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# Gases and Gas Laws

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1. Gases and Gas Laws

2. Introduction The properties of gases will be introduced along with five ways of predicting the behavior of gases: Boyle’s Law, Charles’ Law, Gay-Lussac’s Law, Avogadro’s Law and the Ideal Gas Law.

3. Properties of Gases You can predict the behavior of gases based on the following properties: Pressure Volume Amount (moles) Temperature Lets review each of these briefly…

4. Physical Characteristics of Gases • Although gases have different chemical properties, gases have remarkably similar physical properties. • Gases always fill their containers (recall solids and liquids). No definite shape and volume • Gases are highly compressible: Volume decreases as pressure increases. Volume increases as pressure decreases. • Gases diffuse (move spontaneously throughout any available space). • Temperature affects either the volume or the pressure of a gas, or both.

5. Definition of a Gas • Therefore a definition for gas is: a substance that fills and assumes the shape of its container, diffuses rapidly, and mixes readily with other gases.

6. Kinetic Molecular Theory of Gases A theory to explain the properties of gases • Gases are composed of tiny particles, either atoms or molecules. The particles of gases tend to be relatively small in size compared to liquids or solids. Gases tend to have low atomic (He) and molecular weights (H2, O2, N2). • The gas particles are so small when compared to the distances • between them that the volume the gas particles take up is negligible • and is assumed to be zero. • Because of all the space between individual gas particles, • they can be squeezed together to compress the gas. • Solids and liquids can’t be squeezed, because their particles are • much closer.

7. 3. The gas particles are in constant random motion, moving in straight lines and colliding with the walls of the container. Gases continue to move in straight lines until they collide with something-either with each other or the walls of the container. • The gas particles are assumed to have negligible attractive • or repulsive forces between each other. • In other words, the gas particles are assumed to be totally independent, • neither attracting nor repelling each other.

8. The gas particles may collide with each other. • When gas particles collide with each other no kinetic energy is lost, • but the kinetic energy is transferred. In other words, if a fast gas • particle collides with a slow gas particle, the slow particle moves • away at a faster speed and the faster particle slows down after the collision. • The Kelvin temperature is directly proportional to the • average kinetic energy of the gas particles. • At any given temperature (K) all the gas particles have the • same kinetic energy. A gas that obeys all the postulates of the kinetic molecular theory is called an ideal gas.

9. Pressure • Automobile tires, basketballs, balloons, and soda bottles.

10. Pressure • Evangelista Torricelli invented the • BAROMETER: device to measure pressure • At sea level the height of the column of mercury is 760 mm. Pressure exerted by the atmospheric gases on the surface of the mercury in the dish keeps the mercury in the tube.

11. Measuring pressure of a confined gas Atmospheric pressure > gas Atmospheric pressure < gas Manometer

12. Pressure Units of Pressure -1mm Hg = 1 torr Standard atmosphere (atm) 1 atm. = 760.0mm Hg = 760.0 torr

13. Problem The height of mercury in a mercury barometer is measured to be 732 mm Hg. Represent this pressure in atm and torr. 1 atm. = 760.0mm Hg = 760.0 torr

14. Problem The height of mercury in a mercury barometer is measured to be 732 mm Hg. Represent this pressure in atm and torr. 1 atm. = 760.0mm Hg = 760.0 torr Answer: 0.963 atm; 732 torr

15. Kelvin Temperature Scale Kelvin Temp Scale: based on absolute zero — all kinetic motion stops • Formulas °C = K - 273 K= °C+273 0°C = 273K 30°C =303 K -20°C = 253 K

16. Various gas laws describe the relationships among • four of the important physical properties of gases: • Volume (liters) • Pressure (usually in atms) • 3. Temperature (Kelvin) • 4. Amount (moles)

17. Five Gas Laws • Boyle’s Law • Charles Law • Gay-Lussac’s Law • Avogadro’s Law • Ideal Gas Law

18. Boyle’s Law • Describes the pressure-volume relationship of gases if the temperature and amount are kept constant. • P1V1 = P2V2 • P1V1 = initial pressure and volume • P2V2= final pressure and volume

19. Boyle’s Law Volume and pressure are inversely proportional

20. Illustration of Boyle’s law. P1V1= P2V2

21. Pressure and Volume: Boyle’s Law • A sample of neon gas has a pressure of 7.43 atm in a container with a volume of 45.1 L. This sample is transferred to a container with a volume of 18.4 L. What is the new pressure of the neon gas? P1V1= P2V2 18.2 atm

22. Pressure and Volume: Boyle’s Law • A steel tank of oxygen gas has a volume of 2.00L. If all of the oxygen is transferred to a new tank with a volume of 5.50 L, the pressure is measured to be 6.75 atm. What was the original pressure of the oxygen gas? 18.6 atm

23. Charles’s Law • Describes the temperature-volume relationship of gases if the pressure and amount are kept constant. • the volume of a gas increases proportionally as the temperature of the gas increases. V1 = V2T1 T2

24. Charles’s Law shows that the volume of a gas (at constant pressure) increases with the temperature. Charles’s Law is used to explain what happens to a balloon when placed in a freezer.

