Gas Properties Simulation Activity Worksheet Answer Key

Page 1 Under Pressure: A Gas Properties Homework Activity This activity is designed to help us determine the relationships between the physical properties of gasses, pressure, volume, number of moles, and temperature. We will investigate how a change in one of these properties will affect the rest. The heavy species you will see are a model representation of N2 gas molecules. The N2 gas molecules are shown as blue spheres for simplicity. In reality, we know that N2 molecules are not blue spheres. This exercise is long but you will not be asked to complete the entire thing. Depending on where your last name falls in the alphabet you will be responsible for a different section of the material, as outlined in the chart below. Be sure to take good, clear notes on your results as we will all be sharing the data during the next class period. Everyone must complete part I. In addition to part one: Last Name Additional Part to Complete A-D Part II E-G Part III H-J Part IV K-R Part V S-Z Part VI The website address for the simulation is http://phet.colorado.edu/en/simulation/gas-properties You can either download it and run it from your computer or run it online by clicking “Run Now!” Note: Steps to perform with simulation are in BOLD, questions to answer are in ITALICS. Part I: What units are used to measure temperature, and pressure? How does speed and size of molecules compare to speed and size of familiar objects? Add 100 N2 molecules to the box. To do this, go to the window next to “Heavy Species”. Enter “100” and hit enter key. You can also pump the handle on the bicycle pump by clicking on it and dragging. What is the temperature of the gas molecules? Tgas(K) = __300K___________________ The temperature is given on the Kelvin scale. What would this temperature be on the Celsius scale? Tgas(°C) = ___26.85 °C_________________ How does this compare to the temperature of the room you are in? This is very comparable to room T! Room T is usually around 25°C or 75°C What is the pressure in the box? Pbox(atm) = ____0.52 atm________________ How does this compare to the pressure exerted on you by the air around you? This is less than the external pressure, which is closer to .8 atm (80% of sea level pressure) Page 2 Pause the simulation. Under “Measurement Tools” choose “ruler”. The ruler is in units of nanometers. Click and drag the ruler to measure the diameter of a heavy molecule. What is the diameter of one heavy blue molecule in nm? In m? diametermolecule(nm) = ___0.2 nm__ diametermolecule(m) =__2E-10 m___ The tip of a pencil is about 0.5 mm across. How many heavy molecules could line up across the tip of a pencil? 0.5mm or 5E-4m/2E-10m = 2.5E6 molecules Hit “PLAY” to restart motion. Under “Measurement Tools”, choose “Species Information”. What is the average speed of the molecules? Avg. Speed (m/s) = ____420 m/s________________ Are these molecules moving faster or slower than a car driving 60 miles/hour? 60 mi/hr * (1hr/3600sec) *(5280ft/mi)*(12in/ft)*(2.54cm/in)*(1m/100cm) ~ 26.8 m/s OR 420m/s*(3600sec/hr)*(100cm/m)*(1in/2.54cm)*(1ft/12in)*(1mi/5280ft)~940mi/hr Therefore, the molecule is moving faster by almost a factor of 20. Are these molecules moving faster/slower than a supersonic jet traveling at 2000 miles/hour? The molecule is moving slower by about a factor of 2 How long will it take a heavy molecule to travel 100 meters? (This is approximately the length of a football field.) Time to travel 100 meters (s) = ____.24s__________ Now that we have a frame of reference for how big molecules are and how fast they are moving, we will investigate the relationships between their properties. In looking for a relationship between any 2 properties, we hold all other variables constant. One property (the independent variable) is adjusted, and the impact on another property (the dependant variable) is observed. You do not directly control the dependant variable, but it will change as a result of adjustments you make to the independent variable. Remember that you only have to complete your section, but feel free to play around with changing any of the other variables once you have your necessary data. Page 3 Part II: Pressure versus Volume – Two Properties Enter, One Property Leaves Predict: What will happen to the pressure in a sealed container if you increase the volume, while keeping the temperature and number of molecules in the container constant? The pressure will decrease