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.
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 N = 4.45 lb. 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.
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.
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). Repeat this process until you have added all 6 or 7 books. This will require more than one person. The entire process (from no books to all the books) should be repeated at least three times. You will use the average volume of all your trials 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.
If there is time, use ice and plastic bags to create a lower temperature for the air in the syringe. Repeat your experiments and be prepared to compare these data with those for air at room temperature.
Your teacher may decide to do a demonstration with a gas other than air in the syringe. If so, record the data as it is generated in the demonstration and include the data and appropriate analysis of it in your report.
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. Try to figure out why the y-intercept equals the barometric pressure and why it is negative.
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 extrema of the range for volume. Is there an obvious trend within the range of experimental error? Refer to a similar exercise in chapter 2 of your text book for assistance with this.
A formal lab report will be required for this lab. Graphs and data tables should be presented using Excel or another computer graphing program. Only your final data table showing P (mb), V (mL), 1/V (1/mL), and P· V (mb· mL) needs to be included. Indicate the range of experimental error for each column. Your report should indicate the type of relationship found between the pressure and volume of a given amount of gas at constant temperature. Derive the equation for the relationship using your data, paying attention to units. Report the result concerning the barometric pressure as determined with your experiments and compare it to the pressure reported by the NWS. Finally, discuss the P· V results as regards the effect of unavoidable experimental error on the idealized relationship that pressure times volume is a constant. Especially take into consideration the effects that non-ideal gases have on the product P· V. Remember the van der Waals equation and what adjustments are made in it.