Gas Laws: Boyle s and Amonton s Laws Minneapolis Community and Technical College v.9.08

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1 Gas Laws: Boyle s and Amonton s Laws Minneapolis Community and Technical College v.9.08 I. Introduction The purpose of this experiment is to test the extent real gases (to the limits of our measurements) follow the two ideal gas laws: Boyle's law and Amontons' Law. The experiment design allows for the study of gas pressure (P) as a function of gas volume (V) and gas pressure (P) as a function of gas temperature (T). Conclusions as to whether the gases can be treated as "ideal" in the PV and PT regimes studied will be made. II. Boyle's Law If one considers a constant amount of a gas (n=constant) and an unchanging gas temperature (T=constant), then Boyle's Law states that the pressure externally exerted on a gas is related to the volume occupied by the gas such that PV = k where k is a constant. If the pressure on a gas is varied then the volume will adjust to keep the product PV constant, as long as every variation is done with a constant n and T. tube syringe The apparatus used for this experiment is shown above. A syringe is connected via a tube to a pressure sensor, which is connected to a computer. The volume occupied by the gas is the sum of the syringe volume, V syringe and the small, fixed volume of the tube that connects the pressure sensor to the syringe, V tube. The total volume (V total ): V total = V tube + V syringe (1) is used to calculate the Boyle's Law constant, k: P V total = k (2) Failure to include V tube in the calculation ultimately leads to a Boyle's Law constant that isn't very constant at all! The data you collect consists of nine different pressure-volume readings. The pressure measurement is obtained from the Logger Pro computer readout. The volume measurement, V syringe, is obtained by determining the position of the syringe plunger against the graduated scale on the syringe barrel. V tube is determined mathematically using two different (P, V syringe ) experimental data points and the mathematics that follow. According to Boyle's law the product of P V total should be the same for any set of pressures and volumes so long as the number of moles of gas, n, and the temperature, T, do not change. This can also be stated as: P 1 V total 1 = P 2 V total 2 (3) The total volumes are the combined syringe- tube volumes: V total 1 = V syringe 1 + V tube (4) V total 2 = V syringe 2 + V tube (5)

2 Substituting equations 4 & 5 into equation (3) we obtain: Which can be solved for V tube : P 1 (V syringe 1 + V tube ) = P 2 (V syringe 2 + V tube ) (6) V tube = (P 1 V syringe 1 - P 2 V syringe 2 ) (7) P 2 - P 1 One obtains V tube by substituting any two pressure-volume data points into the equation. This one value of V tube is then added to each of the V syringe values before the respective P V total product is calculated. III. Amontons' Law Amontons' Law states that a pressure-temperature relationship exists for a fixed amount of gas in a fixed volume. At constant volume, the pressure exerted by a fixed amount of gas is directly proportional to the absolute temperature (i.e. Kelvin scale): P = K T (8) Here K is a different constant than the constant expressed in the Boyle's Law. In this part of the experiment you will collect pressure & temperature data in order to test whether the quotient, P/T, is a constant. The apparatus used to collect the pressure-temperature data points (right) consists of an Erlenmeyer flask immersed in a water bath whose temperature is increased slowly using a hot plate. A stopper in the top of the flask traps the gas inside the flask, fixing the volume and amount of gas. The pressure sensor is attached to the flask via a tube inserted into the stopper. Different temperatures are obtained by slowly heating the Erlenmeyer flask indirectly with the water bath using a hot plate. A large magnetic stir bar is used to continuously stir the water bath guaranteeing a uniform temperature throughout. So long as the temperature doesn't change too fast, assuming the temperature of the gas is the same as the temperature of the surrounding water bath is valid. A temperature sensor is used to measure the temperature of the water bath (and flask). Amontons' Law says a graph of pressure versus temperature for an ideal gas is a straight line (figure at right). The straight line can be extended or extrapolated to lower pressures to where the pressure is zero. At this point the lowest possible temperature, absolute zero (defined in the Kelvin system), can be read from the graph's horizontal axis. This temperature, absolute zero, is the theoretical temperature where all molecular motion stops. In reality, real gases condense or liquefy before reaching absolute zero. In your data analysis, you will use M.S. Excel to graph your experimental pressure-temperature data points and perform the trend line analysis of the data to predict the value of absolute zero in the Celsius temperature system.

