Laboratory Experiment No. 8 (Revised 11/01/2016) Introduction: Charles's Law states that at constant pressure, the volume of a confined gas is proportional to its absolute temperature. This is expressed algebraically as V = constant T (Equation 1) The value of the constant depends on the pressure and the amount of gas in the system so it has no fundamental significance. The equation can be rewritten to express the relationship between two sets of conditions for the same sample of gas: V T = V T 1 2 1 2 (Equation 2) In this form, the equation can be solved for one of the volumes or one of the temperatures if the other three variables are known. Equation 1 predicts the volume of any gas will become zero at zero temperature. The equation can be used only with an absolute temperature scale such as the Kelvin scale where zero temperature actually means zero heat and zero molecular motion. The Celsius scale gives meaningless results since it has an arbitrary zero and negative values. Even with the Kelvin scale, the equation does not always work well for several reasons. 1) At low temperatures, especially near their condensation points, many gases do not behave ideally. 2) At low temperatures all gases eventually liquefy and the equation is no longer valid. 3) Matter can never occupy zero volume. At high enough temperatures, however, attractive forces between gas molecules are negligible compared to the kinetic energy of the molecules and most gases exhibit close to ideal behavior and follow the equation well. Since Equation 1 shows that V and T are directly proportional to each other, a plot of volume versus Kelvin temperature will be a straight line going through the origin (zero volume and zero kelvins). The Celsius and Kelvin scales are related only by the constant additive term 273.15, so a plot of volume versus Celsius temperature will also give a straight line but one that is displaced along the temperature axis and does not go through the zero degrees Celsius origin. Extrapolating a plot of volume versus Celsius temperature to zero volume gives the Celsius value for absolute zero. For your prestudy assignment graph and your report graph, use the metric style graph paper specified for this course that has ten small divisions inside each ruled one-centimeter square. Do not use any other style of graph paper. Graphs must be done in black ink and be supplied with a title and properly labeled axes. Your instructor has already given you a handout with graphing instructions. The guidelines must be followed in order for you to get full credit on your graphs. 1
Experimental The apparatus consists of a 600 ml beaker, supported on a ring stand and partly filled with water, a minus 10 to plus 110 degree Celsius thermometer, a centimeter ruler and a 15 cm long narrow bore glass (capillary) tube sealed at one end. A small plug of silicone oil near the open end of the capillary holds in a fixed amount of air. At room temperature, the column of trapped air should be 5 to 8 cm long. The pressure of the trapped air will remain constant when temperature changes because the oil plug will move up and down in response to pressure changes in the capillary. The pressure inside will stay the same as the outside (presumably constant) atmospheric pressure. Use the centimeter ruler to measure the length of the air column. Remember, you are interested in the length of the air column trapped inside the capillary by the oil droplet. Measure only the distance from the inside bottom of the capillary to the bottom of the oil plug. If you do not position the bottom of the air column at the zero mark of the ruler, subtract the bottom reading from the top reading when you write your report to get the correct length of each air column. During the experiment, some oil in the plug may dribble down and accumulate at the bottom of the capillary. This will not affect your results as long as you measure your air column length from the top of the lower oil drop to the bottom of the movable oil plug at the top. Do not include any part of the oil drops in your air column length measurements. Since the radius of the capillary tube is constant, the volume of air is directly proportional to the length or height of the column as shown by the formula for the volume of a cylinder V = π r 2 h (Equation 3) Here, r is the radius of the capillary tube and h is the height of the air column. Because h is proportional to V, you may substitute the height (also called length in this experiment) of the trapped air column for volume in Equations 1 and 2 with no loss of validity. Examine your centimeter ruler and your thermometer carefully and determine to what precision each instrument should be read. Ask your instructor if you need a review of measurement reading techniques. Carefully attach your capillary tube and ruler together with a rubber band. (You may have to move the rubber band later if it obscures any readings.) The simplest arrangement is to position the bottom of the air column at the 0.00 cm end of the ruler. If the bottom of the air column is at any other position, be sure to subtract that value from the top measurement to get the length of the air column alone. Check frequently during the experiment in case oil accumulates at the bottom of the capillary or the tube moves relative to the ruler. Set up a water bath by placing a 600 ml beaker on a wire gauze square supported on a ring stand. Fill the beaker with water to a depth that will immerse the entire capillary air column but not so high that water can enter the open end of the capillary. Lean the ruler diagonally in the beaker with the ruler top pointing away from you and place the thermometer in the water also. Note: A beaker full of hot water is a burn hazard. To avoid making the apparatus top heavy, use the widest ring stand base available and position the iron ring as low as possible, no more than 6 cm above the top of your Bunsen burner chimney. Wear a waterproof apron at all times. When making readings, stand but do not sit in front of the apparatus and do not put your hand under the beaker full of hot water at any time. 2
