Knutsen's Chem 140 Lab: Boyle's Law & Determination of Absolute Zero

Experiment: Boyle’s Law & Determination of Absolute Zero
Part I — Boyle’s Law

Purpose
In this experiment you will determine the relationship between pressure and volume of a gas, and examine the relationship between temperature and pressure of a gas, using this second relationship to determine absolute zero. In the process you will learn to use computer software and probes for data collection, and gain additional experience in using MS Excel for data analysis.

Introduction
Boyle’s Law describes the relationship between the pressure and the volume of a gas when the temperature is held constant. Your task will be to determine a quantitative relationship between pressure and volume of a gas by making a series of measurements using a pressure sensor interfaced to a computer.

Just how are pressure and volume related? Is it a direct relationship, or an inverse relationship? Two quantities are said to be directly proportional if, as one quantity increases, the other does as well. For example, there is a direct relationship between mass and volume. As the mass of a substance increases, so does the volume. Two quantities are said to be inversely proportional if, as one quantity increases, the other decreases. For example, there is an inverse relationship between temperature and density. For most substances, as temperature increases, density decreases.

There are many possible ways that these relationships might be expressed algebraically. Some example are shown below. In all of the examples, a and b represent constants.

Examples of Direct Relationships:

P = aV; P = aV + b; P = aV²+ 5V

Examples of Inverse Relationships:

P = a/V; P = a/V²; P = a/(bV² + V³)

As you can see, the relationship may be either very simple or very complex. It is common for scientists to collect data and then to use a computer to try to “fit” the data. “Fitting the data” means finding an algebraic relationship, i.e., an equation, that expresses the relationship between the measured quantities. After collecting pressure vsvolume data, you will use MS Excel to graph your data and determine the algebraic relationship between P and V.

Note: In this laboratory you will be working with a lab partner.

Procedure

Prepare the Pressure Sensor and an air sample for data collection as follows:

Plug the Pressure Sensor into the left–most USB port that is connected to a computer.
Move the piston of the 20–mL syringe until the black ring nearest the inside end of the piston is exactly over the 10.0 mL mark.
Attach the syringe to the pressure sensor.

Prepare the computer for data collection by opening Logger Pro 3.5.0, go to File/Open, open the “Chemistry with Computers” folder, and open the “06 Boyle’s Law” experiment. The y–axis of the graph should display pressure from 0 to 250 kPa, the x–axis should display volume from 0 to 20 mL.

Click on the “Collect” button to begin data collection.

Collect the pressure vs volume data following the steps below: (It works best for one person to take care of the syringe and for another to operate the computer.)

Move the piston to position the inside black ring exactly over the 5.0–mL line on the syringe. Hold the piston firmly in this position until the pressure value stabilizes.
When the pressure reading has stabilized, click the “Keep” button. Type “5.0” in the dialog box that appears. Press enter to keep this data pair.

Repeat the Step 4 procedures for volumes of 7.5, 10.0, 12.5, 15.0, 17.5, and 20.0 mL.

Click on the “Stop” button when you have finished collecting data. Note that your data appears in the table window. Record the values in your lab notebook, or copy and paste the data into MS Excel and then save the data to your disk. (Be sure to bring your data disk to lab.)

Examine the graph of pressure versus volume. See if you can tell what kind of mathematical relationship exists between these two variables, direct or inverse. Later, you will use Excel to graph the data and find the functional relationship between P and V. When you are finished with the experiment, exit the program.

Part II — Determination of Absolute Zero

Introduction
Gas laws describe the relationship between the pressure, temperature and volume of a gas. In this experiment we will study the relationship between the temperature of a gas sample and the pressure it exerts, and we will use this data to determine the value of absolute zero. Using the apparatus shown in Figure 1, we will place an Erlenmeyer flask containing an air sample in water baths of varying temperature. Pressure will be monitored with a pressure sensor and temperature will be monitored using a temperature probe. The volume of the gas sample and the number of molecules it contains will be kept constant. Pressure and temperature data pairs will be collected during the experiment and then analyzed. From the data and graph, you will determine the relationship between the pressure and absolute temperature of a confined gas. You will then use your data to find a value for absolute zero on the Celsius temperature scale.

