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

Wednesday, September 21, 2016

Density and Kinetic Theory of Matter

Density is the ratio of a substance's mass to its volume and can be expressed mathematically as 

D=M/V. 

Density results from the number of protons, neutrons, and electrons in the atoms that make up the substances and how closely they are arranged to each other either in the substance.

As the temperature of matter increases, its molecules move more rapidly and get farther apart. Solids, liquids, and gases expand as temperature increases.

Since the volume goes up, but the mass stays the same, density, therefore, must decrease as a function of increasing temperature.

When matter changes from a solid to a liquid, in most cases, the liquid will take up more space and thus be less dense. Likewise, when a liquid becomes a gas, the molecules spread out even more, and the density goes down even more.

Since mass stays the same, but volume increases, density must decrease as temperature goes up and as matter changes from solids to liquids and to gasses.

Monday, September 19, 2016

Kinetic Theory of Matter and States of Matter—Solids, Liquids, Gases

All matter in all creation responds to changes in temperature in several ways. One of those ways it in regard to its physical state. Depending on temperature, matter on earth will usually be either solid, liquid or gas (though two other states are possible under extreme conditions.)

To understand why matter changes state, it is necessary to first understand temperature. To understand temperature, it is necessary to understand the Kinetic Theory of Matter.

The Kinetic Theory of Matter says that all particles of matter are in constant motion. This means that in any sample, the molecules are moving. The faster an object (of any size) moves, the more kinetic energy it has.

There is a formula for kinetic energy that relates kinetic energy to mass and velocity:

KE = 1/2MV2

This formula models the observations that KE (kinetic energy) goes up as velocity increases. The Kinetic Theory of Matter says that the warmer something is, the faster the molecules go. Therefore, warmer molecules have more kinetic energy.

This is a key understanding for much of what follows with regard to states of matter.

The understanding of the Kinetic Theory of Matter leads directly to the definition of temperature.

Temperature is a basic measurement that is related to many of the concepts that will follow in the exploration of states of matter.

Temperature
The average kinetic energy of the molecules in a sample.

We measure temperature with a thermometer (A meter of the thermo.). A thermometer is placed in contact with a substance and the molecules of the substance bump into the thermometer until its molecules have the same average kinetic energy as the substance. When this occurs, the thermometer will indicate a temperature in one or more standard temperature scales.

Temperature scales that are commonly used include Fahrenheit, Celsius, and Kelvin. Most science relies on Celsius and Kelvin.
To convert from Celsius to Kelvin:

Kelvin = Celsius + 273.15
Celsius = Kelvin - 273.15

To convert from Celsius to Fahrenheit:

Fahrenheit = Celsius * (9/5) + 32
Celsius = (Fahrenheit - 32) * 5/9

So, temperature can be understood as the average kinetic energy of the molecules as they move in constant motion.

The state of matter depends on its temperature. When the average kinetic energy of the molecules is relatively low, then the matter will be observed as a solid. Extremely low temperatures beyond what is normal can result in another state of matter called a Bose-Einstein condensate, which will be discussed later. As the temperature goes up, matter will change into a liquid, then into a gas. At ultimately high temperatures, matter will be a plasma.


Solids
When in the solid state, matter has a definite shape and volume.

Solids, at any given temperature, will not change in shape or volume. The size and shape of a block of metal does not change unexpectedly.

This is because the molecules are bound to each other by forces that are stronger than the average kinetic energy of the individual molecules at that particular temperature. Though the molecules "wiggle" in place, they are not moving with sufficient energy to break the bonds that hold them in place.

As the temperature goes up, the wiggling will take up more space, and most solids will expand, but the shape will remain uniform and the increase in size is small by comparison to the size of the original.


Liquids
When in the liquid state, matter has a definite volume, but not a definite shape.

Liquids, at any given temperature, change shape to fit the container in which they are kept, but they retain their volume. Pouring a liquid from one container to another changes its shape, but does not change its volume.

The reason that liquids change shape is because the kinetic energy of the molecules exceeds the force that holds them together in the solid. But those forces still are strong enough to keep them from simply scattering anywhere. The liquid sticks to itself, but not so strongly that it has a fixed shape.

As the temperature goes up, molecules in a liquid (as in a solid) move more rapidly. The faster they move, the further they can get from the other molecules, and thus, they take up more space. As with solids, higher temperatures result in most liquids taking up more space, but the volume (as with solids) increase is small by comparison to the volume of the original.


Gases
When in the gas state, matter has neither a definite volume nor a definite shape.

Gases, at any given temperature, change shape and volume to fit and fill the container in which they are kept. Changing the size or shape of the container results in the gas rearranging to fill it.

This is because the molecules in a gas are moving so rapidly that they have exceeded the force that holds solids and liquids together. They have "escaped" and move freely within whatever space they are contained within.

As the temperature continues to go up, they will continue to move more and more rapidly. This change of kinetic energy will affect how hard they crash into the walls of the container—that is, if the volume does not change, as temperature goes up, the pressure in the container will go up.


Bose-Einstein Condensate
A state of matter where molecular kinetic energy is nearly zero (thus, the molecules are nearly motionless).

When in the Bose-Einstein condensate state, all of the atoms of a substance behave as if they were a single particle. This occurs at near -273 C (0 K).
When you get to a temperature near absolute zero, something special happens. Atoms begin to clump. The whole process happens at temperatures within a few billionths of a degree, so you won't see this at home. When the temperature becomes that low, the atomic parts can't move at all. They lose almost all of their energy.
Since there is no more energy to transfer (as in solids or liquids), all of the atoms have exactly the same levels, like twins. The result of this clumping is the BEC. The group of rubidium atoms sits in the same place, creating a "super atom." There are no longer thousands of separate atoms. They all take on the same qualities and, for our purposes, become one blob. 
http://www.chem4kids.com/files/matter_becondensate.html

Plasma
At extremely high temperatures or low pressures, the kinetic energy of the molecules of a gas will be so high the electrons become free.

Plasmas are created when conditions are such that the atoms "shake off" their electrons. The space is filled up with the atom's nuclei and its electrons, but they are not bound to each other. From the framework of the kinetic theory of matter, plasmas exist when the kinetic energy exceeds the force that binds the electrons to the atom. This happens at very high temperatures, very low pressures, or some combination of the two.


Viewing states of matter through the lens of the kinetic theory of matter offers a powerful view of how and why solids, liquids, and gases behave as they do. Understanding the way they respond to increasing temperature (which is a measure of increasing kinetic energy) is more clear when understood from the model of moving molecules.

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Definitions and content from:
New Oxford American Dictionary
Physical Science Concepts in Action, Pearson
http://en.wikipedia.org
http://www.chem4kids.com/files/matter_becondensate.html