## Lab: Boyle’s Law

### Objective

This lab is designed to demonstrate one of the fundamental laws of gas behavior, Boyle’s Law. This law is about the relationship between the pressure and volume of an ideal gas when the number of moles and the temperature are held constant. Furthermore, the law holds true regardless of the identity of the gas. You will use simple tools to accomplish the demonstration, the procedure for which you must in large part invent yourselves. Additionally, you will make your own barometer.

### Overview

Using a gas-filled syringe and several equal-sized masses you will demonstrate Boyle’s Law both qualitatively and quantitatively. You will use your quantitative results to determine the barometric pressure. This is possible because you can find the mass of your standard masses and use the fact that gas pressure is defined as force per unit area (pounds per square inch, newtons per square meter, etc). The SI unit of pressure is the pascal (Pa) and is defined as 1 N/m2. A newton (N) is a unit of force and when used to measure weight is equivalent to the mass of an object in kg times 9.8 m/s2. One newton equals 1 kg· m/s2 and 1 lb = 4.45 N. Knowing this (and that 1 m2 = 1 × 104 cm2) you will be able to calculate the pressure in SI units (Pa) on the top of the plunger of the syringe.

Pressure
`P = F/A                 Pressure = Force/Area                 Pa = N/m2`

Barometric pressure refers to the gas pressure of the atmosphere. It varies constantly and is a major determinant of weather. The web pages of the National Weather Service (NWS) http://www.weather.gov/ reports local barometric pressure in millibars (mb). One millibar equals 100 pascals (1 mb = 100 Pa). You will convert all pressures recorded in this lab to millibars.

### Materials

• large volume plastic syringe w/stopper
• wooden block stand and plunger topper
• thermometer
• lab balance
• constant mass unit devices (books)
• glycerin
• air
• bathroom scale
• clamp
• graph paper
• lab balance

### Safety

• If you choose not to wear safety glasses you are choosing to sit out the lab.
• The tips used to close off the syringes can cause injury if someone ejects them forcibly and strikes an eye. Do not eject the tips forcibly at any time!
• Don’t drop a book on your feet!

### Procedure

Remember to record your observations in your lab notebook before you leave class.

Remove the tip from the syringe and pull out the plunger. Use the glycerin provided to lubricate the rubber gasket of the plunger. Then reinsert the plunger and fill the syringe to the top volume line with air. Replace the tip and put the syringe into the wooden block stand and put the topper on the plunger. Use a clamp attached to a ring stand to hold the syringe in place. Record the temperature of the air in the syringe.

Read off and record the initial volume of air in the syringe. You will need 6 or 7 books of the same size. Carefully center one of the books on top of the syringe plunger and read the new volume in the syringe, estimating to the tenth of a milliliter (0.1 mL). Gently push the syringe down and up a few times to get a feel for the equilibrium position. Add all the books one by one and then take them off one by one. Record the volume each time you add or remove a book. Repeat this process until you have added all 6 or 7 books. The entire process (from no books to all the books back to no books) should be repeated at least three times. You will use the average volume for each number of books to perform data analysis.

At a time that is convenient for your group, someone should find the weight of one book and the weight of the wooden block. The best method is to weigh several books at once (maybe even all that you have) and divide the weight so found by the number of books. This gives an average weight and reduces the error that would be introduced by weighing only one book. Someone should also measure and calculate the cross-sectional area of the plunger of the syringe. This is the area for the calculation of pressure using the idea that pressure is force per unit area.

To complete the data table the amount of pressure in millibars should be calculated based on the weight of the books plus the weight of the block for each step in the addition of books.

### Calculations and Graphing

Do this during your lab period. When you are finished you should have a data table showing pressure in millibars (mb) and average volume in milliliters (mL). Calculate the range of values and the ± amount for the volume measurements (in other words, what is the unavoidable experimental error in your data?)

Use a full sheet of graph paper to construct a graph of your pressure and volume data. Put volume on the x-axis and pressure in millibars on the y-axis. Hint: set the x-axis about 1/3 of the way up from the bottom of the page. You will need some space on the negative side of the y-axis. Indicate the range of variation in your volume data by drawing error bars around your data points. Then lightly draw in the best-fit line that accomodates your average value data points.

Add a column to your data table for the reciprocal of the volume (1/V, in 1/mL) and fill it in. Add a second label to the x-axis of your graph for the values of 1/V that you calculated. Now graph the data as 1/V vs. the pressure. Use a different color or symbol in order to be able to distinguish your data series. Draw the best-fit line through the 1/V vs. P data points. Extend this line to the y-axis and extend the scale of the y-axis to accomodate the y-intercept. The absolute value of the pressure indicated at the y-intercept is equal to the current barometric pressure! Compare this result with the actual barometric pressure as reported by the NWS. Why is this true and why is the value negative? Hint: What was the pressure in the syringe before you added any books?

Derive the equation for the 1/V vs. P data in y = mx + b form. Be sure to report the units of the slope and y-intercept.

Add one more column to the data table for the product of the pressure and the volume and fill it in. Do you notice anything interesting about the results of this calculation? If not, consider the range of variation in the value of the volume. Recalculate a few of the pressure-volume products using the highest and lowest values in the range for volume. Is there an obvious trend within the range of experimental error?

A group short-form report is required for this lab. This includes an introduction paragraph describing the scientific concept behind the lab and a detailed analysis of your data, its relevance to the lab concept and sources of experimental error. In this lab you are collecting data that will allow you to observe the validity of Boyle’s Law relating the pressure and volume of a gas at constant temperature. For guidance as to what should be included in the analysis, see the above paragraph and the instructions below.

Graphs and data tables should be presented in your report using Excel or another computer graphing program. A data table showing P (mb), V (mL) (average values), 1/V (1/mL), and P· V (mb· mL) needs to be included. Another table showing the experimental error in each volume measurement is also required. Indicate the range of experimental error for each column.