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Deriving Gas Laws Using Computer Simulations

Procedure 1

1)

Figure 1: Pressure vs Volume.

2)

Figure 2: Pressure vs 1/Volume.

3) When temperature and quantity are held constant the relationship that exists between pressure and volume is the inverse relationship in which an increase in one causes a decrease in the other. Relating pressure to a constant gives:

Therefore Boyle’s Law states:

4) Pressure and the inverse of volume yields a straight-line relationship between the variables. Which relates the Ideal gas law equation. .

Procedure 2

5)

Figure 3: Volume vs Temperature.

6) When pressure and quantity are held constant the relationship between volume and temperature is directly proportional When temperature of the gas increases the volume increases, which causes frequent collisions of moving particles in a container.

Relating volume and pressure to a constant gives. (Charles Law)

7) Slope= When pressure and quantity are constant the ideal gas equation becomes. Therefore, the slope represents the number of moles in the gas. The number of moles would be different depending on the gas since different gases occupy different volumes at changing temperatures.

Procedure 3

8)

Figure 4: Temperature vs Pressure.

9) When volume and quantity remain constant the relationship that exists between pressure and temperature is that pressure is directly proportional to temperature . As the temperature of a gas increases the pressure increases. The equation relating Pressure and Temperature is:

When volume and quantity are constant the ideal gas law becomes:

.

Therefore, the slope represents the number of moles in the gas. The number of moles would be different depending on the gas.

10) As the temperature increase, the molecular motion of the gas would also increase which would increase the volume of the gas. Moreover, as the temperature decreases the molecular motion of the gas would decrease which then causes the volume of the gas to decrease. Gas particles collision with one another would decrease.

11) Absolute zero would cause the molecular motion of a substance to stop; this would cause the pressure and volume of a sample to decrease to the point that there is no pressure nor volume, in which it would have characteristics of an ideal gas, which is not possible.

Procedure 4

12)

Figure 5: Molecules vs Pressure.

13) When the number of moles of a gas in a container increase, the pressure increases. In other words there are more particles compacted in a small area the distance between the particles decreases. More particles per volume, which means particles are bumping into one another and the walls more often. This would be the same for all gases because all gases behave the same.

14) When pressure and temperature are held constant increasing the number of moles would increase the volume of the gas. Like blowing up a balloon the volume of the balloon increases to keep the pressure constant and the temperature remains the same. Likewise, decreasing the number of moles would decrease the volume of the gas. If pressure and volume were held constant, increasing the number of moles would decrease the temperature since pressure and volume are constant. This would cause the particles to collide more often, which would decrease the energy and heat of the particles. However, decreasing the number of moles would increase the temperature since there is more space for the particles to move. Therefore, temperature is inversely proportional to the number of moles present.

Ideal gas law (P &V are constant):

15)

Slope or from the trendline that is created from the graphs.

· Pressure vs 1/volume

. The number represents the amount of moles of gas assuming the temperature is constant The linear relationship will start to change at low volume due to condensation of the gas. Therefore, the number of moles depends on the type of gas.

· Volume vs Temp

SlopeWhen pressure and quantity are constant the ideal gas equation becomes . Therefore, the slope represents the number of moles in the gas. The number of moles would be different depending on the gas since different gases occupy different volumes at changing temperatures.

· Pressure vs Temperature

Slope when volume and quantity are constant, the ideal gas law becomes. Therefore, the slope represents the number of moles in the gas. The number of moles would be different depending on the gas.

Pressure vs Volume

Voume (nm^3)

0.46 0.51 0.6 0.68 0.81 0.96 1.26 1.85 225.0 200.0 175.0 150.0 125.0 100.0 75.0 50.0

presseure (atm)

Vlume (nm^3)

Pressure vs 1/volume

1/voume

0.46 0.51 0.6 0.68 0.81 0.96 1.26 1.85 0.00444444444444444 0.005 0.00571428571428571 0.00666666666666667 0.008 0.01 0.0133333333333333 0.02

1/ Volume (nm^-3)

Pressure (atm)

Volume vs Temp

200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 4.7 5.9 6.7 7.9 8.4 9.0 9.5 10.0

Temperature (K)

Volume (cm^3)

Pressure vs Temperature

pressure

300.0 355.0 400.0 452.0 500.0 550.0 601.0 650.0 702.0 752.0 801.0 1.17 1.33 1.59 1.75 1.98 2.15 2.3 2.6 2.75 2.99 3.16

Temperature (k)

Pressure (atm)

Molecules vs Pressure

108.0 122.0 143.0 160.0 194.0 231.0 245.0 275.0 0.53 0.65 0.74 0.83 0.98 1.15 1.3 1.39

Number of Molecules

Pressure (atm)