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IDEAL gas law

IDEAL gas law. Solve quantitative problems involving the relationships among the pressure, temperature, and volume of a gas using dimensional analysis. Include : Avogadro, Ideal Gas Law and the mole Additional KEY Terms Molar volume Molar mass. Avogadro (1776-1856)

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IDEAL gas law

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  1. IDEAL gas law

  2. Solve quantitative problems involving the relationships among the pressure, temperature, and volume of a gas using dimensional analysis. • Include: Avogadro, Ideal Gas Lawand the mole • Additional KEY Terms • Molar volume Molar mass

  3. Avogadro (1776-1856) Any sample of anyGAS at the same temperature pressure will contain thesame number of particles.

  4. * Experiment conducted at constant temperature and pressure

  5. Defined 22.4 L as the molar volume for any GAS. Particles are now counted in moles (n). The number of moles is directly proportional to pressure, temperature, and volume.

  6. Experiments with n, V, P, and T give Ideal gas law: P V n R • T = R= experimentally determined ideal gas constant. Value of Rdepends on the units used for pressure. L · atm L · kPa To use this constant value – the units of P, V, T must match the given units 0.0821 8.314 mol · K mol · K L · mmHg 62.4 mol · K

  7. Ideal Gas Model: • particles engaged in random motion (normal) • particles obey conservation of energy(normal) • particles are non-interacting (IMFs alter results) • Real gases don’t behave like “ideal gases” atlow temperatures OR high pressures. • But the formulaworks 99% of the time, so…

  8. A steel container with a volume of 20.0 L is filled with nitrogen gas to a final pressure of 2000.0 kPa at 27.00C. How many moles of gas was used? P 2000 V (20.0) = = n R T 27°C + 273 = 300 K L · kPa 8.314 mol · K 16.0 moles n 8.314 (300)

  9. It is more convenient to measure a mole by mass. The mass of 1 mole is the molar mass - (g/mol) One mole of any particle has a mass equal to its total formula mass – IN GRAMS. The mass of 1 atom of Al = 27.0 µ The mass of 1 mole of Al atoms = 27.0 g The molecular mass of water (H2O) is 18.0 µ ... So...the molar mass of water is 18.0 g/mol.

  10. Molar mass of lead (II) chloride, PbCl2 ? 1 particle of PbCl2 - 1 atom of Pb, 2 atoms of Cl 1 mole of PbCl2 - 1 mole of Pb, 2 moles of Cl PbCl2 = 207.2 g/mol + 2(35.5 g/mol) = 278.2 g/mol The molar mass of lead (II) chloride is 278.2 g/mol.

  11. Dimensional Analysis (Converting Units): Determine the unit ratio needed. Multiply by the unit ratio(new unit on top) • 20 moles O2 = ? g • 1 mole OR 32.0 g • 32.0 g 1 mole • 20 moles O2 x32.0 g = 640 g O2 • 1 mole

  12. 1. 5.00 moles of aluminum atoms. 2. 100.0 g of sugar, C11H22O11 3. 7.25 moles of iron (III) oxide. • Al = 27.0 g/mol • 2. C11H22O11= 330.2 g/mol • 3. Fe2O3= 159.6 g/mol • 5 moles Al • x 27.0 g • 1 mole = 135 g • 100 g sugar • x 1 mol • 330.2 g = 0.303 mol • 7.25 moles Fe2O3 x 159.6 g • 1 mole = 1160 g

  13. What pressure is exerted by 640.0 g of methane (CH4) gas in a sealed 5.35L container at 27 ºC? 1 mol 16.0 g Molar mass of CH4= 16.0 g/mol (5.35) 640.0 g = 40.0 moles P V n R T = 27°C + 273 = 300 K L · kPa 8.314 mol · K • (40.0) 8.314 (300) 1.9 x 104kPa =

  14. A child lung capacity is 2.2 L. How many grams of oxygen gas do lungs hold at a pressure of 1.00 atm and a normal body temperature of 37.00C? 32.0 g 1 mol P 101.3 V (2.2) = = n R T 37°C + 273 = 310 K 0.086 moles 8.314 (310) L · kPa Molar mass of O2= 32.0 g/mol 8.314 mol · K 0.086 mol = 2.75 g of O2

  15. CAN YOU / HAVE YOU? • Solvequantitative problems involving the relationships among the pressure, temperature, and volume of a gas using dimensional analysis. • Include: Avogadro, Ideal Gas Lawand the mole • Additional KEY Terms • Molar volume Molar mass

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