Gas Volumes and Ideal Gas Law 11-3

11-3 Learning Targets Relate the number of particles and volume by using Avogadro’s principle Define Standard Molar volume of Gas Determine volume ratios for gaseous reactants and products using coefficients from a chemical equation Relate the amount of gas present to its pressure, temperature and volume by using the ideal gas law

Gay-Lussac’s Law of Combining volumes of gases At constant temperature and pressure, the volume of gaseous reactants and products can be expressed as ratios of small whole numbers H2 gas+ Cl2 gas → 2HCl gas 1 L 1L = 2L 1 vol 1 vol = 2 vol

Avogadro’s Law Italian Amadeo Avogadro Equal volumes of gases at the same temp and pressure contain equal number of molecules Volume varies directly with number of molecules V = k n Avagadro’s Law V1 = V2 n1 n2 constant T and P

Avogadro's Law Problem Suppose we have 12.2 L sample of 0.50 mol Oxygen gas O2 at 1 atm and 25 °C. If all of this gas is converted to ozone,O3 , at the same temperature and pressure, what will be the volume of the ozone formed? 3O2→2 O3 .5 mol O2 x 2 mol O3 = .33 mol O3 3 mol O2 12.2 L = V2 0.50 mol O2 0 .33 mol O3 V2 = 8.1 L O3

Avogadro's Law Problem 1.5 mol N2 has a volume of 36.7 L. It is at 25 °C and 1 atm. If the temperature and pressure is held constant how many moles will have a volume of 16.5 L? 36.7 L = 16.5 L 1.5 mol N2 n2 n2= 0.674 mol N2

Standard Molar Volume of Gas Volume occupied by one mole of gas at STP = 22.41410 L 22.4 L/mol If know volume of gas can use 1 mol/ 22.4 L as conversion factor to find moles (then mass) of a given volume of gas at STP

Problem At STP, what is the volume of 9.02 mol of oxygen gas? 9.02 mol O2 x (22.4 L/mol) = 202 L O2 A sample of H2 occupies 4.3 L at STP. How many moles of the gas are present? 4.3 L H2 x ( 1 mol/ 22.4L)= 0.19 mol H2

Gas Stoichiometry Volume- Volume calculations- use volume ratios like mole ratios MUST HAVE BALANCED EQUATION!!!!

What volume of hydrogen gas is needed to react completely with 10 What volume of hydrogen gas is needed to react completely with 10.5 L of oxygen gas to produce water vapor? 2H2 + O2 →2 H2O 10.5L O2 (2 LH2 ) = 21.0 L H2 1 L O2

Gas Stoichiometry Volume-mass calculations Volume A to moles A to moles B to mass B Mass-volume calculations Opposite direction as above

Mass to Volume Calculate the volume of CO2 produced at STP from the decomposition of 152 g of CaCO3 according to the reaction. CaCO3 (s) → CaO + CO2 Convert g to moles 152g CaCO3 x 1 mole CaCO3 = 1.52 mol CaCO3 100.09 g 1to 1 mole ratio 1.52 mol CO2 x 22.4 L CO2 = 34.1 L CO2 1 mol CO2 Can only use molar volume because at STP

Volume to Mass How many grams of calcium carbonate must be decomposed to produce 5.00 L of carbon dioxide gas at STP? CaCO3 (s) → CaO + CO2 1to 1 ratio , 1 L of CaCO3 to 1L of CO2 5.0 L CaCO3 (1 mol = .2232 mol CaCO3 22.4 L) 0.2232mol CaCO3 (100.09 g 1mol) = 22.34g CaCO3

Ideal Gas Law Combine all gas laws (Boyle, Charles, and Avogadro) Mathematical relationship of pressure, volume, temperature, number of moles Ideal gas- follows KMT pressure not too high and temperature not too low around a temp of 0 °C or higher Pressure around 1 atm or lower

Ideal Gas Law PV= nRT P= pressure V= volume (L) T= temp (K) n = number of moles R= Ideal gas constant Make sure units in problem match units in R

R= gas constant R= 0.0821 L∙ atm mol∙ K R= 62.4 L∙ mmHg R= 8.314 L∙ kPa

Nitrogen gas has a volume of 1 Nitrogen gas has a volume of 1.75 L at STP, how many moles of the gas are present? PV=nRT n=PV RT n= (1 atm)(1.75L) (0.0821 L∙atm/K∙mol)( 273K) =0.0781 mol N2

How many grams of carbon dioxide must be decomposed to produce 5 How many grams of carbon dioxide must be decomposed to produce 5.00 L of carbon dioxide gas at STP? Ideal gas law PV=nRT (1.00 atm)(5.00 L CO2) = n 0.0821 L∙ atm /mol K (273K) = 0.223 mol CO2 0.223 mol CO2 (43.99 g CO2 ) = 1 mol CO2 = 9.81g CO2