1'1'1 Yllj l'nySICS 1 1111113 umme LIID U? Lab 09: Ideal Gas Law Part II PURPOSE In this experiment, we will study more properties of a gas as governed by the Ideal Gas Law. We will use an online simulation from the University of Colorado, Boulder called Gas Properties. THEORY Gases are made up of molecules that are in constant motion and exert pressure when they collide with the walls of their container. The velocity and the number of collisions of these molecules is affected when the temperature of the gas increases or decreases. In a macroscopic perspective, these effects are governed by the Ideal Gas Law: PV = nRT where for an ideal gas, P is the pressure, V is the volume, 11 is the number of moles, T is the temperature, and R is a universal gas constant equal to R=8.3l J/mol K. In this experiment, the temperature of the gas sample will be kept constant. An isothermal process is one in which the temperature of the system remains constant, i.e. it doesn't change. This can occur when a system is in contact with an outside thermal reservoir, and the change in the system will occur slowly enough to allow the system to continue to adjust to the temperature of the reservoir through heat exchange. An adiabatic process is one which occurs without transferring heat or mass between the system and its surroundings. Sometimes a process can occur so rapidly that energy doesn't have a chance to leave the system as heat. This would approximate an adiabatic process. An example is the sudden compression of gas in an internal combustion engine, resulting in the ignition of the gas. A process is reversible when its direction can be reversed to return the system to its original state, staying in thermodynamic equilibrium with its surroundings throughout. SETUP 1. Click on the link above or the separate link in the Lab 09 folder. Click on [6' the \">\" to initiate the simulation. Choose \"Ideal.\" Gas Properties 2. Select the heavy species of molecule (on left): 3. Click on the \"+\" to open the Particles information. 4. By using either the bicycle pump or the \">>\" button, add 500 Heavy particles to the box. Hold Constant . Nothing 5. With the particles in the box, we now have more options for . mums (V) our Ideal Gas controls. Select to hold constant the \"Temperature (T).\" 0 Temperature (T) . Pressure IV I Pressure IT 6. Finally select \"Width.\" Page 2 YY213 Onlz'ne Lab 09 Hold Constant 7. Your initial screen should look like: ART 1: CONSTANT TEMPERATURE l. The temperature will stay constant at 300 K. Pull the chamber wall all of the way to the left. 2. Since the cross-sectional area, A, of the chamber is constant, we will represent volume in terms of one linear dimensionthe nanometer value of the width, W. Later on we will multiply W by the cross-sectional area A to nd the volume in proper units. 3. The rst width of the container will now be 15 nm. Record the pressure that corresponds to this width in the table below. 4. Repeat for widths of 14 nm to 5 nm. Fill out the corresponding pressures in the table. HEAVY SPECIES LIGHT SPECIES 4. Repeat for widths of 14 nm to 5 11m. Fill out the corresponding pressures in the table. HEAVY SPECIES LIGHT SPECIES " " " 1'11!le Unline Lab ()9 5. \"Reset'D the simulation and select \"light species.\" Repeat the setup steps (1-6) for 500 molecules of the light species. Collect data for the light species and fill out the table. 6. Open the Excel le \"Lab 09 Worksheet.\" For the \"Heavy Species\8. Your C-value for the Heavy species is in units of \"nmAtm.\" We can convert the 11m to meters by multiplying by 109. We can convert the Atm to N/m2 by multiplying by 1.013 x 105. Make these two conversions and write your new C-value here (in N/m): C = N/m Page 4 PHY213 Online Lab 09 9. In this experiment we used N = 500 molecules. Avogadro's number is NA = 6.022 X 1023 molecules/mole. So the number of moles ll of gas we have is: N 500 n: == moles NA 6.022x1023 10. For constant cross-sectional area A, the volume of the container will be V = A*W. Using this, and rearranging the Ideal Gas Law for constant temperature T, we have: P: nRT w_1 A W C 11. We can now solve for the cross sectional area A in terms ofL'. Use the value ofL' you calculated above in units of N/m, use the value of II that you calculated above, use T = 300 K, and R=8.31 J/mol K, and we have: AanT: C 12. Assume the cross-sectional area A is a perfect square of side length \"21.\" Find the side length a in units of nanometers: a: A: m. Page 5 13. 14. 15. 16. 17. 18. %error 2 Compare this to the accepted value of 5.92 nm by calculating the percent error: lAccepted Experimental I ' 100% = % Accepted At a given temperature in your data, you may have observed that 500 molecules of the Light species exerted about the same pressure as 500 molecules of the Heavy species! From Experiment 08, we know that the molecular weight of the Heavy species is 7 times larger than the molecular weight of the Light species. So how can the two species exert the same pressure? Let's check this. Reset the simulation LJ and add 500 Heavy molecules to the container at a temperature of 300 K. Click on the Collision Counter. 8 (iolIISIon (Iountor a In the \"Wall Collisions\" window counter, click on the green arrow. How many collisions does the Heavy species have in 10 ps? wall COIIiSions - Sample Period I 1'3 :3 v1 Reset the simulation LJ and add 500 Light molecules to the container at a temperature of 300 K. Click on the Collision Counter. In the \"Wall Collisions\" window5 click on the green arrow. How many collisions does the Light species have in 10 ps? By roughly what factor does the Light species have more collisions than the Heavy species? This helps to explain how the Light species can exert the same pressure as the Heavy species. But it is still not enough to account for the 7:1 disparity in mass between the species. What else about the Light species allows it to make up for the disparity