## Gases

One of the most amazing things about gases is that, despite wide differences in chemical properties, all the gases more or less obey the gas laws. The gas laws deal with how gases behave with respect to pressure, volume, temperature, and amount.

### Pressure

Gases are the only state of matter that can be compressed very tightly or expanded to fill a very large space. Pressure is force per unit area, calculated by dividing the force by the area on which the force acts. The earth's gravity acts on air molecules to create a force, that of the air pushing on the earth. This is called atmospheric pressure.
The units of pressure that are used are pascal (Pa), standard atmosphere (atm), and torr. 1 atm is the average pressure at sea level. It is normally used as a standard unit of pressure. The SI unit though, is the pascal. 101,325 pascals equals 1 atm.
For laboratory work though, the atm is very large. A more convient unit is the torr. 760 torr equals 1 atm. A torr is the same unit as the mm Hg (millimeter of mercury). It is the pressure that is needed to raise a tube of mercury 1 millimeter.

### The Gas Laws: Pressure Volume Temperature Relationships

#### Boyle's Law: The Pressure-Volume Law

Boyle's law or the pressure-volume law states that the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant.
```
```
Another way to describing it is saying that their products are constant.

PV = C

When pressure goes up, volume goes down. When volume goes up, pressure goes down.
From the equation above, this can be derived:

P1V1 = P2V2

This equation states that the product of the initial volume and pressure is equal to the product of the volume and pressure after a change in one of them under constant temperature. For example, if the initial volume was 500 mL at a pressure of 760 torr, when the volume is compressed to 450 mL, what is the pressure?
Basically, you just plug in the values:
P1V1 = P2V2
(760 torr)(500 mL) = P2(450 mL)
760 torr x 500 mL/450 mL = P2 844 torr = P2
The pressure is 844 torr after compression.

#### Charles' Law: The Temperature-Volume Law

This law states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature.

V T
Same as before, a constant can be put in:

V / T = C

As the volume goes up, the temperature also goes up, and vice-versa.
Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.

V1 / T1 = V2 / T2

#### Gay-Lussac's Law: The Pressure Temperature Law

This law states that the pressure of a given amount of gas held at constant volume is directly proporitonal to the Kelvin temperature.

P T
Same as before, a constant can be put in:

P / T = C

As the pressure goes up, the temperature also goes up, and vice-versa.
Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.

P1 / T1 = P2 / T2

#### The Combined Gas Law

Now we can combine everything we have into one proportion:
```
```
The volume of a given amount of gas is proportional to the ratio of its Kelvin temperature and its pressure.
Same as before, a constant can be put in:

PV / T = C

As the pressure goes up, the temperature also goes up, and vice-versa.
Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.

P1V1 / T1 = P2V2 / T2

### The Ideal Gas Law

The previous laws all assume that the gas being measured is an ideal gas, a gas that obeys them all exactly. But over a wide range of temperature, pressure, and volume, real gases deviate slightly from ideal.
Since, according to Avogadro (see chemical reactions: the mole) showed that same volumes of gas contain the same number of moles, chemists could now determine the formulas of gaseous elements and their formula masses. The idea gas law is:

PV = nRT

Where n is the number of moles of the number of moles and R is a constant called the universal gas constant and is equal to approximately 0.0821 L atm mol-1 K-1.

### Partial Pressures

Basically, Dalton's Law of Partial Pressures states that the total pressure of a mixture of nonreacting gases is the sum of their individual partial pressures.

Ptotal = Pa + Pb + Pc + ...

So, if there was a mixture of nitrogen gas at 3 atm and oxygen gas at 1 atm, the total pressure would be 4 atm.

### Kinetic Theory and the Gas Laws

• A gas consists of an extremely large number of very tiny particles that are in constant, random motion.
• The gas particles themselves occupy a net volume so small in relation to the volume of their container that their contribution to the total volume can be ignored.
• The particles often collide in perfectly elastic collisions with themselves and with the walls of the container, and they move in straight lines between collisions neither attracting nor repelling each other.
These are the postulates of the kinetic theory of gases, which explain why the gas laws work. The pressure-volume law works by that when the volume is decreased, the gas particles more frequently hit the sides of the container, creating more pressure. The temperature-volume law works by that when the temperature is increased, the gas particles move faster, hitting the sides of the container and expanding it to accommodate. The pressure-temperature law works by that when the temperature is increased, the gas particles move faster, hitting the sides of the container more often under a constant volume.