Chapter 5

We already learned that a gas takes the shape & size of its container.

Other General Properties of Gases:

1. Compressibility

2. Diffusion

3. Fill Containers

Exert Pressure – Pressure is the force a substance exerts per unit of area.

Mathematically; P =Area

Force

The SI unit of pressure is the pascal (Pa), but generally in chemistry we will not be using this term.

Measuring atmospheric pressure is measured using a barometer. We will explain its operation using the following figure:

Pressure is measured in several other units: lbs/in2 , dynes/cm2 and then several units derived from how a barometer works, based on the length of the column of mercury supported by air pressure: inches of mercury, cm of mercury, mm of mercury (also called torr, named after barometer inventor, Torricelli).

The normal pressure of air at sea level is 14.67 lbs/in2, which is called 1.00 atmospheres (atm)

1.00 atm = 76.0 cm of Hg = 760 mm of Hg = 760 torr = 1.01325 x 102 kPa

You need to know the underlined values and be able to convert from one to another, except for the value in kilopascals.

All gases obey what chemists know as the Gas Laws.

Boyle’s Law:

When Temp. is held constant, the pressure on a sample of gas will be inversely proportional to its volume.

P1V1 = P2V2

Charles’ Law: If the pressure on a sample of gas is held constant, the volume will be directly proportional to absolute T.

2

2

1

1

T

V

T

V

Avogadro’s Law: At constant T and P, the volume of a gas is directly proportional to the number of moles of the gas present. In a chemical reaction involving only gases, and assuming no change in T and P, then the ratio of volumes is the same as the ratio of moles; in other words the same as the coefficients of the equation:

3H2 (g) + N2 (g) 2NH3 (g)

means that

3 volumes 3H2 (g + 1 volume N2 (g) 2 volumes NH3 (g)

Combined Gas Law: All these individual gas laws can be combined into one equation with no specific restrictions.

2

22

1

11

T

VP

T

VP

REMEMBER: Temperature must be in K to use this equation

Universal Gas Law: Another form of combining these gas laws is called the Universal Gas Law:

PV = nRT , where n = # of moles and R is the Universal Gas Constant. R has the following values:

R = 0.0821 L - atmK -mol

= 82.1 mL - atmK -mol

= 62.4 L - torrK -mol

= 62400 mL - torrK -mol

Sometimes chemists need to know values at some standardized conditions so that they can compare their results accurately. For gases these standard conditions are called STP. STP stands for standard temperature and pressure, which has the specific values of 1.00 atm and 0.0C or 273.15 K

From PV = nRT, other useful relationships can be derived:

MW = mass(RT) / PV or simply

MW = gRT/PV

Also,

d = P(MW) / RT

Use the combined gas law when your problem gives you 2 sets of conditions.

Use the Universal gas law when there is only one set of conditions.

Let’s do examples 5.3 (page 182), 5.4 (page 183), 5.5 (page 184), 5.6 (page 184) and 5.9 (page 188).

Dalton’s Law of Partial Pressures

If there is a mixture of gases, then each gas behaves independently and has its own P (T and V will be the same for all the gases in the mixture) These individual P’s are called Partial Pressures. They are symbolized as PHe or PCO .

Dalton’s Law says that the total pressure of the mixture is the sum of all the partial pressures:

Ptotal = PA + PB + PC etc.

Each individual gas obeys all the gas laws independently.

Another concentration term that chemist frequently use is called the mole fraction (Xa, Xb etc). Mole fraction is

defined as ratio of the number of moles of one substance compared to the total number of moles of all substances in the mixture.

In a mixture containing 3 substances; a, b, and c, the mole fraction of a would be calculated as:

cba

aa molesmolesmoles

molesmoles

Then PA = XAPTotal

Kinetic Molecular Theory:

1. All gases composed of small particles called molecules, whose individual volume is negligible.

2. Molecules are in constant, random straight line motion

3. Molecules have no attractions or repulsions, but do collide with each other and with the walls of their container

4. Collisions are perfectly elastic (no loss of total kinetic energy)

5. Average kinetic energy is directly proportional to absolute (Kelvin) temp. The SI unit of energy is the joule (J) or more commonly kJ

a. Remember that K = C + 273.15

Kinetic Molecular Theory can explain Boyle’s Law. Pressure is caused by molecules hitting the walls of container. The more molecules that hit in a certain amount of time, the higher the pressure. If volume is decreased, molecules have shorter distance to move before hitting wall, therefore more molecules will hit, and pressure will increase. It also explains compressibility, Charles’ Law and Dalton’s Law.

Diffusion: The gradual mixing of molecules of one gas with molecules of another by virtue of the above theory. Gave rise to another law, Graham’s Law of Diffusion:

A

B

B

A

MW

MW

Rate

Rate

In other words, the ratio of the rate of diffusion of 2 gases is inversely proportional to the square roots of the MW’s.

All of the calculations in this chapter assumes that all gases obey the Kinetic-Molecular Theory. This is only true for an Ideal Gas. In reality, there is no such thing as an ideal gas. Most gases come close to ideal behavior under normal conditions and therefore all these laws are very useful. There have been attempts to come up with an equation that accounts for real behavior. The most famous is the Van der Waals equation. None of these work perfectly either and in my opinion are not worth the effort.