1 / 69

Warm-Up

Warm-Up. What does the motion of gas molecules look like? Why does a balloon inflate when you blow it up? Why will soda explode from a bottle if opened after shaking it?. Chapter 5. The Gas Laws. Section 5.1- Pressure. Force per unit area (P = force/area). Gas molecules fill container.

abigail-jacobson
Download Presentation

Warm-Up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm-Up What does the motion of gas molecules look like? Why does a balloon inflate when you blow it up? Why will soda explode from a bottle if opened after shaking it?

  2. Chapter 5 The Gas Laws

  3. Section 5.1- Pressure • Force per unit area (P = force/area). • Gas molecules fill container. • Molecules move around and hit sides. • Collisions are the force. • Container is the area. • Measured with a barometer.

  4. How Does A Barometer Work? Vacuum 760 mm Hg • The pressure of the atmosphere at sea level will cause the column of mercury to rise to 760 mm Hg. • 1 atm = 760 mm Hg Pressure of atmosphere pushes on Hg As a result, Hg rises up into the glass tube *Hg stops rising when it’s equal to atmospheric pressure

  5. Units of pressure • 1 atmosphere = 760 mm Hg • 1 mm Hg = 1 torr • 1 atm = 101,325 Pascals = 101.325 kPa *The first two are provided on the AP equation sheet. No need to memorize the third- I assume you’ll be given that if you need to use it.

  6. Section 5.2 THE GAS LAWS OF BOYLE, CHARLES, AND AVOGADRO

  7. About the Laws… You should be aware of the following laws, however we will not focus heavily on them as they can be derived from the ideal gas law. After briefly going through each of the following laws, we will see how to derive each from the ideal gas law.

  8. Boyle’s Law • Pressure and volume are inversely related at constant temperature. • P1V1 = P2V2 • As one goes up, the other goes down. • Ex: if P increases (at constant T), V must go down • Further studies show that Boyle’s Law is only true at very low P • This will be discussed more in 5.8 • Gases that obey these laws are called ideal gases.

  9. Charles’s Law • Volume of a gas varies directly with the temperature at constant pressure. • V1 V2 T1 T2 • As one goes up/down, so does the other. =

  10. Avogadro's Law • At constant temperature and pressure, the volume of gas is directly related to the number of moles. • V1 V2 n1 n2 • As one goes up/down, so does the other. =

  11. Gay- Lussac Law • At constant volume, pressure and temperature are directly related. • P1 P2 T1 T2 • As one goes up/down, so does the other. =

  12. Combined Gas Law • Combination of Boyle’s Law, Charles’ Law, and Gay-Lussac Law. • Moles of gas remain constant. • P1V1 P2V2 T1 T2 =

  13. Summary Boyle’s: P1V1 = P2V2 Charles’: V1/T1 = V2/T2 Avogadro’s: V1/n1 = V2/n2 Gay-Lussac: P1/T1 = P2/T2 Combined: P1V1/T1 = P2V2/T2 That’s a lot of laws! Or we can just use the Ideal Gas Law!

  14. Combined Gas Law Cont. • Ex: A 2.3L sample of gas has a pressure of 1.2atm at 200.K. If the pressure is raised to 1.4atm and the temperature is increased to 300.K, what is the volume of the gas? • V2 = P1V1T2 T1P2 • V2 = 3.0 L

  15. Practice • Ex: A 12.2L sample of gas has 0.50mol of O2 at 1atm and 25°C. How many moles of O2 would occupy 19.4L at the same temperature and pressure? Solution: V1/n1 = V2/n2 (12.2L)/(0.50mol) = (19.4L)/(n2) n2 =0.80mol *In other words, 0.80mol of O2 would be required to fill 19.4L in order to keep the same pressure as 0.50mol of O2 in 12.2L.

  16. AP Practice Question A sample of argon gas is sealed in a container. The volume of the container is doubled. If the pressure remains constant, what must happen to the temperature? It doesn’t change. It is halved. It is doubled. It is squared.

  17. Demonstration Warm-Up! Observe the demonstration. Keep in mind the properties of gases we have discussed so far: P, V, T, and n. Think about these properties before and after imploding the can. Why do you think the can was crushed? As temperature decreases, so does the pressure and volume. Remind you of a law we looked at?

