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Gas Laws and Ideal Gas Equation Explained

Understand gas laws using kinetic molecular theory and the Ideal Gas Law. Learn how to apply the gas laws mathematically and handle deviations with Van der Waals equation. Calculate gas density and molar mass.

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Gas Laws and Ideal Gas Equation Explained

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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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