Experiment: Relationships in a Gas Worksheet

Pressure-Volume-Temperature Relationships in a Gas

Objectives:

  1. To investigate the relationship between pressure and volume for a confined gas.
  2. To investigate the relationship between pressure and temperature for a confined gas.
  3. To determine the value of absolute zero on the Celsius temperature scale.

Introduction and Procedure Overview:

Pressure, volume, and temperature are readily measured properties of a gas. Early scientists, such as Robert Boyle (1662) and Jacques Alexandre Charles (1787), noticed that these gas properties are interrelated. For example, Boyle observed that the volume of a gas decreased inversely with applied pressure (when the temperature of the gas is held constant). Charles found that the volume of a gas tends to increase linearly with temperature (when the confining pressure of the gas is held constant). These observations were eventually expressed in two simple mathematical relationships, now called Boyle’s Law and Charles’ Law. A gas that obeys these laws exactly is called an ideal gas.

In this experiment, you will collect data that reveals how gas pressure varies with volume (Part A of the experiment) and temperature (Part B of the experiment). Measurements will be carried out using pressure and temperature sensors that are interfaced to a computer. You will be utilizing a computer software package called Logger Pro that allows you to read data directly into a spreadsheet. Once the data is collected, you will analyze and graph the data, and print a hardcopy for your lab report.

Note: The experimental procedure listed below has been performed in the laboratory and recorded for your viewing. Your goal is to record the results from the information provided to allow you to accurately complete your calculation sheet.

Part A: Pressure-Volume Relationship in a Gas (Atmospheric Air):

  1. Prepare the Gas Pressure Sensor and an air sample for data collection.
  • With the 20 mL syringe disconnected from the Gas Pressure Sensor, move the piston of the syringe until the front edge of the inside black ring (indicated by the arrow in Figure 1) is positioned at the 0 mL mark.
  • Attach the 20 mL syringe to the valve of the Gas Pressure Sensor. Now you have trapped a certain amount of air, which you will use for the experiment.
  • Look at the syringe; its scale reports its own internal volume. However, that volume is not the total volume of trapped air in your system since there is a little bit of space inside the pressure sensor. The extra volume in the system is 8 mL. Consequently, the Pressure-Volume apparatus now contains a total volume of 10.8 mL of air at atmospheric pressure. (Remember that you will have to add this extra volume to the syringe volume for all of your data.)
  1. Prepare the computer for data collection: Turn on the computer and one of the partners should log in. Click on Start (the Windows logo at the bottom left of the screen). Scroll through the applications and click on Vernier Software, and open Logger Pro 3.14. Click on File ® Open ® Chemistry with Vernier. Click on Experiment 06 Boyle’s Law.The vertical axis has pressure scaled from 0 to 250 kPa (kilopascals). The horizontal axis has volume scaled from 0 to 20 mL.
  1. Click on the “Collect” button to begin data collection.
  2. Collect the pressure vs. volume data. It is best for one person to operate the gas syringe and for another to operate the computer.
  • Move the piston to position the front edge of the inside black ring (see Figure 2) at the 5.0 mL line on the syringe. Hold the piston firmly in this position until the pressure reading stabilizes.
  • When the pressure reading has stabilized, click on the “Keep” button. (The person holding the syringe can relax after “Keep” is clicked.)
  • Type in the total gas volume, 5.8 mL (5.0 mL in the syringe and 0.8 mL in the pressure sensor) in the edit box. Press the ENTER key to keep this data pair. Note: You can choose to redo a point by pressing the ESC key (after clicking “Keep” but before entering a value).
  1. Repeat Step 4 for syringe volumes of 7.0, 9.0, 11.0, 13.0, 15.0, 17.0, and 19.0 mL and remember to add 0.8 mL to these volumes before typing them in the edit box. You do not have to move the piston back to the 5.0 or 10.0 mL positions between these readings. You just have to push the piston in for the volumes less than 10.0 mL and pull the piston out for the volumes greater than 10.0 mL.
  1. Click “Stop” when you have finished collecting data. Record the pressure and volume data pairs located in the Spreadsheet in the appropriate data table located at the end of this handout.
  1. Inspect the graph of pressure vs. volume. Your graph should reveal a reciprocal relationship between pressure and volume (i.e. the pressure decreases in a curved fashion with increasing volume). If an exact reciprocal relationship exists between pressure and volume, then the pressure measured at 20.0 mL should be half the pressure measured at 10.0 mL. Robert Boyle made the same observation over 300 years ago and expressed this inverse pressure-volume relationship as P µ 1/V. You will now determine whether your P-V data is well represented by ‘Boyle’s Law’. Specifically, you will determine whether your data can be represented by the equation

