Deriving the Gas Laws Background The gaseous state of matter consists of particles (gas molecules like oxygen, nitrogen, and carbon dioxide) which, according to the kinetic theory of gases, are in constant motion with enough kinetic energy such that they rarely interact with one another. When gas particles collide with the walls of a container, they rebound with no apparent loss of energy. These characteristics describe an "Ideal Gas." Experimental evidence suggests that many common gases making up air behave in this manner when studied at temperatures well above their boiling points for a given pressure. We are constantly being exposed to the behavior of gases. Each time we pump up a tire, blow up a balloon, use a spray can, or experience the cooling of gases as they escape from a gas storage container, we are reminded of how gases behave with changes in temperature (T), volume (V), pressure (P), or number of particles (n). On an astronomical scale, we know that star formation involves contraction of gas clouds to produce dense, high-pressure cores capable of fusion reactions. The behavior of gases has been scientifically investigated starting with Robert Boyle's work in 1662, followed by Jacques Charles' (1787) and Joseph Gay-Lussac's work (1802). Together these studies led to the so called "Gas Laws" which relate volume (V), pressure (P), temperature (T) and numbers of particles of gas (n). In a scientific manner, we can hold constant any two of the four primary properties of gases and study the nature of the relationship between the other two by varying one and observing the variation of the other. By doing this, we can derive the mathematical relationships that exist between these variables. Procedure 1: Volume vs. Pressure 1.) Using the lap tops, go to the Physics Education Technology from the University of Colorado at: http://phet.colorado.edu/new/simulations/sims.php?sim=gas_properties 2.) Click the RUN NOW button under the Gas Properties Simulation window (highlighted in green). 3.) On the right side of the screen, click on the MEASURMENT TOOLS button. Next, click on the RULER option to activate the ruler.
4.) In the upper right hand corner, click on the TEMPERATURE button under the Constant Parameter heading. This will hold temperature constant while allowing you to observe the relationship between pressure and volume. 5.) Using the mouse and the right button, drag the ruler into a position that will allow you to measure the length of the container. 6.) Using the mouse and the right button, grab hold of the man pushing against the container and expand the length of the container so that it measures 9.0 cm. Record this as your initial length (the height of the box will remain 5.0 cm and the width of the box will remain 5.0 cm) GRAB AND DRAG
7.) Using the mouse and the right button, grab hold of the pump handle and inject one cycles worth of gas into the chamber by pulling the handle up then pushing it back down. MOVE UP THEN DOWN 8.) Once the pressure has stabilized (this may take a minute), record your pressure value for the chamber length of 9.0 cm. This will represent your initial pressure in atmospheres. PRESSURE (ATM)
9.) Using the mouse and right button, grab hold of the man pushing on the container and decrease the length of the container to approximately 8.0 cm. Once the pressure has stabilized (again, this may take a minute to happen), record the new pressure for a length of 8.0 cm. PUSH IN 10.) Repeat step 9 for approximate lengths of 7.0 cm, 6.0 cm, 5.0 cm, 4.0 cm, 3.0 cm, and 2.0 cm. For each trial, record the length value and resulting pressure value. 11.) Record any qualitative observations on the behavior of the gas molecules as the volume decreases. 12.) Click the RESET button to remove all the gas particles from the chamber before moving on to the next section.
Procedure 2: Volume vs. Temperature 1.) Reset the length of the box to 9.0 cm following the same procedure as you did in step #6 of procedure 1 (once again, the width and height of the box will remain constant at 5.0 cm). 2.) In the upper right hand corner, click on the NONE button under the Constant Parameter heading. This will allow us to establish initial conditions before collecting any data. 3.) Using the mouse and the right button, grab hold of the pump handle and inject one cycles worth of gas into the chamber by pulling the handle up then pushing it back down as you did in step #7 of procedure 1. 4.) Once all three parameters have stabilized (temperature, pressure, and volume), click on the PRESSURE button under the Constant Parameter heading. This will hold pressure constant while allowing you to observe the relationship between temperature and volume.
