Studying the Volume Temperature Relationship of a Gas

Transcription

1 CER Modular Laboratory Program in Chemistry editor: Henry D. Schreiber PROP 524 Studying the Volume Temperature Relationship of a Gas prepared by Conrad L. Stanitski, University of Central Arkansas Purpose of the Experiment Study the relationship between the volume of a gas sample and its temperature. Determine the temperature at which a gas sample has zero volume. Background Required You should be familiar with techniques for measuring distances and temperatures. You should be familiar with the properties of ideal gases, as well as with graphing techniques, either manual or computerized. Background Information The volume of a gas sample increases with heating. For example, dough containing yeast rises because the carbon dioxide gas produced by the yeast and trapped within the dough expands during baking. Automobile tires also expand as the air in them gets hotter. The volume (V) of an ideal gas sample at constant pressure increases linearly with temperature (T, C). This relationship can be expressed by Equation 1: V = mt + b (Eq. 1) The slope and y-intercept of the straight-line graph of this equation are m and b, respectively. However, if we express the temperature in kelvins, the mathematical relationship between volume and temperature (T, K) for an ideal gas sample can be simplified to that represented by Equation 2: V = mt (Eq. 2) Equation 2 is one expression of Charles law, which states that there is a direct proportionality between the volume and temperature of a gas sample, assuming that the pressure and amount of the gas do not change. We can rearrange Equation 2 to form two other common expressions of Charles law, as shown in Equation 3: V/ T = m = constant and V 1 /T 1 = V 2 /T 2 (Eq. 3) The expressions in Equation 3 indicate that the quotient of the volume and temperature of an ideal gas sample is a constant, again assuming that the pressure and amount of gas do not change and the temperature is in kelvins. Copyright 2003 Wadsworth Group. Brooks/Cole is an imprint of the Wadsworth Group, a division of Thomson Learning, Inc. Thomson Learning TM is a trademark used herein under license. For more information about this or any other Brooks/Cole products, contact: BROOKS/COLE, 511 Forest Lodge Road, Pacific Grove, CA USA; (Thomson Learning Academic Resource Center). ALL RIGHTS RESERVED. No part of this work may be reproduced,transcribed, or used in any form or by any means graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution, or information storage and/or retrieval systems without the prior written permission of the publisher. For permission to use material from this work, contact us by fax: ; phone: Printed in United States of America.

2 2 PROP 524/Studying the Volume Temperature Relationship of a Gas Example A student measures the volume of an air-filled balloon as a function of temperature. Throughout the experiment, the mass of gas in the balloon and the atmospheric pressure remain constant. The following table summarizes his measurements. T ( C) V (L) Problem 1 Prepare a graph of volume versus temperature (in C), and use it to determine the relationship between volume and temperature for this gas sample. Solution We plot volume on the y-axis and temperature on the x-axis, as shown in Figure 1. We then draw the best straight line through the data points volume, L temperature, C Figure 1 Volume of air in a balloon as a function of temperature Alternatively, we can use spreadsheet software to determine the trend line for these data, via regression analysis. We can then determine the slope and y-intercept of either the best straight line or the trend line. Based on these results, we can write the equation that represents the volume temperature relationship for this gas sample: V, L = ( L/ C)(T, C) L The graph of the data indicates that the volume of the air in the balloon increases linearly with temperature. Problem 2 The maximum volume of air that this balloon can contain before bursting is 2.50 L. Predict the temperature at which the balloon will burst, by extrapolating the volume temperature relationship. Solution We extrapolate the best straight line (or trend line) to higher volumes and temperatures, as shown in Figure 1. We then locate the volume of 2.50 L on the y-axis. We position a ruler horizontally at that point on the y-axis and note where the ruler intersects the straight line. We then position the ruler vertically at that intersection point and note where the ruler intersects the x-axis. We read the temperature of the intersection point on the x-axis, which is 51 C. Hence, we predict that the balloon will burst once the temperature exceeds 51 C.

