Gas Laws

## Test ReviewTest on

• Be able to explain how gas particles move, according to the kinetic theory.
• Use the kinetic theory to explain gas pressure.
• What is meant by elastic collision?
• What relationship is compared using the Kelvin scale?
• Explain the following statement: The percent of oxygen present in the atmosphere remains the same no matter the altitude. However, at extreme altitudes, breathing becomes laborous.
• Describe what happens to kinetic energy during gas particle collisions and as Kelvin temperature increases.
• How does the kinetic theory explain the compressibility of gases?
• Why do aerosol containers display the warning, "Do not incinerate"?
• Be able to calculate problems using Boyle's Law, Charles' Law, Gay-Lussac's Law, Combined Gas Law, Ideal Gas Law, Dalton's Law of Partial Pressures, and Avogadro's Hypothesis. (Formulas will be given on the test!)

### Learning Goals

• Describe the general characteristics of gases as compared to other states of matter, and list the ways in which gases are distinct.
• Describe how a gas responds to changes in pressure, volume, temperature, and quantity of gas.
• Use the ideal-gas equation to solve for one variable (P, V, n, or T) given the other tree variables or information from which they can be determined.
• Use the gas laws, including the combined gas law, to calculate how one variable of a gas (P, V, n, or T) responds to changes in the one or more of the other variables.
• Calculate the partial pressure of any gas in a mixture, given the composition of that mixture.
• Calculate the mole fraction of a gas in a mixture, given its partial pressure and the total pressure of the system.
• Describe how the distribution of speeds and the average speed of gas molecules changes with temperature.
• Describe how the relative rates of effusion and diffusion of two gases depend on their molar masses (Graham’s Law).
• Use the principles of the kinetic-molecular theory of gases to explain the nature of gas pressure and temperature at the molecular level.
• Explain the origin of deviations show by real gases from the relationship PV/RT = 1 for a mole of an ideal gas.
• Cite the general conditions of P and T under which real gases most closely approximate ideal-gas behavior.
• Explain the origins of the correction terms to P and V that appear in the van der Waals equation.

### Key Concepts

1 atm = 760 mm Hg = 760 torr = 101.3 kPa = 14.7 lb/in2

K = ºC + 273.15

`Avogadro's Law:                V1n2 = V2n1`
`Boyle's Law:                   P1V1 = P2V2`
```Charles' Law:                  V1 = V2
T1   T2```
```Combined Gas Law:             P1V1 = P2V2
T1  =  T2```
```Dalton's Law of Partial Pressures:      Ptotal = P1 + P2 + P3 + ...

derivation:           Pi = ni x Ptotal
ntotal```
```Density:                      g  =  P x MW
V      R· T```
`Gay-Lussac's Law:              P1T2 = P2T1`
```Ideal Gas Law:                  PV = nRT

R = 0.0821 liter· atm/mole· K
= 8.31 liter· kPa/mole· K
= 8.31 J/mole· K
= 8.31 V· C/mole· K
= 8.31 x 10-7 g· cm2/sec2· mole· K
(for calculating the average speed of molecules)
= 6.24 x 104 L· mm Hg/mole· K
= 1.99 cal/mole· K
```
```Molecular Weight:             MW = g· R· T
P· V
van der Waal's          (P + a/V2)(V - b) = R· T
(real gases)                       or
(P + n2a/V2))V - nb) = n· R· T

Here "a" corrects for force of attraction between gas molecules,
and "b" corrects for particle volume.
Graham's Law of Effusion:
__     __
r1   \/d2   \/MW2   t2   u1
=   __ =   __ =    =
r2   \/d1   \/MW1   t1   u2

where,        r = rate of diffusion
d = density
MW = molecular weight
t = time
u = average speed```
• Kinetic Molecular Theory

1. Gases are composed of tiny, invisible molecules that are widely separated from one another in empty space.
2. The molecules are in constant, continuous, random, and straight-line motion.
3. The molecules collide with one another, but the collisions are perfectly elastic (no net loss of energy).
4. The pressure of a gas is the result of collisions between the gas molecules and the walls of the container.
5. The average kinetic energy of all the molecules collectively is directly proportional to the absolute temperature of the gas. Equal number of molecules of any gas have the same average kinetic energy at the same temperature.

```                                Et = m· u2 = cT
2

c = 3R
2Na

u2 = 3· R· T = 3· R· T
m· Na      MW

where,     Et = average kinetic energy of translation
m = mass (of particle)
u = velocity (average speed)
c = constant
Na = Avogadro's number
R = 8.31 x 10-7 g· cm2/sec2· mole· K
T = temperature in K```