, where a is a constant.

Step 1: Create a new column of data, reciprocal of column (1/V), based on your original volume data.

  • In the “Data” menu, click on “New Calculated Column”.
  • In the box that appears, click on the Column Definition tab.
  • Type in 1/Volume as the Long Name, 1/V as the Short Name, and 1/mL as the Unit. Type 1/“Volume” in the Expression box (the quotation marks must be included).
  • Click on “DONE”

Step 2: Plot Pressure vs. 1/Volume and perform a proportionality fit (y = ax) to the data.

  • Click on the vertical axis label and select “Pressure”.
  • Click on the horizontal axis label and select “1/Volume”.
  • In the “Analyze” menu, click on “Curve Fit”, click on the “ax proportional” fitting option, then select “Try Fit”. By selecting this curve fitting option, the Logger Pro software finds the value of a that yields the best-fit line through the P vs. 1/V data. Click “OK”.
  • The best fit line should now appear on your graph, along with a box that shows all the parameters pertaining to your graph. Write down the value of the constant (a) on your report sheet.
  • Note that you can change the scale of your graph by clicking on the appropriate axis label and then clicking “More…” Change the Top and Bottom numbers in the Dialog Box that appears so that your data points maximize your graph in the window.
  • Print copies of the P vs. 1/V graph for your lab report:
  • Click on “File” and click on “Print Graph” in the pull-down menu. When the “Print Options” dialog box opens, check the “Print Footer” box. Now type in your name and your partner’s name and click “OK”. Print one copy for each member of your group.
  1. Close down the software. Do not save your data. Do not log off from the computer.

Part B: Pressure-Temperature Relationship in a Gas (Atmospheric Air):

