1. Gases and Their Properties
Chapter 10

2. Students will be able to
Learning Objectives
Students understand
The experimental basis of Boyle’s law, Charles’ law, Avogadro’s hypothesis, and Dalton’s law of partial pressures
Kinetic-molecular theory as it is applied to gases, especially the distribution of molecular speeds
Why real gases do not behave like ideal gases under some conditions
Students will be able to
Describe how changing one property of a gas changes the others
Apply the gas laws to stoichiometric calculations
Use the principles of kinetic-molecular theory to describe gas behavior
Determine the relative rates of effusion of gases
Use the ideal gas law and the van der Waals equation

3. Gases
Some common elements and compounds exist in the gaseous state under normal conditions of pressure and temperature. Many common liquids can be vaporized.
Our gaseous atmosphere provides one means of transferring energy and material throughout the globe.
Gas behavior is reasonably simple and they are well understood. Simple mathematical models may be used.

4. 10.1 Properties of Gases Gas Pressure
Pressure is the force exerted by particles on an object divided by the area upon which the force is exerted.
Gas pressure may be measured in millimeters of mercury (mm Hg or torr), standard atmospheres (atm), the SI unit pascal (Pa), or the bar.
1 atm = 760 mm Hg = kPa = bar

5. Practice Problem
At the summit of Mt. Everest, atmospheric pressure is 29% of the pressure at sea level. Convert the pressure into its corresponding value in units of mm Hg, bars, and kilopascals.

6. 10.2 Gas Laws: Experimental Basis
The volume of a fixed amount of gas at a given temperature is inversely proportional to the pressure of the gas is a statement of Boyle’s Law.
Therefore, at constant temperature and number of moles…
P1V1 = P2V2

7. Practice Problem
A large balloon contains 65.0 L of He gas at 25oC and a pressure of 745 mm Hg. The balloon ascends to 3000 m, at which the external pressure has decreased by 30.%. What would be the volume of the balloon, assuming it expands so that the internal and external pressures are equal? (Assume the temperature is still 25oC.)

8. Gas Laws: Experimental Basis
Charles’ Law: If a given quantity of gas is held at constant pressure, its volume is directly proportional to the Kelvin temperature.
V1/T1 = V2/T2
Remember that T must always be expressed in kelvins!

10. Practice Problem
A balloon is inflated with helium to a volume of 45 L at room temperature (25oC). If the balloon is cooled to -10. oC, what is the new volume of the balloon? Assume that the pressure does not change.

11. Gas Laws: Experimental Basis
Boyle’s and Charles’ Laws may be combined into one equation to give the general gas law or combined gas law. It applies to situations in which the amount of gas does not change.
(P1V1)/T1 = (P2V2)/T2 OR
P1V1T2 = P2V2T1

12. Practice Problem
You have a 22 L cylinder of helium at a pressure of 150 atm and at 31 oC. How many balloons can you fill, each with a volume of 5.0 L, on a day when the atmospheric pressure is 755 mm Hg and the temperature is 22 oC?

13. Avogadro’s Hypothesis
Avogadro proposed that equal volumes of gases under the same conditions of temperature and pressure have equal numbers of particles.

14. Practice Problem
If 22.4 L of gaseous CH4 is burned, what volume of O2 is required for complete combustion? What volumes of CO2 and H2O are produced? Assume all gases have the same temperature and pressure.
CH4 + 2O2  CO2 + 2H2O

15. 10.3 Ideal Gas Law
The four quantities that can be used to describe a gas include pressure, volume, temperature, and amount.
All three laws can be combined to determine a universal gas constant, R, that can be used to interrelate the properties of a gas.
PV = nRT
R = Latm/Kmol

16. Practice Problem
The balloon used by Jacques Charles in his historic flight in 1783 (see page 381) was filled with about 1300 mol of H2. If the temperature of the gas was 23 oC, and its pressure was 750 mm Hg, what was the volume of the balloon?

17. Since n = mass/molar mass, then PV = (m/M)RT
Density of Gases
Since n = mass/molar mass, then PV = (m/M)RT
Since density is defined as d = m/V, we can rearrange the ideal gas equation to say
D = (PM)/(RT)
M = (DRT)/P
Calculate the density of dry air at 15.0 oC and 1.00 atm if its molar mass (average) is g/mol.

18. Practice Problem
A g sample of a gaseous compound exerts a pressure of 561 mm Hg in a volume of 125 mL at 23.0 oC. What is its molar mass?

