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Chapter 12 : Day 2

Chapter 12 : Day 2. IDEAL GAS LAW. Using KMT to Understand Gas Laws. Recall that KMT assumptions are Gases consist of molecules in constant, random motion. P arises from collisions with container walls. No attractive or repulsive forces between molecules. Collisions elastic.

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Chapter 12 : Day 2

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  1. Chapter 12 : Day 2 • IDEAL GAS LAW

  2. Using KMT to Understand Gas Laws Recall that KMT assumptions are • Gases consist of molecules in constant, random motion. • P arises from collisions with container walls. • No attractive or repulsive forces between molecules. Collisions elastic. • Volume of molecules is negligible.

  3. Properties of Gases Gas properties can be modeled using math. Model depends on— • V = volume of the gas (L) • T = temperature (K) • n = amount (moles) • P = pressure (atmospheres)

  4. IDEAL GAS LAW P V = n R T Brings together gas properties. Can be derived from experiment and theory.

  5. Using PV = nRT How much N2 is req’d to fill a small room with a volume of 27,000 L to P = 745 mm Hg at 25 oC? R = 0.082057 L•atm/K•mol Solution 1. Get all data into proper UNITS V = 27,000 L T = 25 oC + 273 = 298 K P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm

  6. Using PV = nRT R = 0.082057 L•atm/K•mol Solution 2. Now calc. n = PV / RT n = 1.1 x 103 mol (or about 30 kg of gas)

  7. Deviations from Ideal Gas Law • Real molecules have volume. • There are intermolecular forces. • Otherwise a gas could not become a liquid. Fig. 12.20

  8. Measured V = V(ideal) Measured P ( ) 2 n a nRT V - nb P + ----- J. van der Waals, 1837-1923, Professor of Physics, Amsterdam. Nobel Prize 1910. 2 V vol. correction intermol. forces Deviations from Ideal Gas Law Account for volume of molecules and intermolecular forces with VAN DER WAAL’S EQUATION.

  9. Deviations from Ideal Gas Law Cl2 gas has a = 6.49, b = 0.0562 For 8.0 mol Cl2 in a 4.0 L tank at 27 oC. P (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atm

  10. Gases are most ideal when: 1. higher temperatures = more motion hT 2. lower pressures = fewer hits ,P 3 larger volumes = more space between hV 4. less gas in space = fewer number , n

  11. IDEAL GAS LAW P V = n R T Brings together gas properties. Can be derived from experiment and theory.

  12. Chapter 12 : Day 3 GAS DENSITY

  13. Low density High density GAS DENSITY density = mass/ volume d = g/V

  14. IDEAL GAS LAW P V = n R T Brings together gas properties. Can be used to determine molar mass of a gas or determine the density of a gas

  15. Molar Conversions moles = mass/ molar mass n = g/f

  16. GAS DENSITY n = P_ VRT PV = nRT or g = P where gis the mass fV RT where fis the molar mass d = g = Pf V RT d and fproportional

  17. USING GAS DENSITY The density of air at 15 oC and 1.00 atm is 1.23 g/L. What is the molar mass of air? 1. Calc. moles of air. V = 1.00 L P = 1.00 atm T = 288 K n = PV/RT = 0.0423 mol 2. Calc. molar mass mass/mol = 1.23 g/0.0423 mol = 29.1 g/mol

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