  1. Disconnect the syringe from the Pressure Sensor and set it aside. Obtain the rubber-stopper-flask assembly and attach the connector at the free end of the plastic tubing to the Pressure Sensor valve with a clockwise turn.
  1. Assemble the pressure-temperature measuring apparatus shown in Figure 3. Use a clamp to hold the flask apparatus so that it does not rest on the bottom of the 800-mL beaker. Plug the stainless steel temperature probe into the LabPro Data Collection Interface.
  1. Prepare the computer for data collection by opening the folder Chemistry with computers from the file menu of Logger Pro, as you did in Part A. This time, click on Exp 07: Pressure-Temperature.xmbl. The vertical axis has pressure scaled from 0 to 150 kPa. The horizontal axis has temperature scaled from 0 to 100 0
  1. Click “Collect” to begin the experiment.
  • Remove the flask and temperature probe from the 800-mL beaker on the hot-plate/stirrer. Place a mixture of ice and water in the beaker, drop a stir bar into the beaker, and then re-insert the flask. Add additional ice-cold water until the flask is completely submerged up to the rubber stopper. Place the temperature probe into the water bath. Make sure that the flask and temperature probe are not touching the inside walls of the beaker. The probe should touch the wall of the flask. Have one of the lab instructors inspect your apparatus before proceeding with the experiment.
  • Turn on the stirrer (but not the heat) and allow the system to equilibrate for about two minutes. When the pressure and temperature readings displayed in the Meter window stabilize, click on the “Keep” button. You have now saved the first pressure-temperature data pair.
  • Turn on the hot-plate and slowly warm the water solution. Adjust the heating rate so that the temperature of the water increases no more than 15 0C every 10 minutes. (Setting 4 on the hot-plate knob should work well – adjust as needed.) After the temperature has increased 100C, click on the “Keep” button to save an additional pressure-temperature data pair.
  • Continue heating and “Keeping” pressure-temperature data pairs every 10 0C so that you have several P-T readings between your initial temperature and approximately 75 0C.
  • Note that you can change the scale of your graph by clicking on the appropriate axis label and then clicking “More…” Change the Top and Bottom numbers in the Dialog Box that appears so that your data points maximize your graph in the window.
  • Click “Stop” when you have finished collecting data.
  • Record the pressure and temperature data pairs from the spreadsheet in the appropriate data table located at the end of this handout.
  1. Inspect the graph of pressure vs. temperature. Your graph should suggest a linear relationship between pressure and temperature. You will now determine whether your P-T data is well represented by a simple linear expression P = m×T + b, where m and b are the slope and y-intercept of the line, respectively.
  1. Perform a linear fit (y = mx + b) to the pressure vs. temperature data.
  • Click within the area of the pressure vs. temperature graph. This will highlight the graph.
  • In the “Analyze” menu, select “Curve Fit”, click on the “mx + b      linear” fitting option, then select “Try Fit” and click “OK”.
  • A line should appear through the P vs. T data along with a box showing the constants. Write down the slope (m) and y-intercept (b) of the fitted line on your report sheet.
  • Print copies of the P vs. T graph for your lab report (print one copy for each member of your group).
  1. You have now collected all the data associated with this experiment. The remainder of the data analysis can be conducted outside the lab. Turn in your report in one week, as usual.

  1. Exit the software and log off from the computer.
    P-V-T Relationships in a Gas

                                    NAME:              ________                                             ____________

Part A:  P-V Relationship

Volume (mL)Pressure (kPa)

Proportionality Constant (a) from ‘best-fit’ line: ____________

Part B:  P-T Relationship

Temperature (°C)Pressure (kPa)

Slope (m) from ‘P = m´T + b’ line:  _____________

y-intercept (b) from ‘P = m´T + b’ line: _____________

Post Lab Questions to be answered and attached to your lab report:

  1. What experimental factors are assumed to be constant in part A of this experiment? Part B?
  2. Based on your best-fit line from part A, what would you expect the pressure to be if the volume of the gas was increased to 40.0 mL?
  3. Based on your best-fit line from part A, at what volume would the pressure of the gas equal 670 kPa?
  4. Based on your best-fit line from part B, what would you expect the pressure to be if the temperature of the gas was increased to 143 °C?
  5. Based on your best-fit line from part B, at what temperature would the pressure of the gas equal 21.3 kPa?
  6. According to your data, the pressure of the gas should eventually reach zero if the temperature is lowered far enough. This final ‘minimum’ temperature can be used as a definition of absolute zero.  Using your experimentally determined equation, calculate a value for absolute zero (in °C).  Calculate the percent error in your value of absolute zero.

Remember to attach the printouts of the graphs and your calculations page(s) to your report, along with the answers to the post-lab questions.

Ideal Gas Law Simulation Experiment 6

1.     Room Temperature:_________°C_________ K
2.     Room pressure:_________ mm_________ atm
3.     Gas Temperature:_________ °C_________ K
4.     Volume of butane:_________ mL_________ L
5.     Mass of lighter at start:_________ g
6.     Mass of lighter at end:_________ g
7.     Mass of butane:_________ g
8.     Moles of butane:_________ mol
9.     Calculated molar mass:_________ g/mol

Show your calculations below:

Order a unique copy of this paper
(550 words)

Approximate price: $22