and will go as 1/V Sketch the relationship between pressure and volume on the graph below. When graphing variables, the independent variable goes on the x-axis and the dependant variable goes on the y-axis. Be sure to label the axes with the variable name and corresponding units, example: pressure (atm) and volume (liters) Under “Measurement Tools”, choose “Ruler” Measure the width of the box using the ruler. Width box (nm)=______6.6 nm_______________ Under “Measurement Tools”, choose “Layer Tool”. Move the bar to the top of the box. What is the height of the box? Height box (nm) = _____5.4 nm (may have 5.3 nm)_______ Click “Pause” and then “Reset” In the “CONSTANT PARAMETER” section click “TEMPERATURE”. Change the width by clicking the handle on the left wall, and moving it left or right. Using the ruler, set the box width to 3 nm. Add 100 heavy molecules and hit enter. Once pressure and temperature have stabilized record the following data. Then move the wall to a new width and record the temperature and pressure. Make sure pressure and temperature have stabilized before you record new values. Table 1. Number T (K) P (atm) Width (nm) Volume (nm3) (see below) Run 1 100 300 0.85 4 216 Run 2 100 300 0.70 5 270 Run 3 100 300 0.53 6 324 Run 4 100 300 0.50 7 378 Run 5 100 300 0.43 8 432 Page 4 If the width of the box is doubled, what happens to the volume? The volume doubles Here only two dimensions, width and height, are visible. You have already measured both of them. Assume the depth of the box is 10.0 nm. Calculate the volume of the box for each run and enter the values into Table 1. What variable(s) did you adjust? Adjusted the volume Besides the variable(s) you adjusted, what other variable changed? The pressure changed Write one sentence describing how volume and pressure are related. As the volume is increased the pressure decreases. The change in pressure goes as 1/V What is the mathematical relationship between volume and pressure? PV = constant Use EXCEL to make a graph of your Pressure vs. Volume data. Does the graph you sketched in the Predictions section agree with the graph of your data? Describe any differences. Yes they agree Part III: Pressure versus Number of Moles – No Holds Barred Predict: What will happen to the pressure if you add more molecules to the sealed container, while holding temperature and volume constant? The pressure will increase linearly if you increase the moles/molecules of gas Sketch the relationship between pressure and number of molecules on the graph below. Hit the “RESET” button. Make sure “TEMPERATURE” is clicked under constant parameters. Add 100 heavy molecules to box. Page 5 Once pressure has stabilized record the following data. Change the number of molecules, wait for the pressure to stabilize again, and record the new data. Table 2. Number T (K) P (atm) Width (nm) Run 1 100 300 0.37 6.6 Run 2 200 300 0.78 6.6 Run 3 300 300 1.12 6.6 Run 4 400 300 1.55 6.6 Run 5 500 300 1.82 6.6 NOTE numbers could change depending on the width of the box and therefore, the volume What variable did you adjust? The number of N2 molecules Besides the variable you adjusted, what other variable changed? The pressure increased Write one sentence explaining how pressure and number of molecules are related. As you increase the number of molecules the pressure responds in a linear fashion What is the mathematical relationship between pressure and number of molecules? P/no. molecules=constant Use EXCEL to make a graph of the relevant variables. Does the graph you sketched in the Predictions section agree with the graph of your data? Describe any differences. Yes, they are similar Part IV: Pressure versus Temperature – A Fixed Volume Cage Match Predict: What will happen to the pressure if you increase the temperature of the sealed container at a constant volume? The pressure will increase linearly if you increase the temperature Sketch the relationship between pressure and temperature on the graph below. Hit the “RESET” button. Make sure “Volume” is clicked under constant parameters. Under “measurement tools” choose “species information” to view the average speed Add 100 heavy molecules to box. Page 6 Once pressure has stabilized record the following data. Then change the temperature by adding or removing heat using the slider below the box. Wait for the pressure to stabilize again, and record the new data. Table 3 T (K) P (atm) # molecules Average Speed (m/s) Run 1 100 0.20 100 245 Run 2 200 0.34 100 345 