Gas Laws Robert Boyle Jacques Charles Amadeo Avogadro

Gas Laws Robert Boyle Jacques Charles Amadeo Avogadro Joseph Louis Gay-Lussac

The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

Boyle’s Law Pressure is inversely proportional to volume when temperature is held constant.

Charles’s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. (P = constant) Temperature MUST be in KELVINS!

Gay Lussac’s Law The pressure and temperature of a gas are directly related, provided that the volume remains constant. Temperature MUST be in KELVINS!

Avogadro’s Law v For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V = an a = proportionality constant V = volume of the gas n = number of moles of gas

Ideal Gas Law PV = n. RT v P = pressure in atm v V = volume in liters v n = moles v R = proportionality constant v= 0. 08206 L atm/ mol·K v T = temperature in Kelvins Holds closely at P < 1 atm

Real Gases At high pressure (smaller volume) and low temperature (attractive forces become important) you must adjust for non-ideal gas behavior using van der Waal’s equation. corrected pressure Pideal corrected volume Videal

Gas Density … so at STP…

Density and the Ideal Gas Law Combining the formula for density with the Ideal Gas law, substituting and rearranging algebraically: M = Molar Mass P = Pressure R = Gas Constant T = Temperature in Kelvins

Gas Stoichiometry #1 If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios. 3 H 2(g) + N 2(g) 2 NH 3(g) 3 moles H 2 + 1 mole N 2 2 moles NH 3 3 liters H 2 + 1 liter N 2 2 liters NH 3

Gas Stoichiometry #2 How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen? 3 H 2(g) + N 2(g) 12 L H 2 2 L NH 3 3 L H 2 2 NH 3(g) = 8. 0 L NH 3

Gas Stoichiometry #3 How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50. 0 grams of potassium chlorate? 2 KCl. O 3(s) 2 KCl(s) + 3 O 2(g) 50. 0 g KCl. O 3 1 mol KCl. O 3 122. 55 g KCl. O 3 3 mol O 2 22. 4 L O 2 2 mol KCl. O 3 1 mol O 2 = 13. 7 L O 2

Gas Stoichiometry #4 How many liters of oxygen gas, at 37. 0 C and 0. 930 atmospheres, can be collected from the complete decomposition of 50. 0 grams of potassium chlorate? 2 KCl. O 3(s) 2 KCl(s) + 3 O 2(g) 50. 0 g KCl. O 3 1 mol KCl. O 3 122. 55 g KCl. O 3 3 mol O 2 2 mol KCl. O 3 = 0. 612 mol O 2 = 16. 7 L

Dalton’s Law of Partial Pressures For a mixture of gases in a container, PTotal = P 1 + P 2 + P 3 +. . . This is particularly useful in calculating the pressure of gases collected over water.