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Charles' Law -The Volume-Temperature Relationship of a Gas 1.INTRODUCTION In 1787 Jacques Charles observed that for a fixed quantity of gas, the volume at constant pressure changes proportionally with the temperature. However, it was not until 1802 that Joseph Gay-Lussac expressed the relationship mathematically. Charles' law states that when the pressure is held constant, the volume of a fixed mass of ideal gas varies in direct proportion to the temperature, the latter being expressed in degrees Kelvin: V = k X T (1) where Vis the volume of the gas, T is the absolute temperature, and k is a constant that depends on both the pressure and amount of gas. Charles' law applies, for a given pressure and quantity of gas, under all sets of conditions. Thus, for two different sets of T and V conditions, the following can be written: (2) where at constant pressure, V1 and T1 refer to the initial set of conditions and V2 and T2 refer to the final set of conditions. In this experiment, Charles' law will be verified by determining the volume of a sample of air when measured at two different temperatures with the pressure held constant. 2. EXPERIMENTAL SECTION Caution: In this experiment, you will be using boiling water. Extreme care must be exercised when handling: (i) glassware containing boiling water and (ii) apparatus such as hot plates that can be very hot. 2.1 Temperature-Volume Measurements (1) Place approximately 650 ml of water and three boiling chips in a 1 L beaker and, using a hot plate, heat the water until it is boiling. Maintain a gentle boiling throughout this first part of the experiment and ensure the water level is maintained by topping it up if necessary. (2) Whilst the water is heating in Step (1) take a clean, dry 250 ml Erlenmeyer flask '(the flask must be completely dry) and label it "flask #1". (3) Fit the flask with a prepared stopper assembly and tubing, consisting of a single-hole rubber stopper which has a length of tight-fitting glass tubing inserted through to which is connected a 60-cm piece of plastic tubing. One end of the glass tubing should be flush with the inner face of the stopper. (4) With the rubber stopper fitted firmly to the flask, mark the position of the bottom face of the stopper on flask #1 with a marking pen, Support the "flask #1" assembly (i.e. flask, stopper, connected tubing) using a retort stand and clamp and set the entire assembly aside, (5) Prepare an ice-water slurry using a second 1 L beaker that is filled to half its capacity with a mixture of ice and water. Set the ice-water Slurry aside for later use in Step (11). (6) Take a second 250 ml Erlenmeyer flask, label it "flask #2", and put about 200 ml of water into this flask. (7) Place the end of the tubing from "flask #1" into the water in "flask #2". Make sure that the end of the rubber tubing reaches to the bottom of "flask #2" and stays submerged at all times. Use a lab jack to maintain "flask #1" and "flask #2" as close as possible to the same level throughout the remainder of the experiment to prevent any siphoning of water from "flask #2" into "flask #1". (8) Use the clamp holding the neck of "flask #1", to carefully lower this flask into the beaker of boiling water that was prepared in Step (1). The flask needs to be submerged only as far as the bottom of the rubber stopper. Secure the clamp holding "flask #1" onto a retort stand. (9) Continue to boil the water in the beaker gently for at least 5 min. Air bubbles should emerge from the end of rubber tubing submerged in "flask #2". Add hot water to the beaker containing the boiling water if boiling causes the water level to go down. (10) When bubbles no longer emerge from the end of the submerged tubing in "flask #2" (after 5 min, say), record the temperature of the boiling water (i.e. T1 in Kelvin) in Table 1 of the laboratory report sheet (LRS). [See also Question (3) in Section 3.] (11) Carefully lift "flask #1" from the boiling water bath and quickly, but carefully, place it into the ice-water slurry. Be sure to keep the end of the tubing always submerged in the water in "flask #2". Upon submersion of "flask #1" in the ice-water bath, water will be drawn out of "flask #2" and into "flask #1". (12) When no more water is drawn into "flask #1", record the temperature of the ice/water slurry (i.e. T2 in Kelvin) in Table 1 of the laboratory report sheet (L8S). [See also Question (3) in Section 3.] (13) Remove the end of the tube that is in "flask #2" and carefully drain any water that remains in the tube into "flask #1". Remove the stopper and tube from "flask #1" and then remove "flask #1" from the ice/water slurry. (14) Take a graduated cylinder and measure, to the nearest 0.1 ml, the volume of water that was drawn into "flask #1". Record this volume Wwl in Table 1 of the LRS. [See also Question (3) in Section 3.] - (15) Complete Section 2.2 before returning to this section to repeat Steps (1) to (14) two more times in order to collect sufficient data to be analyzed. [Important: It is extremely important to ensure that "flask #1" is completely dry before repeating the experiment.] 