  18. Sections 1&2 Homework Pgs. 217-218 #: 2, 6, 34, 35

  19. Section 5.3 THE IDEAL GAS LAW

  20. Ideal Gas Law KNOW THIS! Choose R value according to units of P • PV = nRT • At standard temperature and pressure (STP): V = 22.4L at 1atm, 0ºC, and n = 1mol. These conditions were used to determine R (ideal gas constant): • R = 0.08206 L atm/mol K • = 8.314 J/mol K • = 62.36 L torr/mol K • Tells you about a gas NOW. • The other laws tell you about a gas when it changes.

  21. Ideal Gas Law Cont. • Looking back at the possible values for R, you will notice that all units for temperature are in K. • When using the ideal gas law for calculations, convert all temperatures to K! • Recall conversion: K = °C + 273 (provided on AP equation sheet)

  22. Ideal Gas Law Derivation Practice • May be asked to prove one of the laws discussed before! • Strategy: get all constants in the ideal gas law on one side and changing variables on the other. • We will go several of these in class.

  23. AP Practice Question A 1.15mol sample of carbon monoxide gas has a temperature of 27°C and a pressure of 0.300atm. If the temperature is lowered to 17°C at constant volume, what is the new pressure? a) 0.290atm c) 0.206atm b) 0.519atm d) 0.338atm

  24. Ideal Gas Law- Why ‘Ideal’? • Ideal gases are hypothetical substances. • Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. • They do not behave exactly according to this law, but they behave closely enough. • Law provides good estimates of gas behavior under these conditions. • Unless told otherwise, assume ideal gas behavior and use the ideal gas law.

  25. AP Practice Question A sample of aluminum metal is added to HCl. How many grams of aluminum metal must be added to an excess of HCl to produce 33.6L of hydrogen gas at STP? 18.0g 35.0g 27.0g 4.50g

  26. Section 3 Homework Complete the gas laws worksheet AND #33, 40, 43, 52 on pg. 219-221.

  27. Section 5.4 GAS STOICHIOMETRY

  28. Gases and Stoichiometry • Reactions involve moles of substances. • Recall that at STP (0ºC and 1 atm) 1mol of any gas occupies 22.4 L. • At STP this can be a conversion factor: 1mol/22.4L or 22.4L/1mol • If not at STP, use the ideal gas law to calculate moles or volume of a substance.

  29. Section 4 Example Can double check using ideal gas law • Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate. Calculate the volume of carbon dioxide produced at STP if 152g of calcium carbonate are completely decomposed. CaCO3 CaO + CO2 • Convert to moles: 152g x 1mol = 1.52mol 100.09g CaCO3 • 1:1 mole ratio of CaCO3 to CO2 1.52mol CO2 • Use STP conditions & stoichiometry: • At STP 1mol = 22.4L • 1.52mol x (22.4L/1mol) = 34.1L CO2

  30. Gas Density and Molar Mass • Recall: D = m/V • Let mmolar stand for molar mass • mmolar = m/n so n = m/mmolar • PV = nRT solve for n: n= PV/RT • Thus m/mmolar = PV/RT • Solve for mmolar: mmolar = mRT/VP • Replace m/V with D: mmolar = DRT/P • If density, temperature, and pressure are known, molar mass can be found.

  31. AP Practice Question Determine the formula for a gaseous silane (SinH2n+2) if it’s density is 5.47g/L at 0ºC and 1.00atm. *There are several ways to solve! SiH4 Si2H6 Si3H8 Si4H10

  32. Section 4 Homework Pg. 220-221 #51, 54, 57, 63, 64

  33. Section 5.5 DALTON’S LAW OF PARTIAL PRESSURES

  34. Dalton’s Law of Partial Pressures • The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. • Total pressure = sum of partial pressures. • Ptot = P1 + P2 + P3 + ... • P1, P2, P3 are individual gases • From the ideal gas law: PTotal = (nTotal)RT V

  35. Partial Pressures Cont. • What does Dalton’s Law tell us about ideal gases? • Total # of gas particles, not their identities, is important. • V of individual gas particles doesn’t affect the total P. • Forces between gas particles doesn’t affect the total P. • If these were important, the different identities of gas particles would affect the total P differently.

