1. Unit 12: Gas Laws

2. The Kinetic Theory of Gases Gases aren’t attracted or repelled by each other. Gas particles are super tiny, but the space between each particle is huge. Gas particles are super tiny, but the space between each particle is huge. Most of the volume of a gas is empty space! Most of the volume of a gas is empty space! Gas particles move constantly and randomly. Gas particles move constantly and randomly.

3. The Kinetic Theory of Gases No kinetic energy is lost when gas particles collide! This is called an elastic collision. No kinetic energy is lost when gas particles collide! This is called an elastic collision. Inelastic CollisionElastic Collision

4. The Kinetic Theory of Gases All gases have the same amount of kinetic energy at a given temperature. So… All gases have the same amount of kinetic energy at a given temperature. So… As the temperature increases, so does the energy! As the temperature increases, so does the energy! http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=296.0 Click for animation

5. Characteristics of Gases Gases expand to fill any container. Gases expand to fill any container. random motion, no attraction random motion, no attraction Gases have very low densities. Gases have very low densities. no volume = lots of empty space no volume = lots of empty space

6. Characteristics of Gases Gases can be compressed. Gases can be compressed. no volume = lots of empty space no volume = lots of empty space Gases undergo diffusion. Gases undergo diffusion. random motion random motion

7. PressurePressure Which shoes create the most pressure?

8. Atmospheric Pressure Here is the earth’s atmosphere. This blanket of air is pushing down on us at all times! Here is the earth’s atmosphere. This blanket of air is pushing down on us at all times! Atmospheric pressure is equal to 14.7 psi (pounds per square inch) at sea level (Houston). Atmospheric pressure is equal to 14.7 psi (pounds per square inch) at sea level (Houston).

9. Torricelli’s barometer: Atmospheric pressure is measured with a barometer. Atmospheric pressure is measured with a barometer. It was invented by Evangelista Torricelli back in the 1600s. It was invented by Evangelista Torricelli back in the 1600s.

10. The higher the altitude, the lower the atmospheric pressure. The higher the altitude, the lower the atmospheric pressure. This is because you have less atmosphere pushing down on you the higher you go up. This is because you have less atmosphere pushing down on you the higher you go up. “The air is thinner”… The higher you go, the less gas molecules. Less oxygen for you. “The air is thinner”… The higher you go, the less gas molecules. Less oxygen for you. LocationElevation Atmospheric Pressure in pounds per square inch (psi) Galveston, TX Sea level 14.7 psi Denver, CO 5280 ft 12.2 psi Pike’s Peak, CO 14,000 ft 8.8 psi Top of Mt. Everest 29,000 ft 4.9 psi

11. Pressure Units and Conversions Pressure units can look a bit strange. Here is an explanation of the ones you will most commonly use: Pounds per square inch = psi; simply expresses the force in pounds over an area in inches 2 Pounds per square inch = psi; simply expresses the force in pounds over an area in inches 2 Atmosphere = atm; 1 atm is the pressure at sea level (the entire atmosphere is pushing down) Atmosphere = atm; 1 atm is the pressure at sea level (the entire atmosphere is pushing down) Millimeters of mercury or inches of mercury = mm Hg or in Hg; comes from the height that Hg climbs in a barometer Millimeters of mercury or inches of mercury = mm Hg or in Hg; comes from the height that Hg climbs in a barometer Torr; named after Torricelli and is equal to mm Hg Torr; named after Torricelli and is equal to mm Hg Pascal = Pa; named after Blaise Pascal, a famous scientist who studied gas pressure Pascal = Pa; named after Blaise Pascal, a famous scientist who studied gas pressure

12. Conversions Kilopascal = kPa; just 1000 times greater than a Pascal Kilopascal = kPa; just 1000 times greater than a Pascal Relationships between pressure units: **important for conversions!!! Relationships between pressure units: **important for conversions!!! 1 atm = 14.7 psi = 760 mm Hg = 29.9 in Hg = 760 Torr = 101,300 Pa = 101.3 kPa 1 atm = 14.7 psi = 760 mm Hg = 29.9 in Hg = 760 Torr = 101,300 Pa = 101.3 kPa

13. Try these pressure conversions: 1. 0.50 atm = ? kPa 1. 0.50 atm = ? kPa 0.50 atm x 101.3 kPa = 50.65 kPa 1 atm 1 atm 2. 744 Torr = ? mm Hg 2. 744 Torr = ? mm Hg 744 Torr x 760 mm Hg = 744 mmHg 760 Torr 760 Torr

14. Pressure and Temperature Relationship As long as the volume stays the same… As temperature increases, the pressure increases. Why? The higher the temp, the more energy they have and they bounce off the walls more often and with more force, creating the pressure.

