1. General Chemistry I 1 KINETIC MOLECULAR DESCRIPTION OF THE STATES OF MATTER CHAPTER 9 The Gaseous State General Chemistry I U N I T III CHAPTER 10 Solids, Liquids, and Phase Transitions CHAPTER 11 Solutions

2. General Chemistry I 2 392 Gas Liquid Solid

3. General Chemistry I 3 THE GASEOUS STATE 9.1 The Chemistry of Gases 9.2 Pressure and Temperature of Gases 9.3 The Ideal Gas Law 9.4 Mixtures of Gases 9.5 The Kinetic Theory of Gases 9.6 Real Gases: Intermolecular Forces 9 CHAPTER General Chemistry I

4. 4 395 Li + H 2 O → LiOH + H 2

5. General Chemistry I 5 9.1 THE CHEMISTRY OF GASES 396

6. General Chemistry I 6 397 CaCO 3 (s) + 2HCl(g) → CaCl 2 (s) + CO 2 (g) + H 2 O(l) K 2 SO 3 (s) + 2HCl(g) → 2KCl(s) + SO 2 (g) + H 2 O(l)

7. General Chemistry I 7 9.2 PRESSURE AND TEMPERATURE OF GASES 398  Pressure Torricelli’s barometer Evangelista Torricelli (ITA, 1608-1647)

8. General Chemistry I 8 Force exerted by the mercury column at its base F = mg  = 13.5951 g cm –3 → density of Hg(l) at 0 o C g = 9.80665 m s –2 → gravitational acceleration h = 76 cm → height of mercury column 399

9. General Chemistry I 9  Pressure and Boyle’s Law ~ Experiments on the compression and expansion of air. “The spring of the Air and Its Effects” (1661).  Boyle’s J-tube experiment Trapped air at the closed end of the J-tube: Add Hg and measure the volume of air (V): Robert Boyle (UK, 1627-1691) or C: a constant at constant T and fixed amount of gas 400

10. General Chemistry I 10 Fig. 9.3 Boyle’s J-tube. (a)Same Hg height on two sides P confined = P air (b) Hg added  Difference in Hg heights, h  V confined compressed 400

11. General Chemistry I 11 (a) P vs. V  hyperbola (b) P vs. 1/V  straight line passing through the origin (slope: C) (c) PV vs. P  straight line independent of P (parallel to P-axis, intercept C on PV-axis) The value of C at 0 o C and for 1 mol of gas, ~ good for all gases at very low pressure C = PV = 22.414 L atm 401

12. General Chemistry I 12  Temperature and Charles’s law Jacques Charles (France,1746-1823) 402

13. General Chemistry I 13 Fig. 9.5 Volume of a gas confined at constant P increases as T increases. 403

14. General Chemistry I 14 Fig. 9.6 The volume of a sample of a gas is a function of temperature at constant pressure. 404

15. General Chemistry I 15 ◈ Absolute Temperature Scale, K Kelvin, Lord William Thomson (UK, 1824-1907) 0 K : ‘absolute zero’ temperature 273.15 K : triple point of water 0 K = - 273.15 o C  0 o C = 273.15 K Kelvin scale: absolute, thermodynamic temperature scale - ‘absolute zero’ is the temperature at which all thermal motion ceases in the classical description of thermodynamics. 405

16. General Chemistry I 16 9.3 THE IDEAL GAS LAW 405 √ Equation of state √ Limiting law for real gases as P  0 √ Universal gas constant, R R = 8.314 J·K –1 ·mol –1 = 8.206 x 10 –2 L·atm·K –1 PV = nRT Boyle’s law: V  1/P (at constant T and n) Charles’ law: V  T (at constant P and n) Avogadro’s hypothesis: V  n (at constant T and P)

17. General Chemistry I 17 408 EXAMPLE 9.5 Concentrated nitric acid acts on copper to give nitrogen dioxide and dissolved copper ions according to the balanced chemical equation Cu(s) + 4H + (aq) + 2NO 3 - (aq) → 2NO 2 (g) + Cu 2+ (aq) + 2H 2 O(l) Suppose that 6.80 g copper is consumed in this reaction, and that the NO 2 is collected at a pressure of 0.970 atm and a temperature of 45 o C. Calculate the volume of NO 2 produced.

