1. Dr. Namphol Sinkaset Chem 200: General Chemistry I
Ch. 5: Gases
Dr. Namphol Sinkaset
Chem 200: General Chemistry I

2. I. Chapter Outline Introduction Gas Pressure Gas Laws Gas Law Problems
Dalton’s Law of Partial Pressures
Kinetic-Molecular Theory of Gases
Real Gases

3. I. The Unique Gas Phase
Physical properties of a gas are nearly independent of its chemical identity!
Gas behavior is markedly different than solid or liquid behavior.
We look at the origins of equations used to describe gases and then theorize the reasons why gas behavior is so universal.

4. II. Pressure
Pressure is simply a force exerted over a surface area.

5. II. Atmospheric Pressure
Patm is simply the weight of the earth’s atmosphere pulled down by gravity.
Barometers are used to monitor daily changes in Patm.
Torricelli barometer was invented in 1643.

6. II. Manometers
In the lab, we use manometers to measure pressures of gas samples.

7. II. Units of Pressure
For historic reasons, we have units such as torr and mm Hg. (Why?)
The derived SI unit for pressure is N/m2, known as the pascal (Pa).
Standard conditions for gases (STP) occurs at 1 atm and 0 °C. Under these conditions, 1 mole of gas occupies 22.4 L.
Note that 1 atm = 760 mm Hg = 760 torr = kPa.

8. III. Gas Laws
A sample of gas can be physically described by its pressure (P), temperature (T), volume (V), and amount of moles (n).
If you know any 3 of these variables, you know the 4th.
We look at the history of how the ideal gas law was formulated.

9. III. Volume and Pressure – Boyle’s Law
The volume of a gas is inversely related to pressure, i.e. if P increases, V decreases.

10. III. Volume and Temperature – Charles’s Law
The volume of a gas is directly related to its temperature, i.e. if T is increased, V will increase.

11. III. The Combined Gas Law
Boyle’s and Charles’s Laws can be combined into a convenient form.

12. III. Volume and Moles – Avogadro’s Law
The pressure of a gas is directly related to the number of moles of gas, i.e. if n increases, V will increase.

13. III. The Ideal Gas Law
The ideal gas law is a combination of the combined gas law and Avogadro’s Law.
R = L atm/K mole

14. IV. Gas Law Problems There are many variations on gas law problems.
A few things to keep in mind:
Temperature must be in Kelvin
If problem involves a set of initial and final conditions, use combined gas law.
If problem only gives information for one set of conditions, use ideal gas law.

15. IV. Sample Problem
What’s the final pressure of a sample of N2 with a volume of 952 m3 at 745 torr and 25 °C if it’s heated to 62 °C with a final volume of 1150 m3?

16. IV. Sample Problem
What volume, in mL, does a g sample of N2 occupy at 21 °C and 750 torr?

17. IV. Sample Problem
A sample of N2 has a volume of 880 mL and a pressure of 740 torr. What pressure will change the volume to 870 mL at the same temperature?

18. IV. Other Uses of Ideal Gas Law
The ideal gas law can be used to find other physical values of a gas that are not as obvious.
gas density, d = mass/volume
gas molar mass, MW = mass/mole
stoichiometry, via moles and a balanced equation

19. IV. Sample Problem
Find the density of CO2(g) at 0 °C and 380 torr.

20. IV. Sample Problem
An unknown noble gas was allowed to flow into a mL glass bulb until the P = 685 torr. Initially, the glass bulb weighed g, but now it weighs g. If the temperature is 27.0 °C, what’s the identity of the gas?

21. H2SO4(aq) + 2NaCl(s)  Na2SO4(aq) + 2HCl(g)
IV. Sample Problem
How many mL of HCl(g) forms at STP when kg of NaCl reacts with excess H2SO4?
H2SO4(aq) + 2NaCl(s)  Na2SO4(aq) + 2HCl(g)

22. V. Partial Pressures
Each gas in a mixture behaves like it’s the only gas there.
Dalton’s Law of Partial Pressures states that the total pressure of a mixture of unreacting gases is the sum of all individual pressures.
Each individual pressure is a partial pressure.
Ptotal = P1 + P2 + P3 + P4 + …

23. V. Partial Pressures
You already have experience with partial pressures.
Ptotal = PH2 + PH2O

24. V. An O2/N2 Gas Mixture
Let’s say we have O2 and N2 as a gas mixture. Then Ptotal = PO2 + PN2. Applying the ideal gas law…

25. V. An O2/N2 Gas Mixture
Now we add the individual pressures to find the total pressure.
Note that the total pressure is related to the total moles.

26. V. An O2/N2 Gas Mixture What happens if we divide PO2 by Ptotal?
A new quantity which we call the mole fraction appears.

27. V. Mole Fraction
We define a new unit of concentration, the mole fraction (X).
Partial pressures are directly related to the mole fraction.
For the O2/N2 mixture, for N2 specifically, we have…

28. V. Sample Problem
Calculate the partial pressures of 5.50 g He, 15.0 g Ne, and 35.0 g Kr at STP.

29. VI. Kinetic-Molecular Theory
Why do gas laws work well for all gases?
The Kinetic-Molecular Theory of gases was proposed which consists of 3 postulates.
Gas particles are negligibly small, and any sample has a huge # of particles. The volume of each particle is so small that we assume they have mass but no volume.
The average kinetic energy of a particle is proportional to the kelvin temperature
Gas particles collide in perfectly elastic collisions w/ themselves and container walls and they move in straight lines between collisions, neither attracting nor repelling one another.

30. VI. Imagining a Sample of Gas
We imagine a sample of gas – chaos, molecules bumping into each other constantly.
After a collision, 2 molecules may stop completely until another collision makes them move again.
Some molecules moving really fast, others really slow.
But, there is an average speed.

31. VI. Gas Molecular Speeds
As temp increases, avg. speed increases.
i.e. avg. KE is related to temp!!
Any 2 gases at same temp will have same avg. KE!

32. VI. Why Do Gas Laws Work So Well?
Recall that the gas laws apply to any gas – the chemical identity is not important.
Gas particles only interact when they collide. Since this interaction is so short, chemical properties don’t have time to take effect!!

33. VI. Explaining Boyle’s Law

34. VI. Explaining Charles’s Law

35. VI. Explaining Avogadro’s Law

36. VI. Explaining Dalton’s Law

37. VII. Deviations from PV=nRT
Under extreme conditions (high P or low T), gases deviate from ideal gas law predictions.
Why? What’s so different about these conditions?

38. VII. Gas Particle Volume
Gas molecules do take up space! When very close to one another, entire volume of container is not available for travel, so actual volume of gas is larger.

39. VII. Intermolecular Forces
Gas molecules interact if they are very close to one another…

40. VII. van der Waals Equation
Under extreme conditions, ideal gas law cannot be used.
correction terms for P and V