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Chapter 5: The Gaseous State Bushra Javed CHM 2 045

Chapter 5: The Gaseous State Bushra Javed CHM 2 045. Contents. 1. Gas pressure & it’s units 2. Empirical Gas Laws Boyle’sLaw Charles’Law Combined gas Law Avogadro’s Law Dalton’s Law Ideal Gas Law. Contents. 3. Kinetic-Molecular Theory 4. Molecular Speeds

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Chapter 5: The Gaseous State Bushra Javed CHM 2 045

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  1. Chapter 5: The Gaseous State BushraJaved CHM 2045

  2. Contents 1. Gas pressure & it’s units 2. Empirical Gas Laws • Boyle’sLaw • Charles’Law • Combined gas Law • Avogadro’s Law • Dalton’s Law • Ideal Gas Law

  3. Contents 3. Kinetic-Molecular Theory 4. Molecular Speeds 5. Diffusion and Effusion Graham’s Law 6. Real Gases

  4. The Gaseous State • Gases differ from liquids and solids: • Have low densities, are compressible & can expand • Physical condition of any gas can be defined • by four variables: • Pressure, P • Volume, V • temperature, T • amount or number of moles n.

  5. Pressure , P of a Gas Pressure is the force exerted per unit area. It can be given by two equations: The SI unit for pressure is the pascal, Pa.

  6. Pressure , P of a Gas Other Units atmosphere, atm mmHg torr bar

  7. Atmospheric Pressure • Atmospheric pressure results from the exertion & pressure of air molecules in the environment. • A barometer is a device for measuring the pressure of the atmosphere. • A manometer is a device for measuring the pressure of a gas or liquid in a vessel.

  8. Atmospheric Pressure

  9. Empirical Gas Laws All gases behave quite simply with respect to temperature, pressure, volume, and molar amount. By holding two of these physical properties constant, it becomes possible to show a simple relationship between the other two properties. T

  10. Boyle’s LawPressure –Volume Relationship The volume of a sample of gas at constanttemperature varies inversely with the applied pressure. The mathematical relationship: In equation form:

  11. Boyle’s LawPressure –Volume Relationship • When the volume decreases, the gas molecules collide with the container more often and the pressure increases. • When the volume increases, the gas molecules collide with the container less often and the pressure decreases.

  12. Boyle’s Law plot of V versus P for 1.000 g O2 at 0°C. This plot is nonlinear.

  13. Boyle’s Law At one atmosphere the volume of the gas is 100 mL. When pressure is doubled, the volume is halved to 50 mL. When pressure is tripled, the volume decreases to one-third, 33 mL.

  14. Boyle’s Law Example 1 A volume of oxygen gas occupies 38.7 mL at 751 mmHg and 21°C. What is the volume if the pressure changes to 359 mmHg while the temperature remains constant? Vi = 38.7 mL Pi = 751 mmHg Ti = 21°C Vf= ? Pf = 359 mmHg Tf= 21°C

  15. Boyle’s Law Vf= ? Pf = 359 mmHg Tf= 21°C Vi = 38.7 mL Pi = 751 mmHg Ti = 21°C = 81.0 mL

  16. Boyle’s Law Example 2 A sample of methane, CH4, occupies a volume of 244.0 mL at 25°C and exerts a pressure of 1135.0 mmHg. If the volume of the gas is allowed to expand to 720.0 mL at 298 K, what will be the pressure of the gas? P2 = ? a. 3350 mmHg b. 385 mmHg c. 4580 mmHg d. 0.0149 mmHg

  17. If you plot volume vs. temperature for any gas at constant pressure, the points will all fall on a straight line If the lines are extrapolated back to a volume of “0,” they all show the same temperature, −273.15 °C, called absolute zero

  18. Absolute Zero The temperature -273.15°Cis called absolute zero. It is the temperature at which the volume of a gas is hypothetically zero. This is the basis of the absolute temperature scale, the Kelvin scale (K).

  19. Charles’s Law The volume of a sample of gas at constant pressure is directly proportional to the absolute temperature (K). The mathematical relationship: In equation form:

  20. A balloon was immersed in liquid nitrogen (black container) and is shown immediately after being removed. It shrank because air inside contracts in volume. As the air inside warms, the balloon expands to its orginial size.

  21. Charles’s Law Example 3 You prepared carbon dioxide by adding HCl(aq) to marble chips, CaCO3. According to your calculations, you should obtain 79.4 mL of CO2 at 0°C and 760 mmHg. How many milliliters of gas would you obtain at 27°C? Vf = ? Pf = 760 mmHg Tf= 27°C = 300. K Vi = 79.4 mL Pi= 760 mmHg Ti = 0°C = 273 K

  22. Charles’s Law Vf = ? Pf = 760 mmHg Tf= 27°C = 300. K Vi= 79.4 mL Pi = 760 mmHg Ti = 0°C = 273 K = 87.3 mL

  23. Charles’s Law Example 4 The volume of a sample of gas measured at 10.0°C and 1.00 atmpressure is 6.00 L. What must the final temperature be in order for the gas to have a final volume of 7.00 L at 1.00 atmpressure? T2 = ? Convert °C into Kelvin then back into °C. a. –30.4°C b. 8.6°C c. 11.7°C d. 57.2°C

  24. Combined Gas Law The volume of a sample of gas at constant pressure is inversely proportional to the pressure and directly proportional to the absolute temperature. The mathematical relationship: In equation form:

  25. Combined Gas Law Example 5 Divers working from a North Sea drilling platform experience pressure of 5.0 × 101atmat a depth of 5.0 × 102 m. If a balloon is inflated to a volume of 5.0 L (the volume of the lung) at that depth at a water temperature of 4°C, what would the volume of the balloon be on the surface (1.0 atm pressure) at a temperature of 11°C? Vf or V2 = ?

