1. How do Gases Behave?
Chem Unit 12

2. Main Ideas
For a fixed amount of gas, a change in one variable – pressure, temperature, or volume – affects the other two.
The ideal gas law relates the number of particles to pressure, temperature, and volume.
When gases react, the coefficients in the balanced chemical equation represent both molar amounts and relative amounts.

3. The Gas Laws
12.1

4. The Gas Laws: Objectives
State the relationship among pressure, temperature and volume of a constant amount of gas.
Apply the gas laws to problems involving the pressure, temperature, and volume of a constant amount of gas.

5. Pressure Units Pressure Units: 1 atm = 1 atmosphere
1 atm = 760 Torr (short for Toricelli)
1 atm = 760 mm Hg
1 atm = 101,325 Pa (short for Pascal)
1 atm = 101 kPa (kilopascal)

6. Boyles Law
Robert Boyle ( ), an Irish chemist, described this relationship between pressure and the volume of a gas.
How are pressure and volume related?
As volume goes down, pressure goes up. Inverse relationship
Example:

7. Boyles Law
Boyle’s law states that the volume of a fixed amount of gas held at a constant temperature varies inversely with the pressure.
Formula: P1V1 = P2V2

8. Practice Problem #1
A diver blows a 0.75 L air bubble 10 m under water. As it rises to the surface, the pressure goes from 2.25 atm to 1.03 atm. What will be the volume of air in the bubble at the surface? 1.6 L

9. Charles Law
Jacques Charles ( ), a French physicist, studied the relationship between volume and temperature.
How are temperature and volume related?
As temperature goes up, volume goes up. Direct relationship
Example:

10. Charles Law
Charles’s law states that the volume of a given amount of gas is directly proportional to its Kelvin temperature at constant pressure.
Formula:
Temperature in Kelvin
A temperature of 0 K corresponds to 0 ml, and doubling the temperature doubles the volume. Zero on the Kelvin scale is also known as absolute zero.
This is the lowest possible theoretical temperature.

11. Practice Problem #2
A helium balloon in a closed car occupies a volume of 2.32 L at 40.0°C. If the car is parked on a hot day and the temperature inside rises to 75.0°C, what is the new volume of the balloon, assuming the pressure remains constant? 2.58 L

12. Lussac’s Law
Joseph Lussac ( ), found that a direct pressure of a fixed amount of gas varies directly with the Kelvin temperature when the volume remains constant.
How are temperature and pressure related?
As temperature goes up, pressure goes up. Direct relationship
Example:

13. Lussac’s Law
Lussac’s Law states that the pressure of a fixed amount of gas varies directly with the Kelvin temperature when the volume remains constant.
Formula:

14. Practice Problem #3
The pressure of the oxygen gas inside a canister is 5.00 atm at 25.0°C. The canister is located at a camp high on Mount Everest. If the temperature there falls to -10.0°C, what is the new pressure inside the canister? 4.41 L

15. Combined Gas Law
The Combined Gas Law states the relationship among pressure, temperature, and volume of a fixed amount of gas. The relationships are the same as the other laws but combined into one mathematical statement.
Formula:

16. Practice Problem #4
A gas at 110kPa and 30.0°C fills a flexible container with an initial volume of 2.00 L. If the temperature is raised to 80.0°C and the pressure increases to 440 kPa, what is the new volume? 0.58 L

17. Homework CALM: 5 questions P443 #1,2; P446 #4-6

18. The Ideal Gas Law
12.2

19. The Ideal Gas Law: Objectives
Relate number of particles and volume using Avogadro’s principle.
Relate the amount of gas present to its pressure, temperature, and volume using the ideal gas law.
Compare the properties of real and ideal gases.

