### It's a Gas!

by

Barbara Pawela

This lesson was created as a part of the SMART website and is hosted by the Illinois Institute of Technology

Seeing the Invisible

`When you put your hand 12 inches away from your face what do you see between your face and your hands?  When you  wave your hands in front  of your face what do you feel?    Even though you  could not see anything, you could feel a breeze.

What happens when you spray perfume?  You smell an odor.  Why?

When someone talks or another sound is made, what happens?

Take a plastic bag (like the ones from the produce section) and wave and scoop, and close the bag.

What happens to the bag?

These activities help to show that although air cannot be seen , it can be felt; an odor can be diffused through it; sound vibrations can be transmitted through it; and it takes up space.  Air is a mixture of gases.  Let us continue an investigation of some information on gases.

### Kinetic Molecular Theory of Ideal Gases

All matter is composed of tiny, discrete particles (atoms or molecules).

Molecules of gas are very small compared to the distances between them.

These particles are in rapid, random, constant  straight line  motion.

Molecules collide with one another and the sides of the container.

Energy is conserved in these collisions, although one molecule may gain energy at the expense of another.

Boyle's Law    states that the pressure -volume  product will always be the same value if the temperature and amount remain constant.

## Animated Boyle's Law

#### Glenn Research Center

A slide and text version of this slide is also available.

Air is a gas. Gases have various properties which we can observe with our senses, including the gas pressure (p), temperature, mass, and the volume (V) which contains the gas. Careful, scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas.

In the mid 1600's, Robert Boyle studied the relationship between the pressure and the volume of a confined gas held at a constant temperature. Boyle observed that the product of the pressure and volume are observed to be nearly constant. (The product of pressure and volume is exactly a constant for an ideal gas.) This relationship between pressure and volume is called Boyle's Law in his honor.

In a scientific manner, we can fix any two of the four primary properties and study the nature of the relationship between the other two by varying one and observing the variation of the other. This slide shows a schematic "gas lab" in which we can illustrate the variation of the various properties. In the lab a theoretical gas is confined in a blue container. The volume of the gas is shown in yellow and is determined by the position of a red piston. The volume can be changed by moving the red piston using the red screw at the top of the piston. The number of moles of the gas is indicated by the number of small black "molecules" in the volume. The moles can be changed by injecting or withdrawing molecules using the pump at the left. There are two probes inserted into the bottom of the container to measure the pressure and the temperature. The pressure can be changed by adding or removing green weights from the top of the red piston, and the temperature can be changed by heating the container with the "torch" at the bottom.

Charles' Law gives the relationship between volume and temperature if the pressure and the amount are held constant.

If the volume of a container is increased , the temperature increases.

If the volume of a container is decreased , the temperature decreases.

### Gases - A "Simple" Place to Start

It was realized early on that gases required the fewest macroscopic parameters to quantify their physical state (to a good approximation). Specifically, we will investigate the parameters: pressure, volume, temperature, and amount to see how they quantify the physical state of a gas. Of course, we need to define these parameters and investigate how they can be measured. After we discuss pressure - and the devices used to measure it - we will analyze some original data made on gas (air - actually a mixture of gases) by Robert Boyle in the 1600's. You will have the opportunity to use your newly-acquired MAPLE skills to investigate this data. First we must talk about pressure and some of the devices that are used to measure it (barometers and manometers).

#### Pressure and its Measurement

Pressure has dimensions of force per Area. The SI unit of pressure is the Pascal (Pa). A Pascal = 1 Newton/m² = kg/(m· s² ). The relationship between atmospheres (atm.) and Pascals is:
`               1.00 atm. = 1.013 x 10^5 Pa`
At 25° C, the density of Hg(l) is 13.6 g/cm³ and the density of H_2O(l) is 1.00 g/cm³. Also, the acceleration due to gravity, g, is 9.8 m/s². From the above information, answer the following:
1. If a barometer, consisting of Hg(l) as the "working fluid", is exposed to a pressure of 1.00 atm. (at 25° C), what will be the height (in cm and in ft.) of the Hg column that is supported?
2. If a barometer, consisting of H_2O(l) as the "working fluid", is exposed to a pressure of 1.00 atm. (at 25° C), what will be the height (in cm and in ft.) of the H_2O column that is supported?

<>Solution to Example:

The relationship between the applied pressure (P) and the height of a fluid is:

`                  P = dgh`
where "g" is the acceleration due to gravity and "d" is the temperature-dependent density of the fluid. The above relationship provides the "working principle" of the barometer.
For Hg(l), d = 13.6 g/cm³. Thus, solving for h, and using dimensional analysis, we have:

Thus, we define 1.00 atm. = 760 mm Hg = 760 torr, where 1 mm Hg = 1 torr. In feet,

The height of mercury is determined by the need to balance the weight of mercury lifted against the weight of the air above it. The weight of air presses down uniformly on everything on the surface of the earth, including the surface of the pool of mercury in the beaker. This pool transmits the pressure uniformly through its volume and therefore maintains the height of mercury in the glass tube. The 76.0 mm of mercury has a weight equal to the weight of a column of air with the same cross-sectional area and a height of 150 km (roughly the height of our atmosphere).
Using a J-tube, we can accurately measure the height of mercury that balances the atmospheric pressure and hence create a barometer.