2.2 Determination of the Volume of Flask #1 (1) Fill "flask #1" with water to the level indicated by the marking pen. Insert the stopper with its glass tubing into "flask #1" and ensure the bottom of the stopper just touches the water. There should be no air space between the surface of the water and the bottom of the stopper. Adjust the water level if necessary. (2) Remove the stopper from "flask #1" and pour the water into a graduated cylinder. Measure to the nearest 0.1 ml the volume of the water. [Note: If a 100-ml graduated cylinder is used, it will be necessary to empty and refill it until all the water from "flask #1" has been measured.] (3) Repeat Steps (1) and (2) in this section three times to obtain an average value of the volume of "flask #1". Record these measurements in Table 2 of the LRS. [See Question (1) in Section 3.] 3. QUESTIONS AND CALCULATIONS (1) Use the data collected in Step (3) of Section 2.2 to calculate an average value of the volume of "flask #1". Note this value in the appropriate place in Table 2 of the LRS. (2) If Vw is the volume of water drawn into "flask #1" when it is immersed in the ice bath, V1 is the volume occupied by the hot air and V2 is the volume occupied by the cooled air, what is the mathematical relationship between Vw, V1 and V2? Explain. (3) Complete Table 1 of the LRS by calculating the values of the ratio V1 T2 /[(V1 - Vw)T1]. Explain the significance of this ratio in terms of Charles' law. 2 (4) Do your experimental results verify Charles' law? Explain. (5) What percentage deviation from Charles' does your experimental results show? Use Table 3 of the LRS to calculate the standard deviation of the ratio values V1 Tzf[(V1 - Vw)T1 ] determined previously. Show your working in the space provided below Table 3. (6) Write out correct statements of Charles' law: As the temperature of a gas decreases its volume (increases/decreases). As the temperature of a gas increases its volume (increases/decreases). (7) When performing Step (9) in Section 2.1, a student allowed all of the water in the beaker to boil away whilst still continuing to heat the system. What effect does this have on the temperature of the gas in the flask? Explain why this effect does not occur if water is still present in the beaker. (8) In calculating values of the ratio V1 T2 / [(V1 - Vw)T1 ] for the results table (see Question (3)), a student assumed the volume of "flask #1" to be 250 ml without actually measuring this volume. On the basis of your measurements, state how this assumption will affect the results. (9) A sample of gas is contained in a balloon with a volume of 35 Lat a temperature of 30°C. What temperature must be reached in order for the balloon to expand to a volume of 50 L, at constant pressure? [Show your working.] (10) A sample of gas occupies 4.50 Lat room temperature, 20°C. If the gas is heated to 100°C, what volume will the sample now occupy? [Show your working.] 3 Charles' Law-The Volume-Temperature Relationship of a Gas Aim The aim/s of this experiment is/are: ro v􀁟,..,f'f (ha.,../es' law 6y <:fefermt'ntng the v-otume of a Jample o/ a.1,,,-.. when rneasur-eot a.I two dtlJ.erenf fempera.fu.reJ whtl1I fhe pre ..rsure is he/ d con J fa 1>. f. Aim/s clearly identified and stated. /2 Method As per laboratory manual Changes: Results and Calculations (1) Measurements made in Steps (10), (12) and (14) of Section 2.1 Measurements made in Step (2) of Section 2.2 Table 1. Charles' Law Data Run# Ti/K 1 .9a.3l. 2 􀀹 9.8£.C Table 2. Volume of "Flask #1" Run# 1 2 3 T2/K VwfmL V1 Tzf[(Vc Vw)T1 ] 􀀸 Q,TI 􀀁 il=-8 Volume of "flask #1"/ml 3.D1.mJ 301ml 303ml All quantities entered in tables and calculated correctly. _/6 (2) Mathematical relationship between Vw, V1 and V2: Correct equation and explanation. /2 1 (3) Significance of the ratio V1T2 /[(V1- Vw )T1 ] calculated in the results table. Correct answer and reasoning. /4 (4) Comment regarding experimental results conforming to Charles' law: Succinct statement regarding experimental results. /2 (5) Table 3. Average deviation for Charles' law: Run# Working: 1 2 3 :E= Ratio X; x= :E= Correct calculation of standard deviation and percentage deviation. /8 (6) Correct statement of Charles' law: • As the temperature of a gas decreases its volume ______ _ • As the temperature of a gas increases its volume ______ _ Correct statements. /2 (7) Effect of allowing the water to boil away whilst continuing to heat the system: Correct answer and reasoning. /2 2 (8) Effect of assuming volume of "flask #1" is 250 ml: (9) Calculation using Charles' law: (10) Calculation using Charles' law: 3 Correct answer and reasoning. _/4 Correct answer and calculation. _/2 Correct answer and calculation. _/2

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