Heat the water in the beaker with a strong blue flame. When the water temperature exceeds 90 ºC, reduce the size and intensity of the flame. When the water boils, turn off the flame. For your approximately 100 ºC reading, stir the water with the thermometer and wait at least 30 s after you extinguish the flame before you take your first bath temperature and air column length readings. Make twelve sets of readings over the range +100 ºC to -10 ºC. After your 100 ºC reading, lower the temperature by approximately 10 ºC intervals by adding cold water to the beaker, stirring well and removing any excess water with a 50 ml beaker or eyedropper. Keep the oil plug below the level of the water bath so all the trapped air will be the same temperature as the bath. Carefully use the glass thermometer to stir the water. After you make a change in the bath temperature, wait until the oil plug stops moving before you measure its position, thereby allowing the system to attain thermal equilibrium. It is not necessary to get the temperatures to exactly 90 ºC, 80 ºC, etc. Just get reasonably close to each target temperature. Be sure to record each actual temperature value. Use small amounts of crushed ice to get the water bath temperatures close to 30 ºC, 20 ºC and 10 ºC. Stir the water bath and be sure all the ice melts before you take the readings. A uniform, well-stirred slurry of ice and water will give a 0 ºC. For this bath, the water level should be as high as the ice and the ice should extend all the way to the bottom of the beaker. Stir the bath with a metal spatula, not the glass thermometer or the centimeter ruler. To measure the melting ice temperature, position the thermometer bulb midway between the top and bottom of the bath. Ten to 12 degrees below zero Celsius is achieved with a mixture of ice and sodium chloride. First, remove the ruler from the beaker to avoid breaking the fragile capillary. Pour off about half of the water from the 0 C bath and add 50 g of sodium chloride. Stir the bath with a metal spatula, not the thermometer. Then carefully reinsert the glass thermometer and the ruler. When the temperature stabilizes below minus 10 ºC, read the temperature and the air column length. After your instructor approves your readings in the +100 to -10 ºC range, rinse the salt from your ruler and capillary and carefully pat them completely dry with a paper towel. Your instructor may provide a low temperature (cryogenic) bath in the range -60 to -30 ºC made with dry ice and ethanol in a Dewar (vacuum) flask. Most organic solvents are expensive, toxic and flammable so the class will share a single low temperature bath in the fume hood. Your liquid-in-glass thermometer does not read below minus 10 ºC so this bath temperature will be measured with a digital thermometer. Bring your driedoff apparatus to the hood and the instructor will help you make the final reading. Read the oil drop position without removing the capillary from the cryogenic bath and then record the temperature from the digital readout. Leave the ruler and capillary in the hood to allow the solvent to evaporate safely. Safety You must wear chemical splash goggles and a waterproof apron from the very beginning to the very end of the laboratory period. Be sure to inspect your beaker for cracks before you use it and observe all the hot water precautions given on page 2. Disposal Your salt-ice bath may be safely poured down the drain. Place broken or unneeded glass capillaries in the labeled cardboard box designed for broken glass disposal. Cleanup At the end of the laboratory period, wipe down all your work surfaces with a wet sponge. Make sure to clean up any salt granules you may have spilled on the bench top or near the balances. 3
Laboratory Experiment No. 8 Data Page Approximate Bath Temperature Measured Bath Temperature Top of Air Column Ruler Reading Bottom of Air Column Ruler Reading 100 ºC 90 ºC 80 ºC 70 ºC 60 ºC 50 ºC 40 ºC 30 ºC 20 ºC 10 ºC 0 ºC -10 ºC -30 ºC 4
Laboratory Experiment No. 8 Report and Calculations 1) Using the graph paper specified for this course, plot your air column length versus temperature and attach it to this report. Your temperature axis must range from -300 ºC to +100 ºC. Draw the best straight line through the data points. (7 points) 2) On the graph, extrapolate the straight-line plot to zero column length (zero gas volume). Show the intercept on the graph and read the Celsius temperature axis to get your value for absolute zero. What is your Celsius value for absolute zero? Write the value on the line below. (2 points) 3) What was your measured temperature in the boiling water bath? Write the value here. What was the length of your air column in the boiling water bath? Write the value here. Use the Charles s law equation to calculate what the air column length would be at 200.0 ºC. Show your setup below (3 points) 5
4) What was your measured temperature in the water bath closest to 20 ºC? Write the value here. What was the air column length at that temperature? Write the value here. Use the Charles s Law equation to calculate the Celsius temperature that would make the air column one-half that length. Show your setup below. (3 points) 5) Draw lines on your graph to show by extrapolation what your air column length would be at minus 100 C. Write the air column length here. (2 points) 6) The accepted value for absolute zero is -273.15 ºC. Compare this to your experimental value and calculate the percent error of your experimental value using the equation below. (Note: for purpose of calculating percent error, ignore the negative sign in the fraction denominator and report the percent error as a positive number.) (2 points) accepted value exp erimental value % error x 100% Show a clearly written setup. accepted value 6
Laboratory Experiment No. 8 Prestudy 1) Convert the following temperatures. Express the answers to the proper number of decimal places. (2 points) a) +22.0 ºC to K b) -270. ºC to K c) 623.84 K to ºC d) 71 K to ºC 2) Why is it necessary to use an absolute temperature scale rather than the Fahrenheit or Celsius scale when carrying out calculations with the Charles's law equation? (1 point) 3) Using the graph paper specified for this course, plot air column length versus Celsius temperature and attach the graph to this sheet. Start your axes at 0.00 cm and -300 ºC. Extrapolate to zero length (equivalent to zero volume) to get a Celsius value for absolute zero. In the space below, state the Celsius value your graph gives you for absolute zero. (7 points) Temperature (ºC) Air Column Length (cm) 98.8 12.20 80.1 11.61 60.8 10.75 39.5 10.28 31.2 9.88 0.1 8.81-10.9 8.45-31 7.75 7