Understanding the Behavior of Gases

The Kinetic Molecular Theory of Gases states that molecules are considered as hard spheres, extremely difficult to compress. They possess mass but have practically no volume. The particles are so far apart that it is the empty space, rather than the matter represented by molecules, that is actually compressed.

Gas molecules are always in motion. They travel in straight lines interrupted only by collisions with other molecules or with the walls of the container. The molecules, therefore, like moving bullets, possess kinetic energy; all objects moving from one place to another have kinetic energy (also known as transational energy)

No attractive or repulsive forces exist between molecules, o between the molecules and the walls of the container. In all collisions, no energy is lost as friction (heat). The energy lost by molecule1 in a collision with molecule2 is gained by the molecule2. This explains the ability of gases to fill the confining container and the failure of gases to come to rest at the bottom of the container.

Pressure

Gas pressure is the result of simultaneous collisions of billions upon billions of gas particles on an object. When there are no gas particles present, there are no collisions therefore resulting in no pressure. We called this a vacuum.

Barometers are commonly used to measure atmospheric pressure.

The SI unit of pressure is the Pascal (Pa). Atmospheric pressure at sea level is about 101 kPa (kilopascals). Two older measurements of pressure are millimeters of mercury and the atmosphere. One millimeter of mercury (1 mm Hg) is the pressure needed to support a column of mercury 1 mm high. This is equal to 133 Pa. One standard atmosphere (1 Atm) is equal to 101 kPa or 760 mm Hg.

1 Atm = 101 kPa = 760 mm Hg

Avogadro's Hypothesis

Avogadro's Hypothesis sates that equal volumes of gas at the same temperature and pressure contain an equal number of particles.
Whenever we have equal volumes of gases at the same temperature and pressure, the volumes must contain equal numbers of particles. Thus, 1 mol (6.02X10^2 molecules) of any gas is equal to 22.4 L.

The Effect of Changing the Size of the Container

If you think about it logically, then this concept really isn't that hard to understand. If you change the internal volume of a container, without the release of the gas inside it, then the pressure of the gas contained inside should increase. This relationship is directly proportional to each other. If you have 1L of gas inside a container at 100 kPa pressure and you decrease the internal volume of that container to 0.5L then the new pressure of the gas is 200 kPa.

The Effect of heating or Cooling a Gas

Just like before, if you think about this logically, this concept will be easy to comprehend. If you change the temperature of a gas, then the pressure of the gas will change accordingly (if the temperature drops, then the particles will slow down. If the temperature increases, then the particles will speed up). For example, if you have a bunch of gas at 100K at 100 Kpa and you increase the temperature of this gas to 200K, then the pressure will increase to 200 kPa.

Real VS Ideal Gases

An ideal gas is a gas that will follow the gas laws at in all conditions of pressure and temperature. An ideal gas is a substance that does not really exist.
The kinetic theory states that an ideal gas has no volume and that the particles are not attracted to each other. Nevertheless, under many conditions the behaviors of other real gases is similar to that of an ideal gas.
Real gases can be liquefied and sometimes solidified by cooling them and applying pressure. Idea gas does not.

Dalton's Law of Partial Pressure

The contribution of each gas in a mixture makes to the total pressure is the partial pressure exerted by that gas. In a mixture of gases the total pressure is the sum of the partial pressures of the gases.

Ptotal = P1 + p2 + p3

At constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures.

Example:
Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of Oxygen (PO2) at 101 kPa if PN2 = 79.1 kPa, PCO2 = .040 kPa and Pother = 0.947 kPa?

We know that Ptotal = 101 kPa.
PO2 = Ptotal - (PN2 + PCO2 + Pother)
20.9 kPa

Boyle's Law of Pressure - Volume Changes

For a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure. ( Vα 1/P ).

P1XV1 = P2XV2

Example:

We have 30 L of helium gas at 100 kPa in a balloon. What is the new volume when the balloon rises to an altitude where the pressure is only 25 kPa? (Assuming that the temperature remains the same)

P1 X V1 = P2 X V2

100 X 30 = 25 X V
3000/25 = V
V = 120L

Charles' Law for Temperature-Volume Changes

It states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.

V1/T1 = V2/T2

Example:

A balloon, inflated in an air-conditioned room at 27C, has a volume of 4.0 L. It is heated to a temperature of 57C. What is the new volume of the balloon if the pressure remains constant?

First, convert the Celsius to Kevin:
27 +273 = 300K
57 + 273 = 330K

4/300 = X/330
X = 4.4L

Gay Lussac's Law for Temperature-pressure Changes

States that the pressure of a gas is directly proportional to the KELVIN TEMPERATURE if the volume stays the same.

P1/T1 = P2/T2

Example:

A balloon, inflated in an air-conditioned room at 27C, has a volume of 100 Kpa. It is heated to a temperature of 927C. What is the new pressure of the balloon if the pressure remains constant?

First, convert everything to Kelvin:

27+273 = 300K
927 + 273 = 1200K

100/300 = X/1200
X = 400 kPa

Ideal Gas Law

An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

An ideal gas can be characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them may be deduced from kinetic theory and is called the

The ideal gas law can be viewed as arising from the kinetic pressure of gas molecules colliding with the walls of a container in accordance with Newton's laws. But there is also a statistical element in the determination of the average kinetic energy of those molecules. The temperature is taken to be proportional to this average kinetic energy; this invokes the idea of kinetic temperature.
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html

(P1)(V1) (P2)(V2)
----------- = ------------
(T1) (T1)

Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure
V2 = Final volume
T2 = Final temperature

Example 1:

P1 = 15 kPa
V1 = 10 L
T1 = 300K
T2 = 300K
P2 = X
V2 = 1 L

(15)(10) (X)(1)
---------- = ---------
(300) (300)

(300)(15)(10) = (X)(1)(300)
(150)(300) = (X)(300)
150 = X

Answer: The final pressure is 150 kPa.

Example 2:

A container with a volume of 1.0L is occupied by a gas at 15 Atm at 25C. The gas pressure increases to 6 Atm and the temperature rises to 100C. What is the new volume?
*Note: mark down all your information*

P1 = 15 Atm
V1 = 1.0 L
T1 = 25C
P1 = 6 Atm
V2 = X
T2 = 100C

(15)(1) (6)(X)
--------- = ---------
(25) (100)

(100)(15)(1) = (6)(X)(25)
1500 = 150X
X = 10

Answer: The new volume is 10L (don't forget to use significant digits).

To solve questions where they do not give you all this information, you can use any of the following formulas. All the following formulas were put together to derive the formula shown above.

Gay Lussac's Law:
P1/T1 = P2/T2

Charles Law:
V1/T1 = V2/T2

Pt = P1 + P2 + P3 etc..

Boyle's Law:
PV = K
P = K/V or V = K/P

The value of, K, depends on the mass of the gas sample and its temperature. Note as the pressure of the gas increases, the volume decreases proportionally so as to keep the product, (P)(V) is constant. If the pressure is doubled, then the volume is reduces by a half.

Other Useful Formulas

(P X V)/(n X R X T) = 1