Gas Laws

1. Gas Laws • The ideal gas law is used to describe the behavior of an idealgas. • Idealgas:hypothetical gas that obeys kinetic molecular theory and the ideal gas law

2. Gas Laws • The ideal gas law is used in calculations for a specific sample of gas that has a constant T, P, V, and n. • i.e. no changes are being made to the sample of gas • If you know 3 of the 4 variables, you can calculate the other using the ideal gas law.

3. Gas Laws Example: Calculate the volume of 1.00 mol of an ideal gas at 1.00 atm and 0.oC.

4. Gas Laws • The temperature and pressure used in the previous problem are commonly used to report the properties of gases. • Standard Temperature and Pressure (STP): • 0.oC and 1 atm. • KNOW THIS !!

5. Gas Laws • Molar volume: • the volume one mol of a gas occupies (L/mole) • At STP, one mole of an ideal gas has a molar volume of 22.4 L: • 22.4 L 1 mol

6. Gas Laws • The ideal gas law applies only to ideal gases. • Does not always accurately describe real gases • The molar volumes for many real gases at STP differ slightly from 22.4 L/mol. • In most cases, the differences between ideal gas behavior and real gas behavior is so small that we can ignore it.

7. Gas Laws Example: A weather balloon contains 4.75 moles of He gas. What volume does the gas occupy at an altitude of 4300 m if the temperature is 0.oC and the pressure is 0.595 atm?

8. Gas Laws Example: A used 425 mL aerosol can contains 0.761 g of propane gas (as a propellant). Calculate the pressure (in torr) in the can if it is accidentally heated to 395oC. (Warning: Don’t do this!!)

9. Gas Laws Example: A tire with an interior volume of 3.50 L contains 0.357 mol of air at a pressure of 2.49 atm. What is the temperature of the air in the tire in oC?

10. Gas Laws • The ideal gas law was useful in determining the properties of a specific sample of gas at constant T, P, V, and n. • We often need to know how a change in one (or more) properties impacts the other properties for a sample of a gas.

11. Gas Laws • Combined Gas Laws: P1V1 = P2V2 T1 T2 This equation is true when the number of moles of a gas is constant.

12. Gas Laws Special cases for the combined gas law: • At constant temperature (T1 = T2), P1V1 = P2V2 • At constant volume (V1 = V2), P1= P2 T1 T2 • At constant Pressure (P1 = P2), V1 = V2 T1 T2

13. Gas Laws Example: A helium-filled balloon occupies 6.00 L at 25oC and 0.989 atm. What volume will the balloon occupy on top of Pike’s Peak if the pressure is 0.605 atm and the temperature is 19oC?

14. Gas Laws Example: Suppose a used aerosol can contains a gas at 0.989 atm at 23oC. If this can is heated to 425oC, what is the pressure inside the can (assuming that the can does not rupture)?

15. Gas Laws--More Applications • The ideal gas equation can be used to determine either the density or the molar mass of a gas. d = P M RT where d = density P = pressure T = temperature in K R = gas constant M = molar mass

16. Gas Laws--More Applications • The density of a gas depends on: • pressure • temperature • molar mass • At constant temperature and pressure the densities of gas samples are directly proportional to their molar masses: • d = PM • RT

17. Gas Laws – More Applications Example: Which of the following gases will be more dense than dry air (assuming an average molar mass of 29 g/mol) at some specific temperature and pressure. methane carbon dioxide helium fluorine

18. d = P M • RT Gas Laws--More Applications • If molar mass and pressure are held constant, then the density of the gas will decrease with increasing temperature. • Hot air rises because density is inversely proportional to temperature.

19. Gas Laws--More Applications Example: What is the density of helium gas at 1.00 atm and 25oC?

20. Gas Laws--More Applications Example: What is the average molar mass of dry air if it has a density of 1.17 g/L at 21oC and 740.0 torr?

21. Gas Laws--More Applications • Understanding the properties of gases is important because gases are often the reactants or products in a chemical reaction. • Often need to calculate the volume of gas produced or consumed during a reaction

22. grams A grams A Moles A Moles A Molar mass Molar mass PV = nRT Molar ratio Molar ratio grams B grams B Moles B Moles B Molar mass Molar mass PV = nRT Gas Laws--More Applications PA, VA, TA PB, VB, TB

23. Gas Laws--More Applications Example:The air bag in a car is inflated by nitrogen gas formed by the decomposition of NaN3: 2 NaN3(s)  2 Na (s) + 3 N2 (g) If an inflated air bag has a volume of 36 L and is to be filled with N2 gas at a pressure of 1.15 atm at a temperature of 26oC, how many grams of NaN3 must be decomposed?

24. PV = nRT Gas Laws--More Applications Moles A Moles N2 Gas Data N2 Molar ratio Molar ratio grams B grams NaN3 Moles B Moles NaN3 Molar mass Molar mass

25. PV = nRT Gas Laws--More Applications 36L N2, 1.15 atm 26oC Moles A Moles N2 Find Molar ratio Molar ratio Given grams B grams NaN3 Moles B Moles NaN3 Molar mass Molar mass

26. Gas Laws--More Applications

27. Gas Laws--More Applications Example: How many mL of oxygen gas can be collected at STP when 1.00 g of KClO3 decomposes: 2 KClO3 (s)  2 KCl (s) + 3 O2 (g)

28. PV = nRT Gas Laws--More Applications mL O2 at STP (1.0atm, 0oC) Moles A Moles O2 Given Molar ratio Molar ratio Find grams B grams KClO3 Moles B Moles KClO3 Molar mass Molar mass

29. Gas Laws--More Applications

30. Gas Laws – More Applications Example: What volume of CO2 at 125oC and 1.15 atm will be produced by the combustion of 1.00 L of C2H6 at 25oC and 1.00 atm? 2 C2H6 (g) + 7 O2 (g)  4 CO2 (g) + 6 H2O (g)