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Understanding Dalton's Law and the Ideal Gas Law: Key Principles and Practice Problems

This learning log covers essential concepts from Dalton's Law of Partial Pressures and the Ideal Gas Law, detailing how the total pressure of a gas mixture equals the sum of its components' partial pressures. It explains practical applications such as collecting gases via water displacement, correcting for vapor pressure, and deriving the Ideal Gas Law equation (PV=nRT). The log includes practice problems for calculating pressures, volumes, and densities, reinforcing comprehension of gas behavior under various conditions.

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Understanding Dalton's Law and the Ideal Gas Law: Key Principles and Practice Problems

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  1. Learning Log • Why are you advised to open windows slightly if a tornado approaches?

  2. Ch. 10 & 11 - Gases Dalton’s LawIdeal Gas Law(p. 322-325, 340-346)

  3. Dalton’s Law of Partial Pressures • Total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases. • In the absence of a chemical reaction PT = P1+ P2+ P3+…

  4. Practice Problem A mixture of four gases exerts a total pressure of 1200 mm Hg. Gases A and B each exert 420 mm Hg. Gas C exerts 280 mm Hg. What pressure is exerted by gas D? PT = P1 + P2 + P3 + P4 1200 = 420 mm Hg + 420 mm Hg + 280 mm Hg + P4 1200 = 1120 mm Hg + P4 P4 = 80 mm Hg

  5. B. Vapor pressure of water • Gases are often collected in lab by water displacement and are mixed with water vapor • Patm = Pgas + PH2O • To determine the pressure of the gas collected – subtract the vapor pressure of the water at that temperature from the current atmospheric pressure

  6. C. Ideal Gas Law • The mathematical relationship among pressure, volume, temperature and the number of moles of a gas. • Derived by combining the gas laws. PV=nRT

  7. D. Ideal Gas Constant = k V n Merge the Combined Gas Law with Avogadro’s Principle: PV T PV nT = R IDEAL GAS CONSTANT R=0.0821 Latm/molK R=8.315 dm3kPa/molK

  8. E. 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

  9. E. 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

  10. Finding Molar Mass from the Ideal Gas Law n = mass n = m Molar mass M PV = mRTOR M PV=nRT M =mRT PV

  11. Finding Density from the Ideal Gas Law D = mass or D = m volume V M = DRT P M =mRT PV D =MP RT

  12. PRACTICE PROBLEMS • At 28°C and 0.974 at, 1.00 L of gas has a mass of 5.16 g. What is the molar mass of this gas? • P = 0.974 atm V = 1.00 L • T = 28°C = 273 = 301 K m = 5.16 g • M = mRT PV = (5.16 g) (0.0821 L∙atm/mol∙K) (301K) (0.974 atm)(1.00 L) = 131g/mol

  13. PRACTICE PROBLEMS • What is the density of a sample of ammonia gas, NH3, if the pressure is 0.928 atm and the temperature is 63.0°C? • P = 0.928 atm T = 63.0°C + 273 = 336 K M = 17.034 g/mol R = 0.0821 L∙atm/mol∙K • D = MP = (17.034 g/mol)(0.928 atm) RT (0.0821L∙atm/mol∙K)((336 K) = 0.572 g/L NH3

  14. Homework Assignment • Workbook. • Complete problems #1 and 2 on pp. 173-174, 1-2 p. 178, 1-2 p. 180

  15. Practice Test Part 2 • P. 181 – 182 #1-7, 12, 18 - 21

  16. Practice test Part 2 • Workbook p. 182 #1-7

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