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Mark S. Cracolice Edward I. Peters Mark S. Cracolice The University of Montana Chapter 14 The Ideal Gas Law and Its Applications

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Avogadros Law Equal volumes of gases at the same temperature and pressure contain the same number of molecules. Volume of a gas is proportional to number of moles: V n V = k × n

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Molar Volume The molar volume is the volume of one mole of gas. The molar volume of an ideal gas depends on the temperature and pressure. One mole of any ideal gas occupies 22.7 liters at 0 0 C and 1 bar (STP).

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The Ideal Gas Law PV = n RT P = pressure of the gas V = volume of the gas T = temperature, in Kelvin n = number of moles R = universal gas constant R = L.atm/mol.K R = 62.4 L torr/mol.K

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The Ideal Gas Law PV = n RT Since the number of moles is equal to the mass m divided by the molar mass MM n = m / MM PV = (m/MM) x RT

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Determination of a single variable What volume will be occupied by mole of nitrogen at atm and 24 0 C? PV = nRT V = nRT/P = mol x ( L.atm/mol.K) x (24+273)K / atm = 9.87 L

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Determination of molar mass 1.67 grams of an unknown liquid are vaporized at a temperature of C. Its volume is measured as liter at 749 torr. Calculate the molar mass. PV = (m/MM) x RT Molar mass= MM = mRT/PV = 1.67g x (62.4 L.torr/mol.K) x ( )K/(749 torr x 0.421L) = 132g/mol

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Gas Density

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Density depends on temperature, pressure and molar mass. Hydrogen and helium have lowest densities. What is the density of nitrogen at 44°C and atm?.

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Molar Mass from Gas Density Find the molar mass of an unknown gas if its density is 3.97g/L at C and 749 torr. Molar mass= MM = D x RT/P = (3.97g/L) x (62.4 L.torr/mol.K) x ( )K/(749 torr) = 132g/mol

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Molar Volume Molar Volume of a Gas The volume occupied by one mole of gas molecules.

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Molar Volume Example: What is the molar volume of a ideal gas at 11°C and 1.33 atm? Solution: Solve with algebra.

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Gas Stoichiometry at STP Example: What volume of hydrogen, measured at STP, is released when a 42.7 g Zinc is added to a hydrochloric acid solution? Zn + 2 HCl H 2 + ZnCl 2 Given: 42.7 g Zn wanted: volume H 2 Molar volume at STP is 22.7 L/mol.

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Gas Stoichiometry at STP Zn + 2 HCl H 2 + ZnCl 2 Mass Zn mol Zn mol of H 2 volume H g Zn x ( 1 mol Zn/ g Zn ) x (1 mol H 2 / 1 mol Zn ) x ( 22.7 L H 2 / 1 mol H 2 ) = 14.8 L H 2

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Stoichiometry: Molar Volume Method Solving a Gas Stoichiometry Problem using Molar Volume Method Step 1: Use the ideal gas equation to find the molar volume at the given temperature and pressure: V/n = RT/P. Step 2: Use the molar volume to calculate the wanted quantity by all three steps of the stoichiometry path.

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Stoichiometry: Molar Volume Method What volume of CO 2, measured at 131°C and 744 torr, is produced when 16.2 g of C 4 H 10 is burned completely? Step 1 is to find the molar volume at the given temperature and pressure. Given: 131°C; 744 torrWanted: MV Molar volume = RT/P = (62.4 L torr/mol. K) x ( ) / 744 torr = 33.9 L/mol

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Stoichiometry: Molar Volume Method Step 2 is to use the molar volume to calculate the wanted quantity by the stoichiometry path. 2 C 4 H O 2 10 H 2 O + 8 CO 2 gram of C 4 H 10 mol C 4 H 10 mol CO 2 L CO gram of C 4 H 10 x (1 mol.C 4 H 10 / g C 4 H 10 ) x(8 mol.CO 2 / 2 mol.C 4 H 10 ) x (33.9 L CO 2 / mol. CO 2 ) = 37.8 L CO 2

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Volume–Volume Gas Stoichiometry At constant temperature and pressure, the gas volume is directly proportional to the number of moles. This means that at the same temperature and pressure the ratio of gas volumes is equal to moles ratio.

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Volume–Volume Gas Stoichiometry Hydrogen and nitrogen gases react to form gaseous ammonia. How many liters of ammonia can be produced from 5.5 L of nitrogen? Both gases are measured at same temperature and pressure. 3 H 2 + N 2 2 NH 3 3 mol of H 2 react with 1 mol N 2 to form 2 mol NH 3 At same T and P, same volumes of gases will have same number of moles. 3 L of H 2 react with 1L N 2 to form 2 L of NH 3

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Volume–Volume Gas Stoichiometry N H 2 2 NH 3 G IVEN: 5.5 L N 2 W ANTED: L NH 3

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Volume–Volume Gas Stoichiometry It is found that 1.75 L of oxygen, measured at 24 0 C and 755 torr, is used in burning sulfur. The sulfur dioxide produced is at C and 785 torr. Find the volume of sulfur dioxide at those condition. O 2 + S SO C,755 torr C,785 torr

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Volume–Volume Gas Stoichiometry First calculate the volume of O 2 at same T and P as SO 2 (165 0 C, 785 torr) Volume of O 2 at C and 785 torr = 1.75 L x ( 755 torr/785 torr) x ( 438 K / 297 K) = 2.48 L O 2

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Volume–Volume Gas Stoichiometry Next calculate the volume of sulfur dioxide from the volume of oxygen O 2 + S SO C & 785 torr Litters SO 2 (165 0 C & 785 torr) = 2.48 L O 2 (165 0 C & 785 torr) x (1L SO 2 /1 L O 2 ) = 2.48 L SO 2

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Homework Homework: 3, 5, 19, 21, 23, 29, 35, 43, 48, 51, 53

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