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Sara Muttaleb Section 044

23 April 2020 Deriving gas laws using computer simulation Data Table 1: Pressure vs Volume ( with constant temperature at 300 k ).

Trial Pressure Val (atm)

Width (nm) Depth (nm) Height (nm) Volume ( )nm3

1 11.3 15.0 04.0 8.75 525

2 12.5 14.0 04.0 8.75 490

3 13.5 13.0 04.0 8.75 455

4 14.5 12.0 04.0 8.75 420

5 15.7 11.0 04.0 8.75 385

6 17.5 10.0 04.0 8.75 350

7 19.4 09.0 04.0 8.75 315

8 22.2 08.0 04.0 8.75 280

9 24.5 07.0 04.0 8.75 245

10 29.5 06.0 04.0 8.75 210

11 35.2 05.0 04.0 8.75 175 Observation: The gas particles condense move around quicker and at a shorter distance. As length decreases, pressure increases at a higher rate.

Table 2: Temperature vs volume with constant pressure at 17.5 atm.

Trial Temperature (K)

Width (nm) Depth (nm) Height (nm) Volume ( nm3)

Initial : 300 10.0 04.0 8.75 525

1 373 12.0 04.0 8.75 490

2 282 09.0 04.0 8.75 455

3 262 08.8 04.0 8.75 420

4 243 08.1 04.0 8.75 385

5 226 07.7 04.0 8.75 350

6 205 07.0 04.0 8.75 315

7 190 06.6 04.0 8.75 280

8 177 05.8 04.0 8.75 245

9 157 05.5 04.0 8.75 210

10 135 05.0 04.0 8.75 175 Observation: As temperature increases, volume decreases. Table 3: Temperature vs pressure with volume held constant at 10.0 nm

Trial Temperatur e (k)

Pressure (atm)

Width (nm) Depth (nm) Height (nm)

Volume ( )nm3

1 104 5.5 10.0 04.0 8.75 350

2 204 11.5 10.0 04.0 8.75 350

3 305 18.1 10.0 04.0 8.75 350

4 407 23.3 10.0 04.0 8.75 350

5 508 29.9 10.0 04.0 8.75 350

6 610 35.5 10.0 04.0 8.75 350

7 706 41.4 10.0 04.0 8.75 350

8 801 47.3 10.0 04.0 8.75 350

9 904 52.2 10.0 04.0 8.75 350

10 1014 59.5 10.0 04.0 8.75 350 Observation: As we increase the temperature, the pressure increases as well. Table 4: Pressure vs quantity and temperature held constant at 300 K.

Trial Pressure (atm)

Quantity of gas particles

Temperat ure (K)

Width (nm)

Depth (nm)

Height (nm)

Volume ( )nm3

1 17.7 150 300 10.0 04.0 8.75 350

2 29 250 300 10.0 04.0 8.75 350

3 40.4 350 300 10.0 04.0 8.75 350

4 52.5 450 300 10.0 04.0 8.75 350

5 64.5 550 300 10.0 04.0 8.75 350

6 77.7 650 300 10.0 04.0 8.75 350

7 87.7 750 300 10.0 04.0 8.75 350

8 99.1 850 300 10.0 04.0 8.75 350

9 110.1 950 300 10.0 04.0 8.75 350

10 115.7 1000 300 10.0 04.0 8.75 350

Observation: As pressure is increasing we notice a significant increase in the quantity of gas particles.

Analysis Procedure: Pressure Volume Relationship 1.

Fig.1 Graph representing the relationship between volume and pressure at constant temperature. 2.

Fig 2 Graph representing the relationship between inverse volume and pressure at a constant temperature. 3.​ The relationship between volume and pressure is an inverse relationship because as pressure increases, volume decreases when the temperature is held constant. The ideal gas equation is PV=nRT, where pressure and volume are equated to n, moles, r, Boltzmann constant, and t, temperature. Boyle's law equation PV=K, where pressure and volume are equated to constant temperature.

4. ​We were asked to graph the inverse volume to state Boyle’s law that pressure is inversely proportional to a constant temperature P=1/V. Analysis Procedure 2: Volume Temperature Relationship 5.

Fig 3. Graph representing the relationship between temperature and volume with constant pressure at 17.5 atm. 6. ​The relationship between volume and temperature is directly proportional. As volume increases, temperature increases. In the equation . for the initial volumeV 1 T 1 = V 2 T 2 V 1 T 1 and temperature of the gas and stand for the final volume and temperature.V 2 T 2 7. ​The temperature is in Kelvin units at the y-axis, it represents the temperature of the gas that we are measuring the volume of. ​ ​Y= 0.568x+33.1. The slope of the graph is 0.568.

Analysis procedure 3: Temperature Pressure Relationship 8.

Fig 4. Graph representing the relationship between pressure and temperature at a constant volume 9. ​When the volume is held constant PV=nRT can be rearranged to . ThisP 1 T 1 = P 2 T 2 relationship is directly proportional as the pressure goes up, the temperature also goes up and vice-versa. Increasing the temperature causes the gas particles to move faster. When we hold the volume of the gas constant , the pressure and temperature will increase. 10. ​Temperature is heat. Heat causes molecular motion to increase causing more speed between the particles. So when temperature decreases, volume and pressure would decrease too. As temperature decreases, the pressure decreases too which causes the molecular motion of the gas particles in the tank to slow down. This will cause the volume to shrink due to the slow movement. 11. ​ Pressure of the gas is due to molecular motion with the walls, so if the motion stops at absolute zero, I would expect the pressure and the volume of a gas sample will also become zero. The pressure is 0 atm at absolute zero and all the molecular motion stops.

Analysis Procedure 4: Pressure Quantity Relationship 12.

Fig 5. This graph represents the relationship between quantity of particles and pressure. 13. ​The more increase in the number of gas particles in the container, the higher the pressure. Adding zero particles will cause the pressure to be at zero and it slowly increases as we add particles to the tank. I would say yes, this should be the same for all gases. 14.​ When the number of moles increases, the volume and pressure increases as well. In the equation v/n=k express if temperature and pressure remain constant. Therefore, the volume of gas has a proportional relationship with the number of moles of gas. If the number of moles increase, the volume of gas increases. 15.​ The slope of the pressure vs quantity of particles relationship graph is 0.116. The full equation is y=0.116x+0.385. If the temperature is constant, then the value should be the same to other gases as well. Citation: Tro, Nivaldo J. (2017). Chemistry; A Molecular Approach. Pearson Education.