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The Mole Concept

2. The Mole Concept. 2.1 The Mole 2.2 Molar Volume and Avogadro’s Law 2.3 Ideal Gas Equation 2.4 Determination of Molar Mass 2.5 Dalton’s Law of Partial Pressures. 2.1. The Mole. An undercover agent, a counterspy, a double agent. A burrowing mammal with fossorial forefeet.

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The Mole Concept

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  1. 2 The Mole Concept 2.1 The Mole 2.2 Molar Volume and Avogadro’s Law 2.3 Ideal Gas Equation 2.4 Determination of Molar Mass 2.5 Dalton’s Law of Partial Pressures

  2. 2.1 The Mole

  3. An undercover agent, a counterspy, a double agent A burrowing mammal with fossorial forefeet A small congenital pigmented spot on the skin A breakwater Mole P. 3 / 66

  4. A mole is the number of atoms in exactly 12.00 g ofpure isotope. This number, known as the Avogadro’s constant, can be determined by mass spectrometry. B is the magnetic field strength. V is the accelerating potential. k is a constant of the instrument.

  5. At fixed e, k, B and V m can be determined.

  6. Mass of one mole of atoms = 12.00 g mol1 = Mass of an Avogadro’s number of atoms Avogadro’s number Q.5 = Avogadro’s number  1.992648  10-23 g = 6.022  1023 mol1

  7. for counting common objects for counting particles like atoms, ions, molecules What is “mole”? 2.1 The mole (SB p.18)

  8. sextillion quadrillion billion million trillion quintillion ~602,200,000,000,000,000,000,000 mol1 千進制 1 mole ~ 602.2 sextillions P. 8 / 66

  9. The fastest supercomputer can count 1.7591015 atoms per second. Calculate the time taken for the superconductor to count 1 mole of carbon-12 atoms.  10.85 years P. 9 / 66

  10. We can count the number of coins by weighing if the mass of one coin is known. Similarly, we can count the number of 12C by weighing if the mass of one 12C is known. P. 10 / 66

  11. Molar mass is the mass, in grams, of 1 mole of a substance

  12. Relative atomic mass Q.6

  13. Q.6 Molar mass of carbon = 12.01 g mol1

  14. Q.6 Relative isotopic mass is not exactly equal to mass number of the isotope

  15. number of particles mass 2 g = = 6.022  1023 mol1 molar mass 16 g mol1 number of oxygen atoms = = 6.022  1023 mol1 Number of moles of a substance Q.7 Number of moles of oxygen atoms

  16. 2 g 16. g mol1 Number of oxygen atoms = Number of atoms number of oxygen atoms = = 6.022  1023 mol1 Q.7 Number of moles of oxygen atoms = 3.011  1019

  17. 2.1 The mole (SB p.20) Example 2-1A Example 2-1B Example 2-1C Example 2-1E Example 2-1D Check Point 2-1 Molar mass is the same as the relative atomic mass in grams. Molar mass is the same as the relative molecular mass in grams. Molar mass is the same as the formula mass in grams.

  18. 2.2 Molar Volume and Avogadro’s Law

  19. 2.2 Molar volume and Avogadro’s law (SB p.24) What is molar volume of gases? Volume occupied by one mole of molecules of a gas.

  20. 2.2 Molar volume and Avogadro’s law (SB p.24) What is molar volume of gases? Depends on T & P Two sets of conditions

  21. 2.2 Molar volume and Avogadro’s law (SB p.24) What is molar volume of gases? at 298 K & 1 atm (Room temp & pressure / R.T.P.)

  22. 2.2 Molar volume and Avogadro’s law (SB p.24) 22.4 dm3 22.4 dm3 22.4 dm3 What is molar volume of gases? at 273 K & 1 atm (Standard temp & pressure / S.T.P.)

