1. Chapter 5 GASES

2. What we’ve had so far! Different ways of calculating moles of substances Solids: Moles = grams molar mass Liquids:Molarity = moles Liter

3. Ideal Gas Law In Chapter 5, everything comes down to another way of solving for moles. PV = nRT where n = number of moles

4. Atmospheric Pressure Pressure exerted by a gas on its surroundings

5. Pressure Units of Pressure –mm Hg –Atm –Torr(in honor of Evangelista Torricelli) –Pascal(Pa)

6. Pressure Conversions: –1 atm = 760 Torr = 760 mm Hg –1 atm = 101,325 Pa

7. The Gas Laws Boyle’s Law PV = k –the product of pressure (P) and volume (V) of a trapped gas is constant

8. Pressure vs. Volume P is inversely proportional to V SincePV = k If k = 1, then P = 1 or V = 1 V P

9. Boyle’s Law only holds true at very low pressures at high pressures, PV is not constant

10. Application of Boyle’s Law commonly used to predict the new volume when pressure is changed If:PV=k Then:(PV) 1 = (PV) 2 for same gas at same temperature

11. Sample Problem on Boyle’s Law An aerosol can contains 400 mL of compressed gas at 5.20 atm pressure. When all the gas is sprayed into a large plastic bag, the bag inflates to a volume of 2.14 L. If the T is constant, what is the pressure of gas inside the plastic bag?

12. Boyle’s Law A gas that strictly follows Boyle’s Law is an IDEAL GAS.

13. Charles’s Law filled balloon with H 2 and made the first solo balloon flight discovered that the volume of a gas at constant P increases linearly with the T of the gas

14. Charles’s Law The V of a gas at constant P is directly proportional to T. Charles’s Law Equation: V=kT where k is the proportionality constant

15. Units of Temperature Celsius Kelvin Conversion: 0 o C=273 K

16. Application of Charles’s Law To predict new volume of a gas when T is changed Thus if :V= kT Then:(V 1 /T 1 )=(V 2 /T 2 )

17. Sample Problem If a gas at 15 o C and 1 atm has a volume of 2.58 L, what volume will this gas occupy at 38 o C and 1 atm?[Note: Convert all T to K]

18. Avogadro’s Law Avogadro’s Postulate: [Chapter 2] Equal volumes of gases at the same T and P contain the same number of particles. Closely obeyed by gases at low P.

19. Avogadro’s Law V=a x n –where n = number of moles – a = proportionality constant So for a gas at constant T and P, the volume is directly proportional to the number of moles of gas.

20. Application of Avogadro’s Law To predict changes in V when the number of moles changes. V 1 /n 1 =V 2 /n 2

21. Charles’ Law the volume of a gas at constant P increases linearly with the T of the gas

22. Summary of 3 Laws Boyle’s Law:V = K/P [at constant T and n] Charles’s Law:V = bT [at constant P and n] Avogadro’s Law:V = an [at constant T and P]

23. Sample Problem on Boyle’s Law An aerosol can contains 400 mL of compressed gas at 5.20 atm pressure. When all the gas is sprayed into a large plastic bag, the bag inflates to a volume of 2.14 L. If the T is constant, what is the pressure of gas inside the plastic bag?

24. Sample Problem If a gas at 15 o C and 1 atm has a volume of 2.58 L, what volume will this gas occupy at 38 o C and 1 atm?[Note: Convert all T to K]

25. Sample Problem A 1-L container contains 2.75 moles of H 2 at 400 o C. What would be the pressure in the container at this temperature?

26. Sample Problem 3.5 moles of N 2 has a pressure of 3.3 atm at 375 o C. What would be the pressure of the 5.3 moles of gas at 900 o C?

27. Boyle’s Law A gas that strictly follows Boyle’s Law is an IDEAL GAS.

28. Ideal Gas Law gives the state or condition of a gas at a given time the state of a gas is described by its T, P, V and number of moles (n)

29. Ideal Gas Law expresses behavior that real gases approach at low P’s and high T’s An Ideal Gas is a hypothetical substance!

30. Ideal Gas Law Since most gases approach close to ideal behavior anyway, we will assume that the gases we encounter in this course are all ideal gases.

31. Ideal Gas Law PV=nRT –where R = universal gas constant – =.08206 L-atm/K

32. Sample Problem A sample of methane gas that has a volume of 3.8 L at 5 o C is heated to 86 o C at constant P. Calculate its new volume.

33. Another Sample Problem A sample of hydrogen gas has a volume of 10.6 L at a T of 0 o C and a P of 2.5 atm. Calculate the moles of hydrogen gas present in this gas sample.

34. Molar Mass and Density Molar Mass =gmRT PV Density= Molar Mass x Pressure RT

35. Dalton’s Law of Partial Pressures For a mixture of gases in a container, the total P exerted is the sum of the pressures that each gas would exert if it were alone. P total = P 1 + P 2 + P 3 …….

36. Dalton’s Law P total = P 1 + P 2 + P 3 ……. If P 1 = n 1 RT/V P 2 = n 2 RT/V P 3 = n 3 RT/V Then: P total = (n 1 RT/V) + (n 2 RT/V) + (n 3 RT/V)

37. CHAPTER 10 GASES

38. Gas Stoichiometry PV = nRT For 1 mole of an ideal gas at 0 o C, the molar volume at STP is 22.42 L. STP = standard T and P where T = 0 o C and P = 1 atm

39. Sample Problem A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N 2 are present?

40. Mole Fraction the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture  = symbol for mole fraction (chi)

41. Mole Fraction mole fraction of each component in a gaseous mixture is directly related to its partial pressure  = n 2 = P 2 n total P total

42. Kinetic Molecular Theory Is a model that attempts to explain the behavior of ideal gases Based on speculations about the behavior of the gas particles

43. Postulates of KMT The gas particles are assumed to: 1]be so small and have V = 0 2] be in constant motion. 3] exert no force on each other 4] have average KE that is  T (in Kelvin)

44. KMT on P and V Since P  1(Boyle’s Law) V As V increases, P decreases. As V decreases, P increases. KMT: As V is decreased, P increases because particles hit walls of container more often.

45. KMT on P and T As T is increased, the speed of the particles increases resulting in more collisions and stronger collisions. Thus P increases.

46. KMT on V and T Charles’s Law:V  T KMT:As T is increased, P normally increases because particles collide more. To keep P constant, V has to increase to compensate for the increased collisions.

47. KMT on V and n Avogadro’s Law: V  n KMT: Normally, an increase in n (moles of particles) increases P if V was held constant. To return P back to normal, V has to be increased.