20. Avogadro’s Principle
Avogadro’s Principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
The size of the molecules do not matter; therefore the identity of the gas does not matter.
Example:

21. Molar Volume
Molar Volume of a gas is the volume that 1 mol occupies at 0.00° C and 1 atm pressure.
STP: The conditions of 0.00°C and atm are known as standard temperature and pressure.
1 mol of gas at STP = 22.4 L

22. Practice Problem #5
How many moles are in a sample of gas that has a volume of 3.72 L at STP? 1.66 L

23. Practice Problem #6
The main component of natural gas used for home heating and cooking is methane (CH4). Calculate the volume that 2.00 Kg of methane gas will occupy at STP. 2.80x103 L

24. Ideal Gas Law
Avogadro’s principle, Boyle’s law, Charles’s law and Lussac’s law can all be combined into a single mathematical statement that describes the relationship among pressure, volume, temperature and number of moles of a gas. Constant

25. Ideal Gas Law
Since ideal gases react the same no matter their identity, every gas has the same constant when using the Ideal Gas Law.
  (L atm)/(mol K)

26. Practice Problem #7
Calculate the number of moles of ammonia gas (NH3) contained in a 3.0 L vessel at 3.00 x 102 K with a pressure of 1.50 atm mol

27. Real vs. Ideal Gases
Ideal gases follow the assumptions of the kinetic molecular theory (KMT). Assumptions:
An ideal gas is one whose particles do not take up space.
Gas molecules do not have volume; their movement creates volume.

28. Real vs. Ideal Gases
Ideal gases follow the assumptions of the kinetic molecular theory (KMT). Assumptions:
Ideal gases do not experience intermolecular attractive forces.
Gas molecules are too far apart to attract or repel each other.

29. Real vs. Ideal Gases
Ideal gases follow the assumptions of the kinetic molecular theory (KMT). Assumptions:
Ideal gas particles are in constant, random motion and collide with each other and the walls of the container.
Collisions of the molecules are elastic and cause pressure.

30. Real vs. Ideal Gases
In reality, no gas is truly ideal. Most gases behave like ideal gases at a wide range of temperatures and pressures. Under the right conditions, calculations made using the ideal gas law closely approximate experimental measurements.

31. Real vs. Ideal Gases When do real gases not behave as ideal gases?
Low temperatures
Gas molecules do not have the kinetic energy they usually do and do not move as fast. Because they are moving slowly, attractive forces can change the way they behave.

32. Real vs. Ideal Gases When do real gases not behave as ideal gases?
High pressures
Gas molecules are crowded and their volume becomes significant to the overall volume of the container.

33. Gas Stoichiometry
13.3

34. Gas Stoichiometry: Objectives
Determine volume ratios for gaseous reactants and products by using coefficients from chemical equations.
Apply gas laws to calculate amounts of gaseous reactants and products in a chemical reaction.

35. Gas Stoichiometry
Stoichiometry of reactions involving gases often give pressure, volume and/or temperature in order to find moles.
The “core” process of the stoichiometry remains the same.

36. Practice Problem #8
What volume of oxygen gas is needed for the complete combustion of 4.00L of propane gas (C3H8)? Assume that pressure and temperature remain constant.
20.0 L O2; because moles and volume are directly related, volume can be used with the mole ratios.

37. Practice Problem #9 Ammonia is synthesized from hydrogen and nitrogen.
N2(g) + 3H2(g)  2NH3(g)
If 5.00 L of nitrogen reacts completely with hydrogen at a pressure of 3.00 atm and a temperature of 298 K, how much ammonia, in grams, is produced?
21.0 g NH3

38. Practice Problem #10
What volume of H2O(g) measured at STP is produced by the combustion of 5.73 g of natural gas (CH4) according to the following equation?
CH4(g) + 2O2(g)  CO2(g)+2H2O(g)
16 L

39. Practice Problem #11
Calcium hydride combines with water according to the equation CaH2(s) + 2H2O(l) 2H2(g) + Ca(OH)2(s) Beginning with 84.0 g of CaH2 and 36.0 g of H2O, what volume of H2 will be produced at 273 K and a pressure of 1609 torr?

40. Practice Problem #12
Ammonia is synthesized from hydrogen and nitrogen. N2(g) + 3H2(g) -> 2NH3(g) You have 15.0g of N2 and 5.0g of H2 at STP. How many grams of NH3 can be produced and what is the mass of the excess reactant?

41. Accumulating Content
12.4

42. Accumulating Content: Objectives
Apply knowledge and skills from previous units to content learned in this unit.

43. Accumulating Content Paper
Write a one page paper (single spaced) about how chemistry and gases are related.
Ideas:
Medical: hyperbaric chamber, ozone, anesthetic gases
Ecological: greenhouse gases, gas pollution
History: Haber, chemical warfare, pneumatic chemists