  23. Gas Molar mass/g Molar volume at R.T.P./dm3 Molar volume at S.T.P./dm3 O2 32 24.0 22.397 N2 28 24.0 22.402 H2 2 24.1 22.433 He 4 24.1 22.434 CO2 44 24.3 22.260 17 24.1 22.079 ~ 24 ~ 22.4 NH3 Not constant

  24. 2.2 Molar volume and Avogadro’s law (SB p.24) Avogadro’s Law Equal volumes of ALL gases at the same temperature and pressure contain the same number of moles of molecules. At fixed T & P, V  n If n = 1, V = molar volume

  25. 2.2 Molar volume and Avogadro’s law (SB p.24) Avogadro’s Law V  n V = Vm  n

  26. 2.2 Molar volume and Avogadro’s law (SB p.24) Example 2-2C Example 2-2B Example 2-2A Check Point 2-2 Example 2-2D Interconversions involving number of moles

  27. 2.3 Ideal Gas Equation

  28. 2.3 Ideal gas equation (SB p.27) Boyle’s law At fixed n and T, PV = constant or n = number of moles of gas molecules

  29. 2.3 Ideal gas equation (SB p.28) Schematic diagrams explaining Boyle’s law

  30. 1/P

  31. 2.3 Ideal gas equation (SB p.28) A graph of volume against the reciprocal of pressure for a gas at constant temperature

  32. 2.3 Ideal gas equation (SB p.28) Charles’ law At fixed n and P, T is the absolute temperature in Kelvin, K

  33. 2.3 Ideal gas equation (SB p.28) Schematic diagrams explaining Charles’ law

  34. 2.3 Ideal gas equation (SB p.28) Volume -273.15 oC 0oC Temperature / oC A graph of volume against temperature for a gas at constant pressure

  35. 2.3 Ideal gas equation (SB p.28) / K A graph of volume against absolute temperature for a gas at constant pressure

  36. Avogadro’s law Boyle’s law Charles’ law 2.3 Ideal gas equation (SB p.27) Ideal gas equation R is the same for all gases R is known as the universal gas constant PV = nRT Ideal gas equation

  37. 2.3 Ideal gas equation (SB p.29) Relationship between the ideal gas equation and the individual gas laws

  38. a constant = a constant At fixed n, Ideal gas behaviour is assumed in all gas laws

  39. Avogadro’s law Boyle’s law Charles’ law 2.3 Ideal gas equation (SB p.27) Gas laws PV = nRT Ideal gas equation

  40. 2.2 Molar volume and Avogadro’s law (SB p.24) Gas laws vs kinetic theory of gases What is the difference between a theory and a law? A law describes what happens under a given set of circumstances. A theory attempts to explain why that behaviour occurs.

  41. Ideal gas behaviour Four assumptions as stated in kinetic theory of gases • Gas particles are in a state of constant and random motion in all directions, undergoing frequent collisions with one another and with walls of the container. • Gas particles are treated as point masses, i.e. they do not occupy volume. Volume of a gas = capacity of the vessel

  42. Ideal gas behaviour 3. There is no interaction among gas particles. 4. Collisions between gas particles are perfectly elastic, i.e. kinetic energy is conserved.

  43. The ideal gas equation is obeyed by real gases only at (i) low pressure (ii) high temperature (less deviation from 24 dm3 at R.T.P.)

  44. At low pressure, gas particles are so far apart that • (1) any interaction among them becomes negligible (assumption 3) • (2) the volume occupied by the gaseous molecules becomes negligible when compared with that of the container (assumption 2)

  45. At high temperature, gaseous molecules possess sufficient energy to overcome intermolecular interactions readily. (assumption 3)

  46. 2.3 Ideal gas equation (SB p.31) Check Point 2-3 (b) A reaction vessel is filled with a gas at 20 oC and 5 atm. If the vessel can withstand a maximum internal pressure of 10 atm, what is the highest temperature it can be safely heated to? T2 = 586 K

  47. 2.3 Ideal gas equation (SB p.31) Check Point 2-3 (c) A balloon is filled with helium at 25 oC. The pressure exerted and the volume of balloon are found to be 1.5 atm and 450 cm3 respectively. How many moles of helium have been introduced into the balloon? Or n = 0.0276 mol n = 0.0276 mol

  48. 2.3 Ideal gas equation (SB p.31) Check Point 2-3 • 25.8 cm3 sample of a gas has a pressure of 690 mmHg and a temperature of 17 oC. What is the volume of the gas if the pressure is changed to 1.85 atm and the temperature to 345 K? • (1 atm = 760 mmHg) V2 = 15.1 cm3

  49. 2.3 Ideal gas equation (SB p.29) Q.8 Calculate the universal gas constant at S.T.P. For one mole of an ideal gas at S.T.P., P = 1 atm or 101,325 Nm-2 (Pa) V = 22.4 dm3 or 0.0224 m3 n = 1 mol T = 273K

  50. atm dm3 K1 mol1 2.3 Ideal gas equation (SB p.29) Or, = 8.314 Nm K1 mol1 = 8.314 J K1 mol1

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