1. Gases
Chapter 10

2. Characteristics of Gases
Expand to fill a volume (expandability)
Compressible
Readily forms homogeneous mixtures with other gases
Have extremely low densities.
These behaviors are due to large distances between the gas molecules.

3. Pressure F P = A Pressure is the amount of force applied to an area.
Atmospheric pressure is the weight of air per unit of area.

4. Units of Pressure Pascals Bar mm Hg or torr Atmosphere 1 Pa = 1 N/m2
1 bar = 105 Pa = 100 kPa
mm Hg or torr
These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury.
Atmosphere
1.00 atm = 760 torr

6. Pressure Conversion Factors 1 atm = 760 mmHg 1 atm = 760 torr
1 atm =  105 Pa
1 atm = kPa.

7. Manometer
Used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.
Manometer at <, =, > P of 1 atm

8. Example
On a certain day the barometer in a laboratory indicates that the atmospheric pressure is torr. A sample of gas is placed in a vessel attached to an open-end mercury manometer. A meter stick is used to measure the height of the mercury above the bottom of the manometer. Level of the mercury in the open end arm of the manometer has a measured height of mm, and that in the arm that is in contact with the gas has a height of mm.
What is the pressure of the gas?
What is the pressure of the gas in kPa

9. The Gas Laws There are four variables required to describe a gas:
Amount of substance
Volume of substance
Pressures of substance
Temperature of substance
The gas laws will hold two of the variables constant and see how the other two vary.

10. Boyle’s Law
The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

11. As P and V are inversely proportional
A plot of V versus P results in a curve.
Since
V = k (1/P)
This means a plot of V versus 1/P will be a straight line.
PV = k

12. A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?

13. Charles’s Law
The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.
i.e., V T
= k
A plot of V versus T will be a straight line.

14. A sample of carbon monoxide gas occupies 3. 20 L at 125 0C
A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?

15. Avogadro’s Law
The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.
Mathematically, this means
V = kn

16. Ammonia burns in oxygen to form nitric oxide (NO) and water vapor
Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?

17. Ideal-Gas Equation V  nT P So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
Combining these, we get
V  nT P

18. The Ideal Gas Equation
Combine the gas laws (Boyle, Charles, Avogadro) yields a new law or equation.
Ideal gas equation:
PV = nRT
R = gas constant = L.atm/mol-K
P = pressure (atm) V = volume (L)
n = moles T = temperature (K)

19. The conditions 0 0C and 1 atm are called standard temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal gas occupies L.
R = L • atm / (mol • K)

20. What is the volume (in liters) occupied by 49.8 g of HCl at STP?

21. Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume. What is the final pressure of argon in the lightbulb (in atm)?

22. Densities of Gases n P V = RT
If we divide both sides of the ideal-gas equation by V and by RT, we get n V P RT =

23. Densities of Gases n   = m P RT m V = We know that
moles  molecular mass = mass
n   = m
So multiplying both sides by the molecular mass ( ) gives P RT m V =

24. Densities of Gases P RT m V = d =
Mass  volume = density
So, P RT m V =
d =
Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas.

25. Molecular Mass P d = RT dRT P  =
We can manipulate the density equation to enable us to find the molecular mass of a gas: P RT
d =
Becomes
dRT P
 =

26. C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l)
Gas Stoichiometry
What is the volume of CO2 produced at 370 C and 1.00 atm when 5.60 g of glucose are used up in the reaction:
C6H12O6 (s) + 6O2 (g) CO2 (g) + 6H2O (l)

27. Gas Mixtures and Partial Pressures
Dalton’s Law
Dalton’s Law - In a gas mixture the total pressure is given by the sum of partial pressures of each component:
Pt = P1 + P2 + P3 + …
- The pressure due to an individual gas is called a partial pressure.

28. PA = nART V PB = nBRT V XA = nA nA + nB XB = nB nA + nB PT = PA + PB
Consider a case in which two gases, A and B, are in a container of volume V.
PA =
nART V
nA is the number of moles of A
PB =
nBRT V
nB is the number of moles of B
XA = nA
nA + nB
XB = nB
nA + nB
PT = PA + PB
PA = XA PT
PB = XB PT
Pi = Xi PT
where i is the mole fraction (ni/nt).

29. A sample of natural gas contains 8. 24 moles of CH4, 0
A sample of natural gas contains 8.24 moles of CH4, moles of C2H6, and moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)?

30. Partial Pressures
When one collects a gas over water, there is water vapor mixed in with the gas.
To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

31. Kinetic-Molecular Theory
This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

32. Kinetic-Molecular Theory
Theory developed to explain gas behavior
To describe the behavior of a gas, we must first describe what a gas is:
Gases consist of a large number of molecules in constant random motion.
Volume of individual molecules negligible compared to volume of container.

33. Kinetic-Molecular Theory
Intermolecular forces (forces between gas molecules) negligible.
Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature.
Average kinetic energy of molecules is proportional to temperature.

34. Kinetic-Molecular Theory
ε = ½ mu2

35. Application to the Gas laws
Effect of Volume increase at constant temperature
More space
Fewer collisions
u is unchanged
Effect of a temperature increase at constant volume
Less Space
More collisions
Increase in u

36. Molecular Effusion and Diffusion
Consider two gases at the same temperature: the lighter gas has a higher u than the heavier gas.
Mathematically:
The lower the molar mass, M, the higher the u for that gas at a constant temperature.

37. Molecular Effusion and Diffusion

38. Effusion
The escape of gas molecules through a tiny hole into an evacuated space.

39. Diffusion
The spread of one substance throughout a space or throughout a second substance.
NH4Cl
NH3
17 g/mol
HCl
36 g/mol

40. Molecular Effusion and Diffusion
Graham’s Law of Effusion
Graham’s Law of Effusion – The rate of effusion of a gas is inversely proportional to the square root of its molecular mass.
Gas escaping from a balloon is a good example.

41. Molecular Effusion and Diffusion
Diffusion and Mean Free Path
Diffusion of a gas is the spread of the gas through space.
Diffusion is faster for light gas molecules.
Diffusion is slowed by gas molecules colliding with each other.
Average distance of a gas molecule between collisions is called mean free path.

42. Real Gases
In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

43. Real Gases: Deviations from Ideal Behavior
From the ideal gas equation, we have PV = nRT
This equation breaks-down at
High pressure
At high pressure, the attractive and repulsive forces between gas molecules becomes significant.
Small volume
At small volumes, the volume due to the gas molecules is a source of error.

44. Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature.

45. Corrections for Nonideal Behavior
The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.
The corrected ideal-gas equation is known as the van der Waals equation.

46. Real Gases: Deviations from Ideal Behavior
The Van der Waals Equation
Two terms are added to the ideal gas equation to correct for volume of molecules and one to correct for intermolecular attractions.
a and b are constants, determined by the particular gas.

47. The van der Waals Equation
) (V − nb) = nRT
n2a V2
(P +

48. Example
Consider a sample of 1.00 mol of carbon dioxide gas confined to a volume of 3.000L at 0.0 C. Calculate the pressure of the gas using the van der waals equation