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III. Ideal Gas Law

Gases. III. Ideal Gas Law. A. Ideal Gas Law. = k. V n. Merge the Combined Gas Law with Avogadro’s Principle:. PV T. PV nT. = R. UNIVERSAL GAS CONSTANT R=0.0821 L atm/molK R=8.315 dm 3 kPa/molK. You don’t need to memorize these values!. A. Ideal Gas Law. PV=nRT.

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III. Ideal Gas Law

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  1. Gases III. Ideal Gas Law

  2. A. Ideal Gas Law = k V n Merge the Combined Gas Law with Avogadro’s Principle: PV T PV nT = R UNIVERSAL GAS CONSTANT R=0.0821 Latm/molK R=8.315 dm3kPa/molK You don’t need to memorize these values!

  3. A. Ideal Gas Law PV=nRT UNIVERSAL GAS CONSTANT R=0.0821 Latm/molK R=8.315 dm3kPa/molK You don’t need to memorize these values!

  4. C. Ideal Gas Law Problems • Calculate the pressure in atmospheres of 0.412 mol of He at 16°C & occupying 3.25 L. GIVEN: P = ? atm n = 0.412 mol T = 16°C = 289 K V = 3.25 L R = 0.0821Latm/molK WORK: PV = nRT P(3.25)=(0.412)(0.0821)(289) L mol Latm/molK K P = 3.01 atm

  5. C. Ideal Gas Law Problems WORK: 85 g 1 mol = 2.7 mol 32.00 g • Find the volume of 85 g of O2 at 25°C and 104.5 kPa. GIVEN: V=? n=85 g T=25°C = 298 K P=104.5 kPa R=8.315dm3kPa/molK = 2.7 mol PV = nRT (104.5)V=(2.7) (8.315) (298) kPa mol dm3kPa/molKK V = 64 dm3

  6. A. Gas Stoichiometry • Moles  Liters of a Gas: • STP - use 22.4 L/mol • Non-STP - use ideal gas law • Non-STP • Given liters of gas? • start with ideal gas law • Looking for liters of gas? • start with stoichiometry conv. C. Johannesson

  7. B. Gas Stoichiometry Problem • What volume of CO2 forms from 5.25 g of CaCO3 at 103 kPa & 25ºC? CaCO3 CaO + CO2 5.25 g ? Lnon-STP Looking for liters: Start with stoich and calculate moles of CO2. 5.25 g CaCO3 1 mol CaCO3 100.09g CaCO3 1 mol CO2 1 mol CaCO3 = 1.26 mol CO2 Plug this into the Ideal Gas Law to find liters. C. Johannesson

  8. B. Gas Stoichiometry Problem • What volume of CO2 forms from 5.25 g of CaCO3 at 103 kPa & 25ºC? GIVEN: P=103 kPa V = ? n=1.26 mol T=25°C = 298 K R=8.315dm3kPa/molK WORK: PV = nRT (103 kPa)V=(1mol)(8.315dm3kPa/molK)(298K) V = 1.26 dm3 CO2 C. Johannesson

  9. B. Gas Stoichiometry Problem • How many grams of Al2O3 are formed from 15.0 L of O2 at 97.3 kPa & 21°C? 4 Al + 3 O2 2 Al2O3 15.0 L non-STP ? g GIVEN: P=97.3 kPa V = 15.0 L n=? T=21°C = 294 K R=8.315dm3kPa/molK WORK: PV = nRT (97.3 kPa) (15.0 L)= n (8.315dm3kPa/molK) (294K) n = 0.597 mol O2 Given liters: Start with Ideal Gas Law and calculate moles of O2. NEXT  C. Johannesson

  10. B. Gas Stoichiometry Problem • How many grams of Al2O3 are formed from 15.0 L of O2 at 97.3 kPa & 21°C? 4 Al + 3 O2 2 Al2O3 15.0L non-STP ? g Use stoich to convert moles of O2 to grams Al2O3. 0.597 mol O2 2 mol Al2O3 3 mol O2 101.96 g Al2O3 1 mol Al2O3 = 40.6 g Al2O3 C. Johannesson

  11. C. Dalton’s Law Ptotal = P1 + P2 + ... • The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. When a H2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H2 and water vapor. C. Johannesson

  12. C. Dalton’s Law • Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H2 and water vapor. GIVEN: PH2 = ? Ptotal = 94.4 kPa PH2O = 2.72 kPa WORK: Ptotal = PH2 + PH2O 94.4 kPa = PH2 + 2.72 kPa PH2 = 91.7 kPa Look up water-vapor pressure on p.899 for 22.5°C. Sig Figs: Round to least number of decimal places. C. Johannesson

  13. C. Dalton’s Law • A gas is collected over water at a temp of 35.0°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas? The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor. GIVEN: Pgas = ? Ptotal = 742.0 torr PH2O = 42.2 torr WORK: Ptotal = Pgas + PH2O 742.0 torr = PH2 + 42.2 torr Pgas = 699.8 torr Look up water-vapor pressure on p.899 for 35.0°C. Sig Figs: Round to least number of decimal places. C. Johannesson

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