## Sunday, September 25, 2016

### The Gas Laws

The Kinetic Theory of Matter models many observed phenomenon related to the way matter behaves in relationship to temperature. It is especially useful to explain how gases behave and serves well to help conceptualize The Gas Laws.

Because gases expand to fill the container they are in, when conditions change, the gases respond. How they respond depends on what changes. In order to work with gases, it is necessary to understand four concepts within the context of the Kinetic Theory of Matter.

Two of the concepts are not new: Volume and Temperature.

Volume
The total space something occupies.

The amount of space that a substance or object occupies, or that is enclosed within a container.

Volume is often measured in some unit cubed. For example, it may be in cm3 or mm3 or cubic inches or cubic meters which is m3Volume can also be measured in liters or millimeters (l or ml). In some of the models, using cubic meters is necessary, so becoming familiar with gases in that unit is important.

TemperatureThe average kinetic energy of the molecules within a substance. An indication of the degree of warmth.
Within the context of the kinetic theory of matter, temperature is the measure of how much energy the molecules have, on average. Another way to think about temperature is (because KE = 1/2MV2) that it tells us how fast the molecules of a substance are moving.
In science, we will use Celsius or Kelvin temperature scales to describe temperature.
To convert:
Celsius = Kelvin - 273.15
Kelvin + 273.15 = Celsius

Kelvin = Celsius + 273.15
Celsius + 273.15 = Kelvin

The last concept related to gas within the kinetic theory of matter is pressure.

Pressure
The continuous physical force exerted on or against an object by something in contact with it. The force exerted per unit area.

Pressure is the result of a force distributed over an area. There are several ways to measure pressure.

Pressure is measured in pascals, Pa - sometimes expressed as newtons per square meter, N/m2. These mean exactly the same thing. Pascals is the SI unit for pressure.

Be careful if you are given pressures in kPa (kilopascals). For example, 150 kPa is 150,000 Pa. You must make that conversion before you use the ideal gas equation.

Should you want to convert from other pressure measurements:

1 atmosphere = 101,325 Pa

1 bar = 100 kPa = 100,000 Pa

http://www.chemguide.co.uk/physical/kt/idealgases.html

Another way to measure pressure in in millimeters of mercury, which is a measure used in weather and comes from the use of mercury barometers.

Within the framework of the kinetic theory of matter, pressure can be understood as the sum of all the forces of all the molecules of a gas colliding with the sides of the container. Each molecule is moving quickly and sometimes the collide with the container. When the molecules of the gas strike the molecules of the container, kinetic energy is transferred, and the effect is noted as pressure. The more often and more energetically molecules strike the container, the higher the pressure will be.

Number of Molecules

One last concept that must be mentioned is the number of molecules being observed. This is rather intuitive: the number of molecules is… the number of molecules in the container.

Counting molecules is not easy. They are… small and do not take up much room. Any sample would have a bazillion molecules in it!

bazillion |bəˈzilyən|
cardinal number informal, chiefly N. Amer.
a very large exaggerated number.

Numbering molecules is usually done by saying how many moles are present.

The mole is the unit of measurement in the International System of Units (SI) for amount of substance. It is defined as the amount of a chemical substance that contains as many elementary entities, e.g., atoms, molecules, ions, electrons, or photons, as there are atoms in 12 grams of carbon-12 (12C), the isotope of carbon with relative atomic mass 12 by definition. This number is expressed by the Avogadro constant, which has a value of 6.022140857(74)×1023/mol. The mole is one of the base units of the SI, and has the unit symbol mol.

Avogadro's Number: 6.0221409e+23 = 6.0221409 X 1023

= 602,214,090,000,000,000,000,000

The Gas Laws

With an understanding of what pressure is added to an understanding of temperature and volume, it is possible to make sense of what happens with gases as changes occur.

Changing Temperature
When the temperature of a sample of gas in a container goes up…

By definition, this means that the molecules have higher kinetic energy. Therefore:
• if the volume of the container cannot change, the molecules (moving faster) will hit the container more often and with more kinetic energy and raise the pressure.
• if the volume of the container CAN change, the molecules (moving faster) will take up more space (spread out) and increase the volume.
Raising the temperature of a gas will increase its pressure if the volume of the gas and number of molecules are constant.

Changing Volume
When the size of the container decreases…

By definition, this means that the molecules have higher kinetic energy. Therefore:
• if the volume of the container decreases and the temperature stays the same, the molecules will strike the walls of the container more often and, thus, increase pressure.
• if the volume of the container decreases and the pressure stays the same, the temperature will decrease.
Reducing the volume of a gas increases its pressure if the temperature of the gas and the number of particles are constant.

Changing the Number of Molecules
When the number of molecules goes up…
• more molecules in the container will result in more frequent collisions with the container.

Increasing the number of particles will increase the pressure of a gas if the temperature and volume are constant.

In each of the cases above, changing the value the other direction (i.e. decreasing temperature, increasing the size of the container, or decreasing the number of molecules) results in the opposite affects. Based on these observations, mathematical models for how gases behave have been developed.

Charles's Law
The volume of a gas is directly proportional to its temperature in kelvins if the pressure and number of molecules are constant.

Boyle's Law
The volume of a gas is inversely proportional to its pressure if the temperature and the number of molecules are constant.

The behavior of gas, when the number of molecules is a constant, can be described by combining Boyle's Law and Charles's Law into a single equation. This is the Combined Gas Law

Combined Gas Law
Pressure is inversely proportional to volume, or higher volume equals lower pressure. Pressure is directly proportional to temperature, or higher temperature equals higher pressure.

Using these three models, we can explain and predict how gases will behave under many different circumstances.

When working with these formulas, you can use a variety of units for pressure and volume and can, should you wish to do so, convert from one to the other. However, the temperature must be expressed in Kelvin.

BONUS!
How fast are molecules moving? Really fast! Molecules move at hundreds of meters per second, which is even more hundreds of miles per hour!

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Definitions and content from:
New Oxford American Dictionary
Physical Science Concepts in Action, Pearson
http://www.chemguide.co.uk/physical/kt/idealgases.html