  26. Vi = 5.0 L Pi = 5.0 × 101atm Ti = 4°C = 277 K Vf = ? Pf= 1.0 atm Tf= 11°C = 284 K = 2.6  102L

  27. Combined Gas Law Example 6 If 7.75 L of radon gas is at 1.55 atm and –19 °C, what is the volume at STP? Standard Temperature and Pressure (STP) The reference condition for gases, chosen by convention to be exactly 0°C and 1 atmpressure (a)4.65 L (b)5.37 L (c)8.33 L (d)12.9 L

  28. Avogadro’s Law Amedeo Avogadro (1776–1856) • Volume directly proportional to the number of gas molecules • V = constant x n • constant P and T • more gas molecules = larger volume • Count number of gas molecules by moles • Equal volumes of gases contain equal numbers of molecules • the gas doesn’t matter

  29. Avogadro’s Law Example 6 If 1.00 mole of a gas occupies 22.4 L at STP, what volume would 0.750 moles occupy? Ans: 16.8 L

  30. Standard Conditions • Because the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy – we call these standard conditions • STP • Standard pressure = 1 atm • Standard temperature = 273 K • 0 °C

  31. Molar Volume • Solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L • 6.022 x 1023 molecules of gas • notice: the gas is immaterial • We call the volume of 1 mole of gas at STP the molar volume • it is important to recognize that one mole measures of different gases have different masses, even though they have the same volume Tro: Chemistry: A Molecular Approach, 2/e

  32. Molar Volume Tro: Chemistry: A Molecular Approach, 2/e

  33. Ideal Gas Law/Ideal gas equation Combining the three Laws V α 1/ P (Boyle’s Law) V α T (Charles’ Law) V α n (Avogadro’s Law) V α T . n / P or V = R . T . n / P Where R = molar gas constant

  34. Ideal Gas Equation • Rearranging the above equation gives: • PV = nRT R = molar gas constant = 0.0821L .atm/ (mol.K) R = 0.0821 atm.L/(K.mol) R = 8.3145 J/(K.mol) R = 8.3145kg. m2 /(.K.mol)

  35. Ideal Gas Law Equation Example 7 A 50.0-L cylinder of nitrogen, N2, has a pressure of 17.1 atm at 23°C. What is the mass of nitrogen in the cylinder? Hint: Find mol first. V = 50.0 L P = 17.1 atm T= 23 C= 296 K Ans mass = 986 g

  36. Density at Standard Conditions • Density is the ratio of mass to volume • Density of a gas is generally given in g/L • The mass of 1 mole = molar mass • The volume of 1 mole at STP = 22.4 L Tro: Chemistry: A Molecular Approach, 2/e

  37. Density at Standard Conditions Example 8: Calculate the density of N2(g) at STP

  38. Gas Density and Molar Mass Gas Density Using the ideal gas law, it is possible to calculate the moles in 1 L at a given temperature and pressure. The number of moles can then be converted to grams (per liter). Molar Mass To find molar mass, find the moles of gas, and then find the ratio of mass to moles.

  39. Gas Density and Molar Mass Example 8 What is the density of methane gas (natural gas), CH4, at 125°C and 3.50 atm? Note: Since density of gases is measured in g/L, you can assume the volume is 1L. Hint: Find mols first, then convert to grams ;Mm= 16.04 g/mol • 1.71g/L • 1.72g/L • 4.5g/L • 0.04g/L

  40. Molar Mass of a Gas • One of the methods chemists use to determine the molar mass of an unknown substance is to heat a weighed sample until it becomes a gas, measure the temperature, pressure, and volume, and use the ideal gas law Tro: Chemistry: A Molecular Approach, 2/e

  41. Gas Density and Molar Mass Example 9 An unknown gas occupies a volume of 4.75 L at 1227 °C and 5.00atm. If the mass is 5.45 g, what is the molar mass of gas? (R = 0.0821 atm•L/mol•K) Hint: Find mols first n = 0.1928 (a)21.5 g/mol (b) 23.8 g/mol (c )28.3 g/mol (d)141 g/mol

  42. Gas Mixtures Dalton found that in a mixture of unreactive gases, each gas acts as if itwere the only gas in the mixture as far as pressure is concerned.

  43. Originally (left), flask A contains He at 152 mmHg and flask B contains O2 at 608 mmHg. Flask A is then filled with oil forcing the He into flask B (right). The new pressure in flask B is 760 mmHg.

  44. Dalton’s Law of Partial Pressures Partial Pressure The pressure exerted by a particular gas in a mixture. Dalton’s Law of Partial Pressures The sum of the partial pressures of all the different gases in a mixture is equal to the total pressure of the mixture: P = PA + PB + PC + . . .

  45. Dalton’s Law of Partial Pressures Example 10 A 100.0-mL sample of air exhaled from the lungs is analyzed and found to contain 0.0830 g N2, 0.0194 g O2, 0.00640 g CO2, and 0.00441 g water vapor at 35°C. What is the partial pressure of each component and the total pressure of the sample? Hint: Convert grams to mols Then use ideal gas equation, PV= nRTto find partial pressure of each gas.

  46. Dalton’s Law of Partial Pressures P = 1.00 atm

  47. Dalton’s Law of Partial Pressures Collecting Gas Over Water Gases are often collected over water. The result is a mixture of the gas and water vapor. The total pressure is equal to the sum of the gas pressure and the vapor pressure of water.

  48. Dalton’s Law of Partial Pressures The partial pressure of water depends only on temperature .(See Table 5.6). The pressure of the gas can then be found using Dalton’s law of partial pressures.

  49. Collecting Gas by Water Displacement Tro: Chemistry: A Molecular Approach, 2/e

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