18. General Chemistry I 18 9.4 MIXTURES OF GASES 408 ▶ Partial pressure ( P i ) of the i th gas in a mixture of gases → pressure that the i th gas would exert if it occupied the container alone

19. General Chemistry I 19 ◆ Dalton’s Law of Partial Pressures The total pressure of a mixture of gases is the sum of the partial pressures of its component. ▶ Mole fraction of the component A is x A 409  P A = x A P

20. General Chemistry I 20 409 EXAMPLE 9.6 When NO 2 is cooled to room temperature, some of it reacts to form a dimer, N 2 O 4, through the reaction 2NO 2 (g) → N 2 O 4 (g) Suppose 15.2 g of NO 2 is placed in a 10.0 L flask at high temperature and the Flask is cooled to 25 o C. The total pressure is measured to be 0.500 atm. What partial pressures and mole fractions of NO 2 and N 2 O 4 are present? (a) (b) (Dalton’s Law)

21. General Chemistry I 21 9.5 THE KINETIC THEORY OF GASES 410 1. A gas consists of a collection of molecules in continuous random motion. 2. Gas molecules are infinitesimally small (mass) points. 3. The molecules move in straight lines until they collide. 4. The molecules do not influence one another except during collisions.

22. General Chemistry I 22 - Collision with walls: consider molecules traveling only in one dimension, x, with a velocity of v x. All the molecules within a distance v x  t of the wall and traveling toward it will strike the wall during the interval  t. If the wall has area A, all the particles in a volume Av x  t will reach the wall if they are traveling toward it. 411 The change in momentum (final – initial) of one molecule: -2mv x = 2mv x momentum change for the wall

23. General Chemistry I 23 The number of molecules in the volume Av x  t is that fraction of the total volume V, multiplied by the total number of molecules: The average number of collisions with the wall during the interval  t is half the number in the volume Av x  t: The total momentum change = number of collisions × individual wall momentum change 411

24. General Chemistry I 24 Force = rate of change of momentum = (total momentum change)/  t  mean-square speed 412

25. General Chemistry I 25 412 - Kinetic energy of N A molecules, - average kinetic energy per molecule, k B = R/N A - root-mean-square speed M = molar mass = N A m Root mean square speeds of some gases at 25 o C

26. General Chemistry I 26 Maxwell-Boltzmann distribution of speed James Clerk Maxwell Ludwig Eduard Boltzmann (Scotland, 1831-1879) (Austria, 1844-1906) Boltzmann constant: 414 Fraction of molecules with speeds between v and v +  v

27. General Chemistry I 27 Fig. 9.13 A device for measuring the distribution of molecular speeds. 414

28. General Chemistry I 28 415 Fig. 9.14 Maxwell-Boltzmann distribution of molecular speeds in N 2 at three different temperatures.

29. General Chemistry I 29 416

30. General Chemistry I 30 9.6 REAL GASES: INTERMOLECULAR FORCES 417 ▶ Compression (or Compressibility) factor, Z z is a measure of deviation from ideality - For an ideal gas, z = 1 - For real gases, z deviates from 1 as P increases: z < 1 when attractive forces dominate z > 1 for repulsive forces dominate

31. General Chemistry I 31 z = PV/nRT 418

32. General Chemistry I 32 ◈ The Van der Waals Equation of State ▶ Corrections to the ideal equation of state - Attraction at long distance: Reduction in collision frequency Reduction in intensity of collision - Repulsion at short distance: No overlap of molecules → excluded volume effect Reduction in free volume  n 418

33. General Chemistry I 33 ▶ Van der Waals equation: a: atm L 2 mol -2 b: L mol -1 R: L atm mol -1 K -1 419 Rearranging this equation to solve for P gives the form of the equation that is most often used in calculations: See Slide 37

34. General Chemistry I 34 Repulsive forces (through b) increase z above 1. Attractive forces (through a) reduce z. The Boyle temperature T B Influence of van der Waals parameters a and b on the compressibility factor z

35. General Chemistry I 35 -Note that the Constant b is the volume excluded by 1 mol of molecules and should be close to V m, the volume per mole in the liquid state.

36. General Chemistry I 36 419

37. General Chemistry I 37

38. General Chemistry I 38  Intermolecular Forces  Lennard-Jones Potential: where  is the depth and  is the distance at which V(R) passes through zero. 421  (Ar)  (He)  (Ar)  (He)

39. General Chemistry I 39 421

40. General Chemistry I 40 10 Problem Sets For Chapter 9, 6, 18, 30, 40, 42, 50, 64, 72, 76, 92