5.) Record your initial length (cm) of the box and temperature (K). RECORD RECORD 6.) Using the Bunsen burner underneath the chamber, decrease the temperature of the gas in the chamber by pulling down on the handle. If done correctly, ice should appear on the burner in place of flames. Decrease the temperature approximately 25 K. PULL DOWN
7.) Record the new length (cm) of the box and temperature (K). 8.) Repeat steps #6 and #7 until a final temperature of 100 K is reached. 9.) Record any qualitative observations on the behavior of the gas molecules as the temperature decreases. 10.) Click the RESET button to remove all the gas particles from the chamber before moving on to the next section. Procedure 3: Temperature vs. Pressure 1.) Reset the length of the box to 7.0 cm following the same procedure as you did in step #6 of procedure 1 (once again, the width and height of the box will remain constant at 5.0 cm). 2.) In the upper right hand corner, click on the NONE button under the Constant Parameter heading. This will allow us to establish initial conditions before collecting any data. 3.) Using the mouse and the right button, grab hold of the pump handle and inject one cycles worth of gas into the chamber by pulling the handle up then pushing it back down as you did in step #7 of procedure 1. 4.) Once all three parameters have stabilized (temperature, pressure, and volume), click on the VOLUME button under the Constant Parameter heading. This will hold volume constant while allowing you to observe the relationship between temperature and pressure.
5.) Record your initial temperature (K) and pressure (atm). 6.) Using the Bunsen burner underneath the chamber, decrease the temperature of the gas in the chamber by pulling down on the handle. If done correctly, ice should appear on the burner in place of flames. Decrease the temperature approximately 50 K. PULL DOWN 7.) Record the new temperature (K) and pressure (atm). 8.) Repeat steps #6 and #7 until a final temperature of 0 K is reached. 9.) Once 0 K is reached, reheat the chamber by applying heat. To do this, push up on the bunsen burner control. Continue to heat until your starting temperature is reached. PUSH UP
10.) Once the starting temperature is reached, continue adding heat and collecting temperature and pressure data in 50 K integrals until a max temperature of 600 K is reached. 11.) Record any qualitative observations on the behavior of the gas molecules as the temperature decreases and increases. 12.) Click the RESET button to remove all the gas particles from the chamber before moving on to the next section. Procedure 4: Temperature vs. Volume vs. Pressure 1.) Reset the length of the box to 7.0 cm following the same procedure as you did in step #6 of procedure 1 (once again, the width and height of the box will remain constant at 5.0 cm). 2.) In the upper right hand corner, click on the NONE button under the Constant Parameter heading. This will allow all three variables to adjust based on changing conditions 3.) Using the mouse and the right button, grab hold of the pump handle and inject one cycles worth of gas into the chamber by pulling the handle up then pushing it back down. 4.) After all values have stabilized, record your initial data for temperature, pressure, and volume (length). 5.) On your own, change either the volume of the box or the temperature of the gas. Record the resulting data for all three variables (pressure, volume (length), and temperature). Be sure to collect multiple pieces of data. 6.) Repeat steps #4 and #5 with the other variable (temperature or pressure). 7.) Record any qualitative observations on the behavior of the gas molecules. 8.) Click the RESET button to remove all the gas particles from the chamber before moving on to the next section.
Procedure 5: Pressure vs. Number of Moles 1.) Reset the length of the box to 7.0 cm following the same procedure as you did in step #6 of procedure 1 (once again, the width and height of the box will remain constant at 5.0 cm). 2.) In the upper right hand corner, click on the NONE button under the Constant Parameter heading. This will allow all three variables to adjust based on changing conditions 3.) Using the mouse and the right button, grab hold of the pump handle and inject one cycles worth of gas into the chamber by pulling the handle up then pushing it back down. 4.) After all values have stabilized, record your initial data for pressure and number of gas molecules. The number of gas molecules is recorded in a box under the heading GAS IN CHAMBER. RECORD 5.) Using the pump, increase the number of gas molecules in the chamber. 6.) After all values have stabilized, record data on the resulting pressure and number of gas molecules. 7.) Record any qualitative observations on the behavior of the gas molecules. 8.) Click the RESET button to remove all the gas particles from the chamber before moving on to the next section.