19. Homework
After reading sections , you should be able to do the following…
P. 403a-b (5-23 odd)

20. 10.4 Gas Laws and Chemical Reactions
Gaseous ammonia is synthesized by the following reaction N2(g) + 3H2(g)  2NH3(g)
in the presence of an iron catalyst at 500 oC.
Assume that 355 L of H2 gas at 25 oC and 542 mm Hg is combined with excess N2 gas. What amount (mol) of NH3 gas can be produced? If this amount of NH3 gas is stored in a 125 L tank at 25.0 oC, what is the pressure of the gas?

21. Practice Problem
If 15.0 g of sodium reacts with water, what volume of hydrogen gas is produced at 25.0oC and a pressure of 1.10 atm?

22. 10.5 Gas Mixtures and Partial Pressures
The pressure of each gas in a mixture of gases (such as our atmosphere) is the partial pressure.
Dalton’s Law of Partial Pressures states that a mixture of gases is the sum of the partial pressures of the different gases in the mixture.
Ptotal = P1 + P2 + P3 +…
Ptotal = ntotal(RT/V)

23. Partial Pressures of Gases
A mole fraction, X, is defined as the number of moles of a substance divided by the total number of moles of all substances present.
PA = XA(Ptotal)

24. Practice Problem
15.0 g of halothane (C2HBrClF3) is mixed with 23.5 g of oxygen gas. If the mixture is placed in a 5.00 L tank at 25.0 oC, what is the total pressure (mm Hg) of the gas mixture in the tank? What are the partial pressures (mm Hg) of the gases?

25. 10.6 Kinetic-Molecular Theory of Gases
The kinetic-molecular theory is a description of the behavior of gases at the molecular level.
Gases consist of particles whose separation is much greater than the size of the particles themselves.
The particles of a gas are in continual, random, and rapid motion. As they move, they collide with one another and the walls of their container.
The average kinetic energy of gas particles is proportional to the gas temperature. All gases, regardless of their molecular mass, have the same average kinetic energy at the same temperature.

26. Kinetic-Molecular Theory
Kinetic energy of a gas particle of mass m may be calculated by
KE = ½ (mass)(speed)2 = ½ mu2
where u is the speed of that molecule.
Average kinetic energy depends only upon Kelvin temperature. Therefore, average kinetic energy for a gas sample is equal to one half the mass times the average of the mean square speed.

27. Kinetic-Molecular Theory
Since average kinetic energy is proportional to temperature, then ½ mu2 must also be proportional to temperature. Therefore the square root of the mean square speed, the temperature, and the molar mass are related.
√u2 = √(3RT)/M
where R is J/Kmol
and 1 J = 1 kg(m2/s2)
All gases have the same average kinetic energy at the same temperature.

28. Calculate the rms speed of helium atoms and N2 molecules at 25 oC.
Practice Problem
Calculate the rms speed of helium atoms and N2 molecules at 25 oC.

29. Case Study p. 394 – The Methane Mystery
Practice Problems
Case Study p. 394 – The Methane Mystery

30. Homework
After reading sections 10.4 – 10.6, you should be able to do the following…
p. 403b-c (31-45 odd)

31. 10.7 Diffusion and Effusion
The mixing of molecules of two or more gases due to their motion is called diffusion. Ex: pizza, bleach
The movement of gas through a tiny hole in a container is called effusion.
Graham’s Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Rate1/Rate2 = √(M2/M1)

32. Common Misconception!
A gas with a lower molar mass does not effuse more quickly because it is smaller, it does so because it is moving more quickly and would have more collisions. This would increase the probability that it would effuse through a tiny hole!

33. Practice Problems
Tetrafluoroethylene, C2F4, effuses through a barrier at a rate of 4.6 x 10-6 mol/h. An unknown gas, consisting of boron and hydrogen, effuses at the rate of 5.8 x 10-6 mol/h under the same conditions. What is the molar mass of the unknown gas?
A sample of pure methane, CH4, is found to effuse through a porous barrier in 1.50 min. Under the same conditions, an equal number of molecules of an unknown gas effuses through the barrier in 4.73 min. What is the molar mass of the unknown gas?

34. 10.8 Nonideal behavior: Real Gases
Most gases behave ideally at low pressures and high temperatures.
Assumptions are not always valid. Sometimes atoms or molecules stick to each other and may be liquified. Volume available to gas molecules may be small.
The van der Waals equation adjusts for nonideal behavior

35. van der Waals Equation (P + a[n/v]2)(V-bn) = nRT
where “a” and “b” are experimentally determined constants
the pressure correction term accounts of intermolecular forces, and the volume correction term accounts for molecular volume

36. Practice Problem
Using both the ideal gas law and the van der Waals equation, calculate the pressure expected for 10.0 mol of helium gas in a 1.00 L container at 25 oC. For helium, a=0.034 (atmL2/mol2) and b= L/mol.

37. Homework
After reading sections , you should be able to do the following…
P. 403d (47-55 odd)