Ideal Gas Law Simulation Lab

12/1/09

Participants: Brian Charron, Kelsey Porter, Evie Bulkeley, Dan Devins

Purpose: The purpose of this lab is to simulate the ideal gas law (PV=N(kb)T). This was done by collecting data in a Phet simulation that allows the person to control the number and type of particles in a box, as well as the pressure, temperature, and volume of the box. The data that was collected is based on Boyle's Law, which shows the relationship between volume and pressure, Gay-Lussac's Law, which shows the relationship between temperature and pressure, and Charles' Law, which shows the relationship between temperature and volume.


Brief Description of Experiment: This experiment used varying levels of pressure, temperature, volume, and the number of particles in a box with a PHet simulation. These factors were evaluated using Boyle's law, Gay-Lussac's law, and Charles' law. To prove the exponential relationship between pressure and volume that is illustrated through Boyle's law, the volume of the box was adjusted (with the size being noted in increments) and the pressure was measured at each one. We graphed the data and found a line of best fit to show that the law correctly illustrates the relationship. The line of best fit follows the equation Y=A/V which is derived from the ideal gas law P=(N(kb)T)/V. Gay-Lussac's Law was also tested to prove the linear relationship between pressure and temperature, and Charles' Law proved the linear relationship between temperature and volume. The relationship between temperature and velocity was then measured for the heavy species and again for the light species of particles by using a line of fit for the graph of this data, which allowed us to determine weights for each of the particles.

Data:

Boyle's Law:

Boyle's_Law_Ideal_Gas_Law.JPG

Gay-Lussac's Law:

Gay-Lussac's_Ideal_Gas_Law.JPG

Charles' Law:

Ideal_Gas_Law_Charle's.JPG

Sample Calculations:

Ideal Gas Law
This law shows how an ideal gas will react.
PV=NKbT
P= pressure
V= volume
N= number of atoms
Kb= Boltzmann Constant
T= temperature
Boyle's Law
Ideal gas law: PV=N(kb)T. Boyle's law can be derived from this equation because it shows the relationship between pressure and volume and will have the equation:
P=(N(kb)T)/V
Gay-Lussac's Law
Gay-Lussac's law can be derived from the ideal gas law because it is the relationship between pressure and temperature and will therefore have the equation:
P=(N(kb))/V * T, and the slope of the graph will be N(kb)/V
Charles' Law
Charles' law can be derived from the ideal gas law because it shows the relationship between temperature and volume and will therefore have the equation:
PV=(N(kb))T

Results:

We were able to prove in this lab that Boyle's law, Charles' Law, and Gay-Lussac's laws are accurate descriptions of physical properties. We confirmed our data by comparing the slope of the line of best fit for the data we had plotted to actual values that were found from deriving slope equations from the equations that are associated with each of these laws and manipulating them to solve for specific variables. Each of these values that we had found were different from the expected values based on the derivations of the actual equations, except for one because the graph allowed room for error, thus proving that these laws hold true.

Lab Questions:

Create a graph for the data you've collected in each of parts 2, 3, and 4. Fit the data appropriately and compare your fit parameter to the expected values for your particular experiment.

The equation we derived for Boyle's Law is P=(N(kb)T)/V. The line of best fit equation is Y=A/V. A is equivalent to N(kb)T. This is proved with the following data substitution example:
T = 300
N = 100
kb = 1.38 x 10^-23
A is 3.798 x 10^-19 according to the graph for Boyle's law above, and (N(kb)T) with the above values is 4.14x10^-19. The line of best fit was therefore very close to the expected values for the experiment with Boyle's Law and the ideal gas law.

The equation we derived for Gay-Lussac's Law is P= (N(kb))/V*T. The slope of the line of best fit should be equal to (N(kb))/V.
N = 100
kb = 1.38 x 10^-23
V = 6.996 x 10^-24
The slope of the line of best fit according to the graph is 174.5. The expected value with the above variables is 197.256. The line of best fit was therefore very close to the expected values with Gay-Lussac's Law.

The equation we derived for Charles's Law is V= (N(kb))/P*T. The slope of the line of best fit should be the same as (N(kb))/P.
N = 100
P = .52Atm (52520Pa)
kb = 1.38 x 10^-23
The slope of the line of best fit on the graph is about 19.93, but could be off by 1.605. The expected value according to the equation is 2.8827x10^-26. These values do not compare well because of the large amount of error that could be present in the graph.


Create a graph for the data you've collected in each of parts 5 and 6. Fit the data appropriately and use your fit parameter to determine the mass of the light and heavy species.

The graphs of the heavy and light particles compare the temperature and the velocities of the particles. This corresponds to the Kinetic Temperature of gases equation: (3/2)(kb)T = (1/2)mv^2. This equation can be re-arranged so it is solving for velocity.
v = ((3)(kb)/m)^0.5*T
The slope of the line of best fit for the heavy and light particle graphs is ((3)(kb)/m)^0.5. This can be re-arranged to solve for mass. The following example is for a heavy species particle.

0.6911 = (3(1.38x10^-23)/m)^0.5
m = 3(1.38x10^-23) / 0.6911 =
5.99x10^-23


Conclusion:

This lab allowed us to gain a better understanding of the various applications of the ideal gas laws through an online simulation. The ideal gas law describes numerous relationships between pressure, volume, and temperature of particles in a closed container. We got to play with these equations and test to see if they accurately describe these relationships. This was done by comparing the slope of the line of best fit for our plotted data to the values that should have been given based on the equation derivations and manipulations. The results we got were nearly perfect, because there were no outside forces or major sources of error acting on the system since it was an online simulation. This experiment helped connect the dots between the relationships between the equations we have been learning in class, and how they all relate to each other. There is no way to really improve the experiment, because the conditions it was performed under (on a website) were nearly perfect. Maybe this is how all labs should be done!



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