25. Volume and Temperature: Charles’s Law • A sample of methane gas is collected at 285 K and cooled to 245K. At 245 K the volume of the gas is 75.0 L. Calculate the volume of the methane gas at 285K. V1 = V2T1 T2 V1 = 87.2 L

26. Volume and Temperature: Charles’s Law • A 2.45 L sample of nitrogen gas is collected at 273 K and heated to 325K. Calculate the volume of the nitrogen gas at 325 K. V1 = V2T1 T2 V2 = 2.92 L

27. Volume and Temperature: Charles’s Law • Consider a gas with a volume of 5.65 L at 27 C and 1 atm pressure. At what temperature will this gas have a volume of 6.69 L and 1 atm pressure. V1 = V2T1 T2 T2 = 355K (82oC)

28. Volume and Temperature: Charles’s Law • Consider a gas with a volume of 9.25L at 47oC and 1 atm pressure. At what temperature does this gas have a volume of 3.50 L and 1 atm pressure. T2 = -152oC (121K)

29. Gay-Lussac’s Law • Describes the temperature-pressure relationship of gases if the volume and amount are kept constant. • the pressure of a gas increases proportionally as the temperature of the gas increases. P1 = P2T1 T2

30. Pressure and Temperature: Gay-Lussac’s Law • If you have a tank of gas at 800 torr pressure and a temperature of 250 Kelvin, and it is heated to 400 Kelvin, what is the new pressure? P1 = P2T1 T2 P2 = 1,280 torr

31. Combined Gas Law • This is when all variables (T,P, and V) are changing P1 V1= P2 V2T1 T2

32. The Combined Gas Law Consider a sample of helium gas at 23oC with a volume of 5.60 L at a pressure of 2.45 atm. The pressure is changed to 8.75 atm and the gas is cooled to 15oC. Calculate the new volume of the gas using the combined gas law equation. P1 V1 = P2 V2 T1 T2 V2 = 1.53 L

33. The Combined Gas Law Consider a sample of helium gas at 28oC with a volume of 3.80 L at a pressure of 3.15 atm. The gas expands to a volume of 9.50 L and the gas is heated to 43oC. Calculate the new pressure of the gas using the combined gas law equation. P2 = 1.32 atm

34. Avogadro’s Law • Describes the amount-volume relationship of gases if the pressure and temperature are kept constant. • Equal volume of gases at the same temperature and pressure contain equal number of moles of gas. • the volume of a gas is directly proportional to the number of moles of gas V1 = V2n1 n2

35. Avogadro’s Law V1 = V2 n1 n2

36. Volume and Moles: Avogadro’s Law If 2.55 mol of helium gas occupies a volume of 59.5 L at a particular temperature and pressure, what volume does 7.83 molof helium occupy under the same conditions? V1 = V2n1 n2 V2 = 183 L

37. Volume and Moles: Avogadro’s Law If 4.35 g of neon gas occupies a volume of 15.0 L at a particular temperature and pressure, what volume does 2.00 g of neon gas occupy under the same conditions? V2 = 6.90 L

38. Avogadro’s Law A very useful consequence of Avogadro’s law is that the volume of a mole gas can be calculated at any temperature and pressure. An extremely useful form to know when calculating the volume of a mole of gas is 1 mole of any gas at STP occupies 22.4 liters. STP stands for standard temperature and pressure. Standard Pressure: 1.00 atm (760 torr or 760 mm Hg) Standard Temperature: 273K

39. Molar Volume • When gases are at STP: • 1 mole of any gas = 22.4 L/mol • We will return to this concept with gas stoichiometry problems.

40. Ideal Gas Equation • Ideal Gas — is ahypothetical gas that obeys all the gas laws perfectly under all conditions. It is composed of particles with no attraction to each other. (Real gas particles do have atiny attraction) • The further apart the gas particles are, the faster they are moving, the less attractive force they have and behave the most like ideal gases • The smaller the molecules, the closer the gas resembles an ideal gas • We assume ideal gases always. .

41. The Ideal Gas Law PV=nRT R=Universal gas constant (proportionality constant) R= 0.08206 L atm/ K Pressure is in atm. Volume is in liters Temperature is in Kelvin (K)

42. The Ideal Gas Law A sample of neon gas has a volume of 3.45 L at 25oC and a pressure of 565 torr. Calculate the number of moles of neon present in the gas sample. PV=nRT R=0.0821 L atm/K Convert pressure to atm and temperature to K n = 0.105 mol

43. The Ideal Gas Law A 0.250 mol sample of argon gas has a volume of 9.00 L at a pressure of 875 mm Hg. What is the temperature (in K) of the gas? PV=nRT T = 505K

44. The Ideal Gas Law - Expanded PV=nRT Suppose that the pressure, volume, temperature and mass are known for a gas sample. You can calculate the number of moles (n) in the sample using the ideal gas law. The number of moles (n) is equal to the mass (m) divided by the molar mass (M).

45. Substituting m/M for n into PV = nRT gives the following: PV = mRT M M = mRT PV m = mass (g) M = molar mass (molecular weight)

46. At 28oC and 0.974 atm, 1.00 L of gas has a mass of 5.16 g. What is the molar mass of this gas? Given: P of gas = 0.974 atm V of gas = 1.00 L T of gas = 28oC + 273 = 301K m of gas = 5.16g Calculate: molar mass (M) Use: M = mRT PV

47. M = mRT PV PV = mRT M M = (5.16 g)(0.0821)(301 K) (0.974 atm)(1.00L) M = 131 g/mol All other units cancel except for g/mol

48. An equation showing the relationship between density, pressure, temperature and molar mass can be derived from the ideal gas law. Density (D) is mass (m) per unit volume (V). Writing this is an equation gives D = m/V. m/V appears in the right-hand side of the equation. M = DRT P M = mRT PV =

49. M = DRT P Solving for density (D) gives the following equation: D = MP RT The density of a gas varies directly with molar mass and pressure and inversely with temperature (K).

50. What is the density of a sample of ammonia gas, NH3, if the pressure is 0.978 atm and the temperature is 63oC? D = MP RT Given: P of gas = 0.978 atm T of gas = 63oC + 273 = 336 K M of ammonia = 17.0 g/M Calculate: density (D)