# A Gas 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. P1V1 P2V2

T1 T2 Boyles Law Pressure is inversely proportional to volume when temperature is held constant. P1V1 P2V2 Charless Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. (P = constant)

V1 V2 T1 T2 Temperature MUST be in KELVINS! Gay Lussacs Law The pressure and temperature of a gas are directly related, provided that the volume remains constant. P1 P2 T1 T2 Temperature MUST be in KELVINS! Avogadros Law 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 = nRT P = pressure in atm V = volume in liters n = moles R = proportionality constant = 0.08206 L atm/ molK

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 Waals equation. 2 n Pobs a x (V nb) nRT V

corrected pressure Pidea l corrected volume Videa l Gas Density

mass molar mass Density volume molar volume so at STP molar mass Density 22.4 L Density and the Ideal Gas Law Combining the formula for density with the Ideal Gas law, substituting and rearranging algebraically:

MP D RT 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 H2(g) 2NH3(g)

3 moles H2 NH 3 3liters H 2 + N2(g) + 1 mole N2 + 1 liter N2

2 moles 2 liters NH3 Gas Stoichiometry #2 How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen? 3 H2(g) + N2(g) 12 L H2 2 L NH3 3 L H2

2NH3(g) = 8.0 L NH3 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 KClO3(s) 2 KCl(s) + 3 O2(g) 50.0 g KClO3

1 mol KClO3 3 mol O2 22.4 L O2 122.55 g KClO3 2 mol KClO3 1 mol O2 = 13.7 L O2 Gas Stoichiometry #4 How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium 2 KClOchlorate?

(s) 2 KCl(s) + 3 3 O2(g) 50.0 g KClO3 1 mol KClO3 3 mol O2 122.55 g KClO3 2 mol KClO3 nRT V P

L atm (0.612mol)(0.082 1 )(310K) molK 0.930atm = 0.612 mol O2 = 16.7 L Daltons Law of Partial Pressures For a mixture of gases in a

container, PTotal = P1 + P2 + P3 + . . . This is particularly useful in calculating the pressure of gases collected over water.