3 PROP 524/Studying the Volume Temperature Relationship of a Gas 3 Alternatively, we could substitute the maximum volume (2.50 L) into the equation we wrote in Problem 1 and calculate the bursting temperature directly L= ( L/ C)( T, C) L ( 250. L 208. L) T, C = = 51 C ( L/ C) In this experiment, we will study the volume temperature relationship of air by measuring the changes in the length of a column of trapped air as it varies with temperature. The length of the trapped air column is directly related to its volume. As the temperature changes, so does the length of the air column. Note that under the conditions of this experiment, the pressure remains essentially constant. Procedure Caution: Wear departmentally approved safety goggles while doing this experiment. Hot oil can cause burns. Take all precautions necessary to prevent such burns. In particular, do not handle or move the beaker of hot oil. Note: Record all measurements on your Data Sheet. Record all lengths to the nearest 0.01 cm. 1. Add about 425 ml of corn or cooking oil to a 600-mL beaker. Put the beaker on a hot plate. Place a support ring around the beaker for stability, as shown in Figure 2. Turn the hot plate to its highest setting and heat the oil. 2. Obtain a thermometer, a capillary tube, and two small rubber bands. support ring oil Figure 2 Hot-oil bath OFF 5 6 7

4 4 PROP 524/Studying the Volume Temperature Relationship of a Gas thermometer closed end rubber band capillary tube 3. Use the rubber bands to attach the inverted capillary tube to the thermometer, as shown in Figure 3. The open end of the capillary tube should be 4 6 mm from the tip of the thermometer bulb. 4. Using a microclamp, suspend the thermometer capillary tube assembly in the oil bath, as shown in Figure 4. The capillary tube should be completely immersed in the oil. Continue heating the oil bath until the temperature is relatively constant at about 110 C. Record the exact temperature. rubber band open end 4 6 mm Figure 3 Thermometer capillary tube assembly thermometer oil capillary tube OFF Figure 4 Thermometer capillary tube assembly in oil bath NOTE 1: Turn off the hot plate while you are waiting for the temperature of the assembly to drop. 5. Raise the thermometer capillary tube assembly until about three-quarters of the capillary tube is above the surface of the oil. Hold the raised assembly in place for a few seconds, in order to allow some oil to rise partway up the capillary tube. Air will be trapped in the capillary tube between the oil plug and the top of the tube. Then, quickly remove the thermometer capillary tube assembly from the oil bath. 6. Lay the hot assembly on several layers of paper towels. Position the assembly so that you can read the temperature scale easily. On the top paper towel, make a reference mark aligned with the inside edge of the closed end of the capillary tube, as shown in Figure 5. Similarly, make a mark aligned with the upper end of the oil plug. Simultaneously, write the temperature next to the oil plug mark. Do not move the assembly until you have completed Step [NOTE 1] As the assembly cools, make marks on the towel, at approximately 10-degree intervals, aligned with the upper end of the oil plug. Write the corresponding temperature next to each mark. The goal is to have five or six marks covering the temperature drop from the first to the last reading (room temperature).

5 PROP 524/Studying the Volume Temperature Relationship of a Gas 5 reference mark reference mark trapped air mark for each temperature oil plug paper towel Figure 5 Marking the lengths of trapped air samples NOTE 2: Position the assembly on the paper towel so that your previous reference mark aligns once again with the inside edge of the closed end of the capillary tube. NOTE 3: Also discard the used rubber bands as directed by your laboratory instructor, after your second determination. 8. Measure the distance, to the nearest 0.01 cm, from the reference line (marking the inside edge of the closed end of the tube) to each of the other marks. Record these distances, along with the corresponding temperatures. 9. Prepare an ice-water bath by half-filling a 150-mL beaker with tap water and adding ice. Keeping the thermometer capillary tube assembly intact, place the assembly into the ice-water bath until the temperature drops to approximately 0 C. Quickly remove the assembly from the ice bath and repeat Steps 6 and 7 [NOTE 2], but this time, record the increase in temperature and location of the upper end of the oil plug at approximately 5 8 degree intervals. Once the assembly reaches room temperature, measure the distance from the reference line to each of the other marks. Record these distances, along with the corresponding temperatures. 10. Discard the used capillary tube as directed by your laboratory instructor [NOTE 3]. Wipe the thermometer dry. Discard the paper towels in the regular trash. 11. Obtain another capillary tube. Reheat the oil to about 110 C. Repeat Steps 3 10 to obtain a second set of data. Caution: Wash your hands thoroughly with soap or detergent before leaving the laboratory.

