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Gas Laws: Boyle's Law, Charles's Law, and Kinetic Theory

This chapter explores Boyle's Law and Charles's Law, the variables that affect gas behavior, and how to apply gas laws to pressure, temperature, and volume problems. It also discusses the assumptions of the kinetic theory of gases and the interdependence of gas variables. Additionally, it covers the quantitative properties of gases, such as pressure, volume, and temperature, and provides examples of calculations using gas laws.

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Gas Laws: Boyle's Law, Charles's Law, and Kinetic Theory

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  1. CHAPTER 14: GASES

  2. Chapter 14 Objectives • State Boyle’s Law and Charles’s Law • Know the variables that influence the behavior of gases • Apply the gas laws to problems involving pressure temperature and volume of a gas • Compare the separate laws to the universal gas laws

  3. Kinetic theory: • You must remember the following about the kinetic theory. It assumes the following concepts are true about gases. • 1. gas particles do not attract or repel each other • 2. Gases particles are much smaller than the distances between them

  4. Kinetic theory: • 3. Gas particles are in constant random motion • 4. No kinetic energy is lost when gas particles collide with each other or the walls of their container • 5. all gases have the same average kinetic energy at a given temperature

  5. All of these assumptions are based on four factors: the number of gas particles present, the temperature, the pressure and the volume of the gas sample. These four things work together to determine the behavior of gases. When one variable changes, it affects the other three.

  6. Think about squeezing a balloon. As the volume is decreased, its pressure is increased • This interdependence of the variable is the basis for our gas laws.

  7. Getting started with gas calculations • Before we can start talking about how gases behave in numerical terms, we need to define some of the quantitative properties that are characteristic of gases:  • Pressure (P): The force of gas molecules as they hit the sides of the container in which they are placed. • Common units of pressure:

  8. Getting started with gas calculations • *atmospheres (atm): The average air pressure at sea level. • kilopascals (kPa): The SI unit for pressure; 101.325 kPa = 1 atm. • mm Hg (Torr): 760 Torr = 1 atm.

  9. Volume (V): The amount of space in which a gas is enclosed. • The only commonly used unit of volume is liters (L).

  10. Temperature (T): A measurement of the amount of energy that molecules have. The higher the energy, the higher the temperature. • Common units of temperature: • Kelvin (K): The only units that can be used when doing numerical problems with gases. • Degrees Celsius (0C): Must be converted to Kelvin before doing problems (by adding 273).

  11. Other terms frequently used: • STP: Stands for “standard temperature and pressure”, namely 273 K (00 C) and 1.00 atm. • “Room temperature”: 298 K (250 C)

  12. PT V P T V PT V 1 V Boyle’s P a ___ a Charles V T a Gay-Lussac’s P T Pressure - Temperature - Volume Relationship

  13. A whirlwind tour through the early gas laws: • Boyle’s Law: P1V1 = P2V2 • For any gas, the product of the pressure and the volume before a change is equal to the product of the pressure and the volume after a change. • In plain English, what this means is that if you put pressure on a gas, it gets smaller. If you decrease pressure on a gas, it gets larger.

  14. Think about if you sit on balloons to demonstrate that decreasing the volume increases the pressure inside the balloon so much that it pops! • Or, You can use a vacuum pump to decrease the pressure around a balloon – the balloon will get bigger (until it pops, probably).

  15. Boyle’s Law • As the pressure on a gas increases • As the pressure on a gas increases - • the volume decreases • Pressure and volume are inversely related 1 atm 2 atm 4 Liters 2 Liters

  16. Sample problems: • If I have 10 L of gas at a pressure of 1 atm and double the pressure, what will the new volume of the gas be? 5 L • If 250 L of a gas is in a sealed container at a pressure of 1.5 atm and I decrease the volume of the container to 100 L, what will the gas pressure inside the container be? 3.8atm.

  17. practice • 1) If I have 3.4 liters of gas in a piston at a pressure of 2.5 atm and compress the gas until its volume is 5.1 L, what will the new pressure inside the piston be? • 2)I have added 32 L of air to a balloon at sea level (1.0 atm). If I take the balloon with me to Denver, where the air pressure is 0.95 atm, what will the new volume of the balloon be?

  18. 3)I’ve got a car with an internal volume of 13,000 L. If I drive my car into the river and it implodes, what will be the volume of the gas when the pressure goes from 1.0 atm to 1.7 atm?

  19. Charles’s Law:

  20. Have you ever noticed on a cold day that your car tire might look like it is low on air? Then after driving the car for a while the tire looks less flat. What makes the difference? • *Charles law relates the volume of a gas and temperature

  21. If you increase the temperature of a gas, the volume also increases. (Note: The temperature must be in Kelvin, NOT degrees centigrade) • Why? The Kinetic Molecular Theory, tells us that the amount of energy that a gas has is determined by the temperature of the gas. The more energy a gas has, the faster the gas molecules move away from each other, causing more space between the molecules and a larger overall volume.

  22. V1 V2 = T1 T2 Charles’ Law Timberlake, Chemistry 7th Edition, page 259 (Pressure is held constant)

  23. Demonstration: Show the students two balloons, both of which originally had the same volume. One goes into a freezer and comes out smaller than the one at room temperature.