Name: Period: Deriving the Gas Laws Results: Procedure 1 Procedure 2 Length of Pressure (atm) Temperature (K) Length of Chamber (cm) Chamber (cm) Qualitative Observations: Results: Procedure 3 Temperature (K) Pressure (atm) Temperature (K) Pressure (atm) Qualitative Observations:
Results: Procedure 4 Changing Temperature (K) Length (cm) Pressure (atm) Changing Length (cm) Temperature (K) Pressure (atm) Qualitative Observations: Results: Procedure 5 # Gas Molecules Pressure (atm) Qualitative Observations:
Calculations: Procedure 1 Procedure 2 Volume of Chamber (cm 3 ) 1/Volume (cm 3 ) Volume of Chamber (cm 3 ) Calculations: Procedure 4 Volume (cm 3 ) (Changing Temperature) Volume (cm 3 ) (Changing Volume) Graphs: Procedure 1: Generate a computer graph of Pressure (atm) vs. Volume (cm 3 ). Procedure 1: Generate a computer graph of Pressure (atm) vs. 1/Volume (cm 3 ). Procedure 2: Generate a hand done graph of Volume (cm 3 ) vs. Temperature (K). Procedure 3: Generate a computer or hand done graph of Pressure (atm). vs. Temperature (K). Include temperature data from 0 K to 600 K. Analysis Questions: Procedure 1 1.) Identify the mathematical relationship that exists between pressure and volume, when temperature and quantity are held constant, as being directly proportional or inversely proportional. Explain your answer. 2.) Calculate the slope of the line for your pressure vs. 1/volume graph. What does this number represent? Would you expect it to be the same for all gases? Explain your answer. 3.) What was the purpose of graphing pressure vs. 1/volume?
Analysis Questions: Procedure 2 4.) Identify the mathematical relationship that exists between volume and temperature, when pressure and quantity are held constant, as being directly proportional or inversely proportional. Explain your answer. 5.) Calculate the slope of the line for your volume vs. temperature graph. What does this number represent? Would you expect it to be the same for all gases? Explain your answer. Analysis Questions: Procedure 3 6.) Identify the mathematical relationship that exists between pressure and temperature, when volume and quantity are held constant, as being directly proportional or inversely proportional. Explain your answer. 7.) Calculate the slope of the line for your pressure vs. temperature. What does this number represent? Would you expect it to be the same for all gases? Explain your answer. Analysis Questions: Procedure 4 8.) Describe what happens to pressure and volume when the temperature of a gas is increased and/or decreased. Suggest an explanation for this. 9.) Describe what happens to pressure and temperature when the volume of a gas is increased and/or decreased. Suggest an explanation for this. 10.) Predict what would happen to the volume and temperature of a gas if the pressure was increased and/or decreased. Suggest an explanation for this. 11.) Explain the effects of temperature on molecular motion. Using this explanation, explain why both pressure and volume decrease with decreasing temperature. Analysis Questions: Procedure 5 12.) Describe the impact of increasing the number of moles of a gas on the pressure of a gas sample. Would you expect this trend to be the same for all gases? Explain your answer. 13.) Based on your previous observations, predict the impact of changing the number of moles of a gas sample on the volume of the gas sample (if pressure and temperature are held constant) and on the temperature of a gas sample (if pressure and volume are held constant). Conclusion Questions: 1.) Absolute zero is theorized to be the temperature that all molecular motion stops. Based on this, what would you predict to be the pressure and volume of a gas sample whose temperature is decreased to absolute zero? Explain. 2.) A scuba diver inflates a balloon to 1.5 L at a depth of 99 ft (where the pressure is about 4 atm) to mark the location of a sunken treasure. Assuming the temperature remains constant, what will happen to the volume of the balloon as it approaches the surface? Explain your answer. 3.) You purchase a bunch of helium filled balloons for a friend s birthday party. You plan on storing the balloons in your car until the party on a very hot summers day. Explain why this is a bad idea. 4.) Why do aerosol cans have a recommended storage temperature? Why should you never store one in high temperatures? 5.) On a cold winters day you inflate the tires of your bike to their recommended pressure. During your first ride of the summer, you notice that both tires seem very hard and you ultimately end up blowing out one of your tires. Suggest a reason for this.