Run 3 300 0.55 100 420 Run 4 400 0.69 100 480 Run 5 500 0.84 100 545 What variable did you adjust? Temperature Besides the variable you adjusted, what other variable changed? The pressure and average speed increased Write one sentence explaining how pressure and number of molecules are related. As you increase the temperature, the pressure responds in a linear fashion Write one sentence explaining how temperature and pressure are related. As the T doubles so does the pressure What is the mathematical relationship between temperature and pressure? P/T = constant Use EXCEL to make 2 graphs. In one, demonstrate the relationship between pressure and temperature. In the second, show the relationship between average speed and temperature. The first should be linear just like in the predictions and the second should be v α (T)1/2 Does the graph you sketched in the Predictions section agree with the graph of your Pressure vs Temperature data? Describe any differences. They are similar Part V: Volume versus Number Of Moles – Too Many Cooks In The Kitchen Predict: What would happen to the volume of a sealed container if you increased the number of moles of gas at a constant pressure (think of a container with a piston). The volume will increase directly with number of moles. Sketch the relationship between Volume and # of moles on the graph below. V ol um e  (c m ^3 ) # of Moles Volume vs # Of Moles Page 7 Hit the “RESET” button. Make sure “Pressure” is clicked under constant parameters. Under “measurement tools” choose “ruler” to be able to measure the length of the box Add 70 heavy molecules to box. After each addition be sure that the temperature is still at 300K, adjust as necessary. Once pressure has stabilized record the following data. (It may be helpful to pause the simulation) To calculate the Volume of the box, assume the depth of the box is 10nm Table 4 T (K) P (atm) # molecules Length Of Box (nm) Volume Of Box (nm3) Run 1 300 0.84 70 2.9 156.6 Run 2 300 0.86 90 3.5 189.0 Run 3 300 0.85 110 4.4 237.6 Run 4 300 0.85 130 5.2 280.8 Run 5 300 0.84 150 5.9 318.6 What variable did you adjust? Number Of Molecules Besides the variable you adjusted, what other variable changed? The width of the box and hence volume changed Write one sentence explaining how temperature and pressure are related. As the number of molecules doubles so does the volume What is the mathematical relationship between volume and number of moles? V/n = constant Use EXCEL to make a graph of the relationship between number of molecules and volume. The graph should be linear increasing Does the graph you sketched in the Predictions section agree with the graph of your Volume vs Number of Molecules data? Describe any differences. They are similar Part VI: Volume versus Temperature – If you can’t stand the heat… Predict: What would happen to the volume of a sealed container if you increased the temperature of the gas at a constant pressure (think of a container with a piston). The volume will increase directly with temperature. Sketch the relationship between pressure and temperature on the graph below. V ol um e  (c m ^3 ) Temperature (K) Volume vs Temp Page 8 Hit the “RESET” button. Make sure “Pressure” is clicked under constant parameters. Under “measurement tools” choose “ruler” to be able to measure the length of the box Add 100 heavy molecules to box. Once pressure has stabilized record the following data. Then change the temperature by adding or removing heat using the slider below the box. Wait for the pressure to stabilize again, and record the new data. To calculate the Volume of the box, assume the depth of the box is 10nm Table 5 T (K) P (atm) # molecules Length Of Box (nm) Volume Of Box (nm3) Run 1 200 0.86 100 2.5 135.0 Run 2 250 0.86 100 3.3 178.2 Run 3 300 0.85 100 3.9 210.6 Run 4 350 0.85 100 4.6 248.4 Run 5 400 0.84 100 5.6 302.4 What variable did you adjust? Temperature Besides the variable you adjusted, what other variable changed? The width of the box and hence volume changed Write one sentence explaining how temperature and pressure are related. As the temperature doubles so does the volume What is the mathematical relationship between volume and temperature? V/T = constant Use EXCEL to make a graph of the relationship between volume and temperature. The graph should be linear increasing Does the graph you sketched in the Predictions section agree with the graph of your Volume vs Temperature data? Describe any differences. They are similar