  24. Examples: • Remember to change degree C to Kelvin • If you heat a 1.25 L balloon from a temperature of 250 C to 40.0 C, what will the new volume of the balloon be? 1.3 L • What temperature will be required to raise the volume of a 1.0 L balloon to 1.25 L if the initial temperature is 250 C? 370 • * watch sig figs

  25. practice • If I have 37 liters of helium in a balloon at 270 C and increase the temperature of the balloon to 430 C, what will the new volume of the balloon be? • 2) Calcium carbonate decomposes at 12000 C to form carbon dioxide and calcium oxide. If 25 liters of carbon dioxide are collected at 12000 C, what will the volume of this gas be after it cools to 200 C • 3) I have 115 liters of gas in a piston at a temperature of 2750 C. If I cool the gas until the volume decreases to 80. liters, what will temperature of the gas be (in degrees Celcius)?

  26. Gay-Lussac’s Law

  27. When you increase the temperature of an enclosed gas, the pressure of the gas goes up. • This is why it’s a bad idea to put a spray can into a campfire – eventually the pressure rises so much that the sides of the can split and the can explodes.

  28. Example: • If you have a spray can at a pressure of 20.0 atm at room temperature and put it into a campfire at a temperature of 12000 C, what will the pressure in the canister be right before it explodes? 99 atm

  29. 14.2 The Combined Gas law and Avogadro’s Principle • The combined gas law: • If we put the last three gas laws together, we can devise another law that encompasses all three of them (making it unnecessary to memorize the three):

  30. How to use this law: Whenever you have a problem in which you change the pressure, volume, and/or temperature, just plug the values into it. • If one of the variables isn’t mentioned, we can assume that it’s kept constant and we can just cross it out of the equation.

  31. Examples: • If I have 25 mL of a gas at a pressure of 2.1 atm and a temperature of 300 K, what will the pressure become if I raise the temperature to 400 K and decrease the volume to 10 mL? 7 atm • If I have a container with an internal pressure of 1.5 atm and temperature of 250 C, what will the pressure be if I heat the container to 1500 C? 2.1 atm

  32. practice • 1) If I initially have 5.0 L of a gas at a pressure of 1.17 atm, what will the volume be if I increase the pressure to 5.2 atm? • 2) A toy balloon has an internal pressure of 1.32 atm and a volume of 4.0 L. If the temperature where the balloon is released is 200 C, what will happen to the volume when the balloon rises to an altitude where the pressure is 0.65 atm and the temperature is –230C?

  33. 3) A small research submarine with a volume of 1.9 x 105 L has an internal pressure of 1.0 atm and an internal temperature of 210 C. If the submarine descends to a depth where the pressure is 150 atm and the temperature is 50 C, what will the volume of the gas inside be if the hull of the submarine breaks? • 4) People who are angry sometimes say that they feel as if they’ll explode. If a calm person with a lung capacity of 3.2 liters and a body temperature of 310 C gets angry, what will the volume of the person’s lungs be if their temperature rises to 370 C. Based on this, do you think it’s likely they will explode?

  34. Avogadro’s principle:One mole of every gas has the same volume. 22.4L • This law assumes that all gases behave perfectly and identically according to the rules of the kinetic molecular theory. Though not precisely true, it gives us very good answers under most conditions.

  35. Ideal Gases: • Now that we know how gases behave when we manipulate P, V, and T, it’s time to start thinking about how to deal with things like moles and grams. • After all, if we’re going to do chemical reactions with gases, we’ll need to know how to calculate these!

  36. Ideal gas: A gas that behaves according to the kinetic molecular theory. • No intermolecular forces, infinitely small, etc. • There is no ideal gas in the real world, but some gases come closer than others:

  37. The gas molecules are small. • The gas molecules have very weak intermolecular forces. • The gas molecules are very hot, so they move quickly around and don’t interact with each other much. • The gas is at low pressure, so the molecules have a lot of space between them.

  38. Remember the molar volume for a gas is the volume that one mole occupies at 0 C and 1 atm pressure. • This is STP. • Because the volume of one mole of a gas at STP is 22.4 L, you can use the conversion factor: 22.4 L/1 Mol

  39. Assuming that all gases are ideal, we can use an equation to relate the number of moles to the pressure (P), volume (V), and temperature (T), giving us the…

  40. Ideal gas law: PV = nRT • P = pressure (in atm of kPa) • V = volume (L) • n = number of moles • T = temperature (Kelvin) • R = ideal gas constant (depends on the unit of pressure used) • 8.314 L kPa/mol K • 0.08206 L atm/mol K

  41. Examples: • If I have 10 liters of a gas at a pressure of 1.5 atm and a temperature of 250 C, how many moles of gas do I have? 0.61 mol.

  42. practice • 1) What volume will 50.0 grams of Neon occupy at STP?

  43. 14.4Gas Stoichiometry • at STP, the conversion factor between liters and moles is 22.4 L = 1 mole. • What this means is that, whatever method of stoichiometry we use, we need only replace the molar masses of the gases with the number 22.4 – for compounds that are solids, we still use the molar mass.

  44. Example: Using the equation 2 H2 + O2 2 H2O, how many liters of water can be made from 25 liters of oxygen at STP? Answer: 50 L

  45. Dalton’s law of partial pressure states that the total pressure of a mixture of gases is equal to the sum of the pressures of gases in the mixture • P(total) = P1 + P2 + P3 + P4…

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