Figure 1

Procedure

Obtain 3 1–L beakers. Use the beakers to prepare three water baths: one at room temperature, one with a slurry of ice water, and one with boiling water.

Prepare the pressure and temperature probes for data collection as follows:

Plug the Pressure Sensor into left–most USB port that is connected to a computer.
Insert the 2–hole stopper, already fitted with a plastic tube and blue stopcock, into a 125–mL Erlenmeyer flask. Twist the stopper to insure a tight fit. Attach the plastic tubing to the pressure sensor. Your apparatus should look similar to that in Figure 1.
You must be careful to get a good seal. Any leaks in the system will invalidate your results. You will know you have a leak if the pressure does not vary as the temperature is changed.
Open the blue valve so that the pressure sensor and flask are open to the atmosphere.
Close the blue valve so that air can no longer enter/leave the Erlenmeyer flask. The air sample to be studied is now confined in the flask and sensor.
Plug the temperature probe into the USB port next to the pressure sensor.

Prepare the computer for data collection by opening the “07 Pressure–Temperature” experiment. The y–axis of the graph displays pressure from 0 to 150 kPa, and the x–axis displays temperature from 0 to 100 °C.

Collect pressure versus temperature data for your gas sample as follows:

Place the flask into the ice–water bath. Make sure the entire flask is submerged (see Figure 1). However, you do not want the flask to be resting on the bottom of the 1–L flask.
Place the temperature probe into the ice–water bath. Hold the temperature probe so that is suspended in the water bath, but not in contact with the sides of either the 1–L beaker or the Erlenmeyer flask.
Click on the “Collect” button to begin data collection.
When the pressure and temperature readings displayed on the computer monitor stabilize, click on the “Keep” button.
Repeat the above steps a, b, and d (Omit c!) using the room temperature water bath and the boiling water bath. If the pressure does not change, you have a leak and will need to start over.

Analysis and Calculations
Part I — Boyle’s Law

Use MS Excel to prepare a graph (chart type “Scatter”) of pressure vsvolume. Make sure that the chart has a name, the axes are labeled (including appropriate units), that there are major and minor gridlines, and then place the chart on a new sheet.

Use the regression feature to “fit” the data (add a trendline). In the past, we have only used regression lines for linear data. Is a linear fit appropriate for this data? Here’s how to find out. Try out several different regression options. Excel can fit linear, logarithmic, polynomial, power and exponential data. Try the linear, polynomial and power options. You will find these options in the “Trendline” option of the “Format” menu, under the “Type” tab. In each case, under the “Options” tab, check the boxes for “Display Equation on Chart” and “Display R–squared Value on Chart”. In general, the best fit will have R² close to 1.0, but this does not necessarily mean you have chosen the correct function. Try to incorporate some common sense and textbook research when selecting the function that best describes the relationship between pressure and volume. After deciding which functional relationship best fits your data (linear, polynomial or power), print the graph with the equation displayed on the chart.

Staple a copy of the graph (with the best regression line and equation of the line) into your lab notebook.

In your lab notebook, answer the following questions:

According to your experimental results, what is the functional relationship between P and V? Do your experimental results agree with the relationship given in the text? Explain.
What is the role of temperature in this experiment? Explain.
How might the data be plotted to achieve a straight line relationship?

Part II — Determination of Absolute Zero

Use MS Excel to prepare a graph (chart type “Scatter”) of pressure vs temperature (°C). Again, make sure that your chart has a name, the axes are labeled (including appropriate units), that there are major and minor gridlines, and then place the chart on a new sheet.
Use the regression feature to insert a trendline, and extrapolate the line to P=0. Print the graph with the equation of the line displayed on the chart.
Staple a copy of this graph into your lab notebook.
From the equation of the line, determine the value of absolute zero on the Celsius scale. Show the calculations in your lab notebook. Compute a percent error between your results and the accepted value for absolute zero, and evaluate your results in your analysis of the experiment.

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