3 Procedure: Boyle's Law Procedure (n & T held constant): Plug the pressure sensor into CH 1 of the Vernier Interface and activate Logger Pro software. Navigate to the share drive (S://coursework/boraas) and open the file named "MCTC Pressure Sensor I" found in the boraaski folder. Calibration: Before the Pressure Sensor can be used, it must be calibrated. This will involve comparing the pressure sensor s reading to that of a known pressure gauge. Two such pressure measurements are made as part of the LoggerPro pressure sensor calibration. Your instructor will assist you with the calibration procedure at the beginning of the period. Pressure/Volume Measurements: Position the plunger of the syringe at the 60 ml mark. Assemble the apparatus shown below. Push the clear plastic tube firmly on the end of the syringe as there must be NO LEAKS! Record the pressure as indicated by the LoggerPro display. Push the plunger in to the ml mark and again record the pressure on your data table. The pressure display will fluctuate and so for each pressure measurement you should record only those digits that are significant. Also, record your estimate of the pressure s uncertainty as a +/- atm for each pressure measurement. on the data sheet. Obtain pressures for each of the following nine syringe volumes: ml ml ml ml ml ml ml ml ml Do not attempt volumes smaller than ml as you may damage the syringe and pressure sensor!

4 V. Amontons's Law Procedure (n & V constant): Obtain the following equipment: 125 ml Erlenmeyer flask with wired stopper and glass tube 1 L beaker Stopper with glass tube Pressure sensor Temperature sensor Large magnetic stir bar Hot/stir plate Plug the pressure sensor into channel 1 and the temperature sensor into channel 2 of the Vernier interface. Assemble the apparatus as shown in the figure below. Be sure the hot plate is turned off initially. Keep wires and tubes away from the hot plate, as they will melt. Push the pressure tubing firmly on the glass tube sticking out of the stopper. Should the tubing pop off during the experiment, you will have to start over from the beginning. Use a utility clamp around the flask stopper to support it and to keep it submerged in the water. (clamp not shown in figure) Use the articulated arm (not shown in figure) to support the temperature probe. Position the tip of the temperature sensor halfway down the flask and as close to the flask as possible. Support the pressure gauge and wires. Twist ties are available to tie wires and tubes to the articulated arm. Keep wires away from the hotplate s hot surface. PROTECT THE LAPTOP COMPUTER! Fill the 1 L beaker with enough COLD TAP water to cover the 125 ml flask as shown in the figure above. The beaker will be almost completely full. (All of the gas inside the flask must experience the same temperature provided by the water bath). Before you begin, have the instructor check over your apparatus. Start the stir bar. Very vigorous stirring is required to keep such a large amount of water well mixed. Set the hot plate heating dial at approximately 5. As the temperature rises past 60 degrees C, you will want to increase the hotplate to higher settings. As the water warms up, record on your data sheet at least 30 pressure/temperature data points that are roughly evenly distributed between your start temperature and 80 C. If you believe some gas has escaped during these measurements, it will be necessary to repeat the entire experiment from the beginning.

5 C1151 Data Sheet Name Gas Laws Date of Exp. Instructor Initia ls Lab Section Your individual experimental report will be due at the beginning of class next week. Data Table: (All entries must be in written in ink before you leave the lab). Data table: Boyle s Law Trial # Pressure (atm) Pressure Uncertainty (+/-) V syringe (ml) V tube (ml) V total (ml) P V total = K (atm*ml) D% K average = Calculate V tube ONCE using Equation #7 and data from Trials 1 & 5. This one calculated value of V tube will be used in all V total = V syringe + V tube calculations. Calculate P V total for each set of points and record the result with the correct S.F. in the data table. Calculate an average value for K and report it also in the table For each P V "constant" calculate % (percent difference), as follows: ( const. trial const. average) % = const. average 100% Data table: Amontons's Law Procedure Temp. Pressure Temp. Pressure Temp. Pressure Temp. Pressure Temp. Pressure

6 Writeup: Answers must be readable and make sense for full credit. Copied work will result in all involved students receiving a zero score Boyle s Law: How constant were the values for the P V total product you obtained above? Good data may show some minor variation, but the values should be relatively constant. Do you see any error patterns that may explain nonconstant behavior? Amontons' Law Create a pressure vs. temperature ( C) graph using M.S. Excel o The x-axis should range from -300 C to +100 C. o The y-axis should range from 0 atm to 1.5 atm. o Extend (extrapolate) the trendline backwards far enough for it to cross the temperature axis. o Perform a trendline analysis of the data and display the equation on the graph with 8 decimal place accuracy. o Be sure to include a graph title and axis labels. o Staple the graph to this report. Your predicted value for absolute zero. Mathematically determine your value for absolute zero by letting the pressure = 0 in your trendline equation and solving for temperature. Show your work and the result below. 1. Is it necessary to know the volume of the apparatus in this part of the experiment? Why or Why not? 2. Ideally, what should happen to the pressure of a gas if the Kelvin temperature is doubled? Verify this using your trendline equation to determine the pressure at -73 C (200 K) and at 127 C (400 K). How many times greater is the pressure at 400 K in comparison to 200 K? 3. Extrapolation (making predictions outside of a range of data) was used to determine the value for absolute zero in your experiment. Another technique, interpolation (making predictions between data points) is used in other experiments. Which technique is more reliable and why?