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**Gas Laws Robert Boyle Jacques Charles Amadeo Avogadro**

Joseph Louis Gay-Lussac

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

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

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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!

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**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!

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Avogadro’s 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

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**PV = nRT Ideal Gas Law P = pressure in atm V = volume in liters**

n = moles R = proportionality constant = L atm/ mol·K T = temperature in Kelvins Holds closely at P < 1 atm

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**Real Gases Pideal Videal**

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 corrected volume Pideal Videal

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Gas Density … so at STP…

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**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

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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) N2(g) NH3(g) 3 moles H mole N moles NH3 3 liters H liter N liters NH3

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**Gas Stoichiometry #2 3 H2(g) + N2(g) 2NH3(g)**

How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen? 3 H2(g) + N2(g) 2NH3(g) 12 L H2 2 L NH3 = L NH3 8.0 3 L H2

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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 g KClO3 2 mol KClO3 1 mol O2 = 13.7 L O2

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Gas Stoichiometry #4 How many liters of oxygen gas, at 37.0C and atmospheres, 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 0.612 = mol O2 g KClO3 2 mol KClO3 = 16.7 L

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**Dalton’s Law of Partial Pressures**

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

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