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7 name section date Data Sheet determination 1 determination 2 T = C upon removal of T = C upon removal of tube from oil bath tube from oil bath T, C distance, cm T, C distance, cm PROP 524/Studying the Volume Temperature Relationship of a Gas 7

8 8 PROP 524/Studying the Volume Temperature Relationship of a Gas Results Sheet 1. Using a separate sheet of graph paper for each determination, graph distance versus temperature. Plot distance on the y-axis and temperature on the x-axis.* The y-axis scale should range from 0 to the maximum distance, in cm; the x-axis scale should range from 350 C to 100 C. 2. Draw the best straight line that fits the plotted points on each graph. 3. Extrapolate each line until it intersects the x-axis. T (extrapolated) at which your air column would have a length of 0 cm, C T (extrapolated) at which your air column would have a length of 0 cm, C determination 1 determination 2 *Your laboratory instructor may have you graph the data using graphing or spreadsheet software, rather than doing it manually. Your laboratory instructor may also have you use spreadsheet software to perform the extrapolation.

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11 name section date Interpretation of Your Results Use the spaces provided for the answers and additional paper if necessary. 1. (a) Compare your two determinations of the temperatures at which your air column would have a length of 0 cm. This is the temperature at which your air sample would have zero volume. Which of your two determinations would you consider the better estimate of the actual zero-volume temperature? Briefly explain. (b) Compare your answer to (a) with absolute zero. Should the zero-volume temperature equal absolute zero? 2. Discuss how your graphs would have looked if you had plotted T in K instead of C. 3. Would your results have varied significantly if you had used pure nitrogen in place of air? Briefly explain. 4. Several simplifying assumptions have been made in this experiment. Cite two of them. PROP 524/Studying the Volume Temperature Relationship of a Gas 11

12 12 PROP 524/Studying the Volume Temperature Relationship of a Gas 5. The volume of air trapped in your capillary tube can be calculated by using the equation for the volume of a cylinder, as shown in Equation 4, V = πr 2 h = (3.14)(0.080 cm) 2 (distance, cm) (Eq. 4) given a capillary tube in which the radius of the interior cross section averages cm. (a) Choose the three data points from determination 2 that are closest to 90 C, 30 C, and 10 C, and use them to complete the following table: T, C T, K distance, cm V, cm 3 V/ T, cm 3 /K average V/ T, cm 3 /K (b) Using your average V/ T from the table in (a), calculate the volume of your air sample at 125 C. Could this volume be measured in a capillary tube with an average radius of cm and a length of 9.0 cm?

13 name section date Pre-Laboratory Assignment 1. Briefly describe two safety precautions you must take when using hot oil in this experiment. 2. A student performing this experiment collected the following data. The highest oil-bath temperature was 110 C. temperature, C distance, cm (a) Graph the data. Plot distance on the y-axis and temperature on the x-axis. The y-axis scale should range from 4.00 to 6.00 cm. The x-axis scale should range from 0 to 100 C. Draw the best straight line that fits the plotted points.* (b) Based on your graph in (a), how does the volume of an ideal gas sample change when its temperature increases, assuming constant pressure? *Your laboratory instructor may have you graph the data using graphing or spreadsheet software, rather than doing it manually. PROP 524/Studying the Volume Temperature Relationship of a Gas 13

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