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**Ideal Gas Law & Dalton’s Law**

Ch. 12 & 13 - Gases III. Two More Laws Ideal Gas Law & Dalton’s Law

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**A. Avogadro’s Principle**

Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for any gas V n

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**UNIVERSAL GAS CONSTANT**

B. Ideal Gas Law Merge the Combined Gas Law with Avogadro’s Principle: PV T PV nT V n = k = R UNIVERSAL GAS CONSTANT R= Latm/molK R=8.315 dm3kPa/molK You don’t need to memorize these values!

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**UNIVERSAL GAS CONSTANT**

B. Ideal Gas Law PV=nRT UNIVERSAL GAS CONSTANT R= Latm/molK R=8.315 dm3kPa/molK You don’t need to memorize these values!

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**C. Ideal Gas Law Problems**

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

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**C. Ideal Gas Law Problems**

Find the volume of 85 g of O2 at 25°C and kPa. GIVEN: V = ? n = 85 g T = 25°C = 298 K P = kPa R = dm3kPa/molK WORK: 85 g 1 mol = 2.7 mol 32.00 g = 2.7 mol PV = nRT (104.5)V=(2.7) (8.315) (298) kPa mol dm3kPa/molK K V = 64 dm3

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**Ptotal = P1 + P2 + ... D. Dalton’s Law**

The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. Ptotal = P1 + P

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**D. Dalton’s Law GIVEN: PO2 = ? Ptotal = 1 atm PCO2 = 0.285 torr**

Three of the primary components of air are CO2, N2, and O2. In a sample containing only these three gases at a pressure of 1.00 atm, PCO2 = torr and PN2 = torr. What is the partial pressure of O2? GIVEN: PO2 = ? Ptotal = 1 atm PCO2 = torr PN2 = torr WORK: Ptotal = PCO2 + PN2 + PO2 1 atm = atm atm + PO2 PO2 = atm = atm = atm

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**Patm = Pgas + PH2O D. Dalton’s Law**

When H2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H2 and water vapor. Water exerts a pressure known as water-vapor pressure So, to determine total pressure of gas and water vapor inside a container, make total pressure inside bottle = atmosphere and use this formula: Patm = Pgas + PH2O

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D. 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 = PH 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.

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**D. Dalton’s Law GIVEN: Pgas = ? Ptotal = 742.0 torr PH2O = 42.2 torr**

A gas is collected over water at a temp of 35.0°C when the barometric pressure is 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 = torr PH2O = 42.2 torr WORK: Ptotal = Pgas + PH2O 742.0 torr = PH torr Pgas = 700. torr Look up water-vapor pressure on p.899 for 35.0°C. Sig Figs: Round to least number of decimal places.

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