Math Review

1. Math Review • Solve for x: 2x - 3 = 1 7x + 2 = 4 4

2. 1 ≠ seconds seconds • 1 = seconds-1 seconds

3. Gases

4. Properties of Gases • Kinetic = motion • Kinetic Theory:all matter is in motion • Absolute Zero:0 K or -273.15 ° Celsius; all motion theoretically stops at this temperature

5. Kinetic Theory Review Small Gas Particles: • Size: • Distance from each other: • Attraction/Repulsion: • Collisions: Far Apart None; travel in a straight line Perfectly Elastic

6. Standard Temperature and Pressure (STP) • Temperature: 0° Celsius or 273 K • Pressure: 1 atm or 101.3 kPa *Heat is going to speed up particles!

7. SI unit of pressure = kilopascals (kPa) 1 atm = 760 mm Hg = 101.3 kPa • All temperatures need to be in Kelvins, so you must convert: TCelsium = TKelvin – 273.15

8. Perfectly Elastic collisions = no energy being lost, it just transfers from one particle to another. • Total Kinetic Energy remains constant • The motion of gas particles is rapid, constant, and random • Gas Pressure: due to collisions of gas particles with an object

9. Vacuum:empty space with no particles in it and therefore no pressure • Atmospheric Pressure: collision of atoms in the air with objects • Barometer: instrument that measures atmospheric pressure

10. 4 Variables that describe a gas… • Pressure = P in kilopascals (kPa) • a. Other units you might see: mm Hg & atm • Volume = V in liters (L) • a. Other units you might see: mL & cm3 • Temperature = T in Kelvins (K) • a. Other units you might see: °C • 4. Amount of gas; number of moles = n

11. Conversion Practice • Convert the following: 27°C to Kelvin 125 K to °C 788 mm Hg to kPa 1.26 atm to kPa

12. Boyle’s Law • Relates Pressure and Volume at constant Temperature. • Volume varies inversely with pressure • Mathematically: P1 * V1 = P2 * V2 P and V can be in any pressure or volume unit as long as they are the SAME on both sides of the equation.

13. Steps to solving gas law problems. • Read problem, record all values given in the problem. • P1 = • V1 = • P2 = • V2 = 2. Re-arrange the variables to solve for the appropriate one 3. Plug in the numbers with units 4. Solve. * Steps 2 and 3 can be switched

14. Boyle’s Law Example: • If I have 5.6 L of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be?

15. Boyle’s Law Example: Your Turn • I have added 15 L of air to a balloon at sea level (1.0 atm). If I decrease the pressure to 0.85 atm, what will the new volume of the balloon be?

16. Charles Law • Relates Temperature and Volume at constant Pressure • Volume is directly proportional to Temperature in Kelvin. • Mathematically: V can be in any volume unit as long as it is the SAME on both sides of the equation.

17. Charles Law Problems: • I have 130 L of gas in a piston at a temperature of 250°C. If I cool the gas until the volume decrease to 85 L, what will the temperature of the gas be?

18. Charles Law: Your turn • If I have 45 L of helium in a balloon at 25°C and increase the temperature of the balloon to is 55°C, what will the new volume of the balloon be?

19. Gay- Lussac Law • Relates Temperature and Pressure at constant Volume • Pressure is directly proportional to Temperature in Kelvin. • Mathematically: P can be in any pressure unit as long as it is the SAME on both sides of the equation.

20. Real life gay-lussac law

21. Gay - Lussac • If a gas in a closed container is pressurized from 15.0 atm to 16.0 atm and its original temperature was 25.0°C, what would the final temperature of the gas be if the volume doesn’t change?

22. Gay - Lussac • Calculate the final pressure inside a scuba tank after it cools from 1.00 x 103°C to 25.0°C. The initial pressure in the tank is 130.0 atm.

23. Allows you to do calculations when the only thing that stays constant is the amount of gas. Combined Gas Law

24. Combined Gas Law • A gas takes up a volume of 17 L, has a pressure of 2.3 atm, and a temperature of 299 K. If I raise the temperature to 350 K and lower the pressure to 1.5 atm, what is the new volume of the gas?

25. Combined Gas Law • A gas has a temperature of 14°C, a volume of 4.5 L, and a pressure of 1.5 atm. If the temperature is raised to 29°C and the pressure is raised to 1.8 atm, what is the new volume of the gas?

26. Warm-Up 12/17 • The pressure in an automobile tire is 198 kPa at 27 °C. At the end of the trip the pressure has risen to 225 kPa. What is the temperature of the air in the tire? • A 5.00 L air sample at -50 °C has pressure of 107 kPa. What will the new pressure be when the temperature is raised to 102 °C and the volume expands to 7.00 L?

27. Warm-Up 12/18 • A gas at 155 kPa and 25 °C occupies a container with initial volume of 1.00 L. By changing the volume, the pressure of the gas increases to 605 kPa as the temperature is raised to 125 °C. What is the new volume?

28. Ideal Gas Law • Allows calculation of the number of moles of a gas (n). • R = The ideal gas constant: • 8.31 (L*kPa/mol*K)

29. Ideal Gas Law: • When the temperature of a rigid, hollow sphere containing 685 L of He at 621 K, the pressure is 1,890 kPa. How many moles of Helium are in the sphere?

30. Ideal Gas Law • What pressure would be exerted by 0.450 moles of gas at 25 degrees Celsius if it is contained in a 0.650 L container?

31. Ideal Gas Law: • A child has a lung capacity of 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37 degrees Celsius? (Assume the molar mass of air is 29 g/mol)