  36. AP Practice Question A gaseous mixture at 25°C contained 1mol CH4 and 2mol O2, and P = 2atm. The gases underwent the following reaction: CH4(g) + 2O2(g)  CO2(g) + 2H2O(g) What is the P in the container after the reaction goes to completion and the T is allowed to return to 25°C? 1atm 2atm 3atm 4atm

  37. AP Practice Question A sealed, rigid container is filled with three identical gases: A, B, and C. The partial pressure of each gas is known as well as T and V. What additional information is needed to find the masses of the gases in the container? a) average distance travelled between molecular collisions b) the intermolecular forces c) the molar masses of the gases d) the total pressure

  38. The mole fraction • Ratio of moles of a substance to the total moles. • symbol is Greek letter chi c • c1 = n1 = P1 ntot Ptot • Mole fractions have no units!

  39. AP Practice Question A reaction makes a mixture of CO2, CO, and H2O. The gaseous products contained 0.60mol CO2, 0.30mol CO, and 0.10mol H2O. If the total P is 0.80atm, what is the partial P of CO? 0.24atm 0.34atm 0.080atm 0.13atm

  40. Vapor Pressure • Water evaporates! • When water evaporates, the resulting water vapor has a pressure. • Vapor pressure changes with T- must be looked up. • Gases are often collected over water so the vapor pressure of water must be subtracted from the total pressure. • Vapor pressure must be given.

  41. AP Practice Question A sample of methane gas was collected over water at 35°C. The sample had a total pressure of 756mm Hg. Determine the partial pressure of methane gas in the sample. (Vapor pressure of water at 35°C is 41mm Hg.) 760mm Hg 41mm Hg 715mm Hg 797mm Hg

  42. Section 5 Homework Pg. 221-222 #65, 67, 69, 72

  43. Collapsing Can Demo Watch the demonstration. Why did the can collapse? -The heat vaporized the water, which in turn increased P and pushed air out of the can. -When the can was inverted the water vapor quickly cooled. This caused a quick drop in P (created a partial vacuum because essentially no air was left to maintain P). -The atmospheric P outside of the can was much greater than P inside of the can, which allowed the can to be crushed.

  44. Section 5.6 THE KINETIC MOLECULAR THEORY OF GASES

  45. Kinetic Molecular Theory (KMT)- Explains Behavior & Properties of Gases Gases are made up of molecules or atoms. V of particles can be ignored (very small in comparison to distance b/t particles). Particles constantly move and collide with each other and the walls of the container. Collisions with the walls of the container cause P of the gas. Particles don’t attract or repel each other; when they collide, it’s elastic (no KE is lost- it’s transferred). The average KE is proportional to the Kelvin T.

  46. KMT Cont. • Assumes gases are ideal. • BUT no gases are truly ideal- they only approach ideal behavior (specifically nonpolar gases at low P and high T). • In reality, gases DO have V (although small), and they CAN interact with each other. • Even so, assuming ideal behavior gives us good enough answers about properties of gases.

  47. KMT Large! For H2 at 20°C = 2,000m/s • #3 describes motion; let’s quantify it: urms = √(3RT/mmolar) • urms is root mean square velocity • R value used is 8.314J/molK • molar mass in kg/mol (b/c J = kgm2/s2) • #5: KE per mole (average KE) = 3/2 RT • Recall definition of T! Directly related! • Units: J/mol • KE per molecule = ½ mv2 this is the only equation given on AP exam! -Units: J

  48. Root Mean Square Velocity Example What is the root mean square velocity for the atoms in a sample of He gas at 25°C? Convert T to K: 25 + 273 = 298K M = 4.00g/mol  0.004000kg/mol urms = 136m/s

  49. Range of velocities • The average distance a molecule travels between collisions with another gas particle is called the mean free path and is small (near 10-7) • Results in a range of velocities. • Temperature is an average. There are molecules of many speeds in the average. • This is shown on a graph called a velocity distribution.

  50. Maxwell-Boltzmann Distribution Notice that with higher T, average velocities increase and so does the velocity range. 273 K 1273 K 2273 K number of particles Molecular Velocity

More Related