15. Pressure and Temperature Relationship Click for animation. Click for animation. http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties

16. Pressure and Temperature Relationship DIRECT relationship. P is directly proportional to T. DIRECT relationship. P is directly proportional to T. Graph: Graph: P T

17. Volume and Temperature Relationship As long as the pressure remains the same, as the temperature increases, the volume increases. As long as the pressure remains the same, as the temperature increases, the volume increases. Why? The higher the temperature, the more energy the particles get. The increased motion causes the volume to expand. Why? The higher the temperature, the more energy the particles get. The increased motion causes the volume to expand.

18. Temperature and Volume Relationship Click for animation. Click for animation. http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties

19. Temperature and Volume Relationship DIRECT relationship. V is directly proportional to T. DIRECT relationship. V is directly proportional to T. V T

20. Pressure and Volume Relationship As long as the temperature doesn’t change, As long as the temperature doesn’t change, As volume increases, pressure decreases. As volume increases, pressure decreases. Why? When there is more volume, the particles are less crowded, so they have space to move around. The pressure will drop. Why? When there is more volume, the particles are less crowded, so they have space to move around. The pressure will drop.

21. Pressure and Volume Relationship Click for animation. Click for animation. http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties http://phet.colorado.edu/en/simulation/gas- properties

22. Pressure and Volume Relationship INVERSE relationship. P is inversely proportional to V. INVERSE relationship. P is inversely proportional to V. Graph: Graph: P V

23. TemperatureTemperature ºF ºC K -45932212 -273 0100 0273373 K = ºC + 273 Always use absolute temperature (Kelvin) when working with gases. Always use absolute temperature (Kelvin) when working with gases.

24. STPSTP Standard Temperature & Pressure 0°C 273 K 0°C 273 K 1 atm 101.3 kPa 1 atm 101.3 kPa-OR- STP

25. Boyle’s Law The pressure and volume of a gas are inversely related The pressure and volume of a gas are inversely related at constant mass & temp at constant mass & temp P V P 1 V 1 =P 2 V 2

26. Example: A 5.0 L container of nitrogen gas is at a pressure of 1.0 atm. What is the new pressure if the volume is decreased to 500 mL, and the temperature remains constant? A 5.0 L container of nitrogen gas is at a pressure of 1.0 atm. What is the new pressure if the volume is decreased to 500 mL, and the temperature remains constant? Formula needed Rearrange for unknown Plug-in to formula Include units and cancellation! Final answer Unit Unit conversion(s) needed:

27. V T Charles’ Law The volume and absolute temperature (K) of a gas are directly related The volume and absolute temperature (K) of a gas are directly related at constant mass & pressure at constant mass & pressure

28. Example: A container of helium gas at 25°C in an expandable 500 mL container is heated to 80.°C. What is the new volume if the pressure remains constant? A container of helium gas at 25°C in an expandable 500 mL container is heated to 80.°C. What is the new volume if the pressure remains constant? Formula needed Rearrange for unknown Plug-in to formula Include units and cancellation! Final answer Unit Unit conversion(s) needed:

29. P T Gay-Lussac’s Law The pressure and absolute temperature (K) of a gas are directly related The pressure and absolute temperature (K) of a gas are directly related at constant mass & volume at constant mass & volume

30. Example: A tank of propane gas at a pressure of 3.0 atm is cooled from 90.°C to 30.oC. What is the new pressure if the volume remains constant? A tank of propane gas at a pressure of 3.0 atm is cooled from 90.°C to 30.oC. What is the new pressure if the volume remains constant? Formula needed Rearrange for unknown Plug-in to formula Include units and cancellation! Final answer Unit Unit conversion(s) needed:

31. Combined Gas Law We use the Combined Gas Law when nothing remains constant. We use the Combined Gas Law when nothing remains constant. P 1 V 1 = P 2 V 2 T 1 T 2 T 1 T 2

32. Example: A helium-filled balloon at sea level has a volume of 2.1 L at 0.998 atm and 36 o C. If it is released and rises to an elevation at which the pressure is 0.900 atm and the temperature is 28 o C, what will be the new volume of the balloon? A helium-filled balloon at sea level has a volume of 2.1 L at 0.998 atm and 36 o C. If it is released and rises to an elevation at which the pressure is 0.900 atm and the temperature is 28 o C, what will be the new volume of the balloon? Formula needed Rearrange for unknown Plug-in to formula Include units and cancellation! Final answer Unit Unit conversion(s) needed:

33. Ideal Gas Law Used when there are only one set of conditions. We also use MOLES!! Used when there are only one set of conditions. We also use MOLES!! You will also need the ideal gas constant, R. R = 0.0821 L atm You will also need the ideal gas constant, R. R = 0.0821 L atm K mol K mol The units in your problem must match the units in R. The units in your problem must match the units in R.

