# Gas Laws

Simulation Used: Gas Properties from the PhET at the University of Colorado.

Goal of the Lab Experiment: To verify Boyle's and Charle's law for ideal gasses.
• Theory: In a gas where the molecules interact with each other only through collisions, the temperature T, the pressure P, and the volume V satisfy the Ideal Gas Law:

Here T is in Kelvin, P in Pascal, V in cubic meters, and the universal gas constant R equals 8.314 J/K. The number of moles n is defined as:
,
where      is the Avogadro's number and Vmol is the volume of 1 mol of substance also called molar volume.
At Standard Temperature and Pressure (STP) conditions, that is T = 273 K and P = 1 Atm, the molar volume can be directly calculated through the Ideal Gas Law as:

When the temperature is kept constant, the process is called isothermic and the product of the pressure and the volume remains constant (Boyle's Law):
,
If V is kept constant, Charle's Law gives:

• Initial settings:
• Open the simulation Gas Properties
• Click on the "Measurement Tools" button and select "Ruler" and "Species Information"
• Pump in about 200 heavy molecules. If you pump too many, you can open the container at the top and let some molecules out, but the number does not need to be exactly 200.
Record the exact number of the molecules: No:
Calculate the number of moles in the container, n =
• Set up STP conditions:
• Select "Volume" as a constant parameter from the menu on the right. Add or remove heat until the Temperature indicator shows 273 K.
• Select "Temperature" as a constant parameter from the menu on the right. Drag the left wall of the container until the Pressure indicator shows approximately 1 Atm. (The pressure will be variable, but should be around as close to 1 Atm as possible.) Make sure the equilibrium state is reached, that is T and P remain 273 K and 1 Atm, respectively. Now, you have the STP conditions.
• Calculate the volume of the container
• At STP the volume of one mole of particles is given by:
.
• On the other hand, the volume can be calculated using the number of moles as follows:

Combining both formulae, calculate the volume Vo =   m3
• Determine the dimensions of the container.
• Measure the length of the container, Lo =   m
• Click on the "Layer tool" from the menu on the left. Drag it to the utmost top of the container and measure the height of the container.
Record the height value: h =   m
• Determine the width of the container:

Record the width value: w =   m
• Unclick the "Layer tool".

• Activity 1: Verify Boyle's Law
• Perform the experiment:
• Keeping STP conditions, drag the left wall of the container so that the length is L=9 nm
• Wait until the temperature has reached its equlibrium value T = 273 K and measure the pressure, P. Record the value.
• Repeat for lengths: 9 nm, 8 nm, 7 nm, 6 nm, 5 nm, 4 nm, and 3 nm.
• In your lab notebook, write down the data in the following table. Use the dimensions of the container to calculate the volume of the gas in m3.

 L (nm) P (Atm) V (m3) P (Pa)

• Results:
• Plot the PV diagram. What kind of curve is it?
• Plot P vs. (1/V). What kind of curve is it?
• Find the slope of the P vs. (1/V) graph. You can use your calculator, spreadsheet, or you can go to this website. If you choose the latter, clear the data and type in your own data. The slope of the line is given by "m" in the box below the graph.
• What is the physical meaning of the slope of the graph P vs. (1/V)?

• Activity 2: Verify Charle's Law
• Initial settings:
Keep volume constant.
• Record the current number of particles in the container:
N =
• Record the current length of the container and calculate the volume of the container:
L =   nm, V = m3
• Record your initial temperature and pressure in the table below.
• By adding or removing heat, change the state of the gas. Record the new equilibrium temperature and pressure in the table below.
• Repeat the procedure 10 times.
• Record your data in the following table:

 T (K) P (Atm) P (Pa)
• Results:
• Plot P vs. T diagram.
• What is the slope of the graph:
• What is the physical meaning of the slope?

Last modified: Fri Dec 05 18:37:45 Eastern Standard Time 2008