gas acts like a liquid. Air (1 atm) b = 3400 x 10-6 C-1 For a 40 C change this would be a 14% volume change. Not a small fraction of the total

Boyle’s Law Experimental observations show that the volume of gas is inversely proportional to the pressure. Fixed temperature Use absolute pressure, not gauge pressure Named after Robert Boyle who observed it in the 17th century.

Charles’ Law Pressure and mass can be kept constant for a gas. The gas then does behave in a very linear way Volume and temperature Named after Jacques Charles who observed it in the 18th century.

Gay-Lussac’s Law Pressure is also related to the temperature. The effect is linear if the volume is kept the same. Named after Joseph Gay-Lussac who observed it in the early 19th century. hot high P cold low P

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 Number of atoms N Constant pressure and temperature This describes the state of the system, and is called an equation of state. + =

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