34. A. Ideal Gas Law UNIVERSAL GAS CONSTANT R=0.0821 L  atm/mol  K PV=nRT You don’t need to memorize these values!

35. YOU MUST CONVERT: P into atm P into atm Use pressure conversions Use pressure conversions V into L V into L Divide by 1000 if mL Divide by 1000 if mL n into moles n into moles divide by molecular weight divide by molecular weight T into K T into K Add 273 to Celcius Add 273 to Celcius

36. Example: 32.0 g of oxygen gas is at a pressure of 760 mm Hg and a temperature of 0 o C. What is the volume of the gas? 32.0 g of oxygen gas is at a pressure of 760 mm Hg and a temperature of 0 o C. What is the volume of the gas? Formula needed Rearrange for unknown Plug-in to formula Include units and cancellation! Final answer Unit Unit conversion(s) needed:

37. Example: A sample of helium gas is in a 500. mL container at a pressure of 2.00 atm. The temperature is 27 o C. What is the mass of the gas? A sample of helium gas is in a 500. mL container at a pressure of 2.00 atm. The temperature is 27 o C. What is the mass of the gas? Formula needed Rearrange for unknown Plug-in to formula Include units and cancellation! Final answer Unit Unit conversion(s) needed:

38. Gas Stoichiometry Review the 4 basic steps in stoichiometry: Review the 4 basic steps in stoichiometry: 1) Identify the given. 1) Identify the given. 2) convert it to moles if not already in moles. 2) convert it to moles if not already in moles. 3) Identify the unknown, and do a mole-to-mole ratio between given and unknown using the 3) Identify the unknown, and do a mole-to-mole ratio between given and unknown using the coefficients from the balanced equation. This is the key step: it gets you from moles of given to coefficients from the balanced equation. This is the key step: it gets you from moles of given to moles of unknown. moles of unknown. 4) Convert the unknown to the unit specified in the problem. 4) Convert the unknown to the unit specified in the problem.

39. Example: 4 Fe(s) + 3 O 2 (g)  2 Fe 2 O 3 (s) 4 Fe(s) + 3 O 2 (g)  2 Fe 2 O 3 (s) Calculate the volume of oxygen gas at STP that is required to completely react with 52.0 g of iron. Calculate the volume of oxygen gas at STP that is required to completely react with 52.0 g of iron.

40. Example: 4 Fe(s) + 3 O 2 (g)  2 Fe 2 O 3 (s) 4 Fe(s) + 3 O 2 (g)  2 Fe 2 O 3 (s) Refer to the equation above. If 22.4 L of oxygen gas is reacted at STP (with an excess of iron), how many grams of iron (III) oxide will be formed? Refer to the equation above. If 22.4 L of oxygen gas is reacted at STP (with an excess of iron), how many grams of iron (III) oxide will be formed?

41. Avogadro’s Law Avogadro’s Law says that equal volumes of gases at the same temperature and pressure contain equal numbers of moles. Avogadro’s Law says that equal volumes of gases at the same temperature and pressure contain equal numbers of moles. This means that the coefficients in the balanced equation stand for volume as well as moles, but only for the gases. This means that the coefficients in the balanced equation stand for volume as well as moles, but only for the gases.

42. Example N2(g) + 3 H2(g)  2 NH3(g) N2(g) + 3 H2(g)  2 NH3(g) If 25.0 L of nitrogen gas is reacted with an excess of hydrogen, what volume of ammonia is produced? If 25.0 L of nitrogen gas is reacted with an excess of hydrogen, what volume of ammonia is produced?

43. Example 2 H 2 (g) + O 2 (g)  2 H 2 O(g) 2 H 2 (g) + O 2 (g)  2 H 2 O(g) If 300. mL of water vapor is produced in the above reaction, how many mL of oxygen reacted? If 300. mL of water vapor is produced in the above reaction, how many mL of oxygen reacted?