Experiment 9 - Exploring Properties of Gases Report

Ideal Gas Law Experiments Report Abstract The ideal gas law equation is used to determine the relationships between Pressure, Volume, and Temperature. Three experiments are performed to understand how one affects another while the third remains constant. Hypotheses are made for each experiment and the results determine k= P (V )n is used to find the proportionality constant, if the hypotheses are correct. The equation k in each experiment. In the second and third experiments, the variables m and n are used to write an equation that describes the relationship between the dependent and independent variable. For the third experiment, the total volume is found by adding the volume of the syringe, bottle, and tubing. The standard deviation is found for each experiment. In the discussion, a reexamination of each hypothesis is performed depending on if the hypothesis was incorrect. A conclusion is then found and an explanation of the reasoning behind why the formulated hypothesis was incorrect is stated. Introduction The physical behavior of a sample gas can be described by four variables: pressure (P), volume (V), temperature (T), and amount (number of moles, n). For an ideal gas these variables are interdependent; meaning, any one of them can be determined by measuring the other three. The relationships that exist between them are called “gas laws” and each of the gas laws expresses the pair-wise relationship between two of the variables, while the remaining two are held constant. These gas laws can be combined into one relationship called the ideal gas law: PV=nRT The ideal gas law quantitatively describes the physical state of an “ideal gas.” Though no such “ideal gas” actually exists, most simple gases (i.e., N 2 , O2 , H 2 , Ar) show nearly ideal behavior at ordinary temperatures and pressures. For these gases deviations from ideal behavior become noticeable only at extreme pressures or temperatures. Hypotheses In Experiment I, Boyle’s Law was used to measure the relationship between pressure and volume at constant temperature. Before the experiment, I predicted that as volume increased, the pressure would increase. I predicted this because as you add more water, then it pushes down adding more pressure. In Experiment II, Gay-Lussac’s Law was used to measure the relationship between pressure and temperature at constant volume. Before this experiment, I predicted that as temperature increased, the pressure would decrease. I predicted this because as you heat water, it will evaporate therefore letÝng up on the pressure. In Experiment III, Charles’s Law was used to measure the relationship between volume and temperature at constant pressure. Before the experiment, I predicted that as temperature increased, the volume would decrease. I predicted this because, like in the second experiment, as you heat water, it will evaporate so the volume will decrease. In all experiments, n will be held constant because all experiments will be conducted on an enclosed sample of air and the relationships among the other three (P,V,T) will be examined by holding one at constant in each experiment and observing relationship between the other two. Methods Experiment I: Boyle’s Law In the lab a plunger was used to position the piston of a syringe so that there is a measured volume of air trapped in the barrel. The volume was adjusted to 55 mL. The LabQuest instrument was used to record the pressure and volume. A table was set up in the notebook to record pressure and volume to the nearest 0.1 mL. The clamp handle was used to push down the plunger in order to decrease the volume in the syringe. A 5 mL drop in volume is sufÏcient enough to obtain a significant change in pressure. This procedure was repeated to obtain a total of 6 measurements of volume and pressure. Volume was converted from mL to L and graphed on Logger Pro. Experiment II: Gay Lussac’s Law The LabQuest instrument was used to measure temperature and pressure. A 25 mL Erlenmeyer flask was sealed with a one-holed rubber stopper to contain a sample of air. The falsk was then connected to the gas pressure sensor. An ice-water bath was created in a 400 mL beaker. The flask and temperature probe were placed in the bath. The other end of the tubing was connected to the pressure sensor after 2 minutes of the flask being immersed. The bath was stirred periodically until the pressure stabilized. A table was set up in the notebook to record pressure and temperature. The temperature was varied by approximately 10 K. This procedure was repeated to obtain a total of 5 measurements of temperature and pressure. Experiment III: Charles’s Law An ice-water bath was created in the cooler provided. The bath was stirred periodically to ensure a uniform temperature. The LabQuest instrument was used to measure temperature and volume. A utility clap was tightened around a syringe that was connected to a bottle and rubber stopper. The tubing was connected to the bottle and was fully depressed in the bath. The utility clamp was adjusted so that the syringe and bottle were just above the top of the cooler and the bottle and most of the syringe was immersed in the water. The temperature probe was inserted through the middle of the clamp. The other end of the tubing was connected to the pressure sensor after 2 minutes of being immersed. The bath was periodically stirred while the pressure stabilized. A table was set up in the notebook to record volume and temperature of gas in the syringe. The temperature was varied by approximately 10 K. This procedure was repeated to obtain a total of 5 measurements of temperature and pressure. However, in each bath, the pressure was stabilized and the plunger manually adjusted the volume of gas in the syringe until the pressure returned to the original value measured. Calculations Experiment I: Boyle’s Law k= The equation P (V )n is used to find the proportionality constant. The average of k will be equivalent to m on the Logger Pro graph. Standard deviation is to be calculated as well. Experiment II: Gay Lussac’s Law The variables m and n are used to write an equation that describes the relationship n between the dependent and independent variable. i.e., P=m(T ) . The equation k= P (T )n is used to find the proportionality constant. The average of k will be equivalent to m on the Logger Pro graph. Standard deviation is to be calculated as well. Experiment III: Charles’s Law V total of the air in the apparatus is calculated using the equation V total=V bottle +V syringe +V tubing . V tubing is a constant of 4.0 mL. V syringe was recorded during the experiment. V bottle is found by filling the bottle with water and pouring the contents into a 100 mL graduated cylinder. The volume is recorded and all volumes are converted from mL to L. They are then plugged into the equation to determine V total . The variables m and n are used to write an equation that describes the relationship between the dependent and independent variable. i.e., n V total =m(T ) . The equation k= V total (T )n is used to find the proportionality constant. The average of k will be equivalent to m on the Logger Pro graph. Standard deviation is to be calculated as well. Results Experiment I: Boyle’s Law k= P (V )n is used to find proportionality constant, k. P = 0.9917 atm k= 0. 9917 =18 .03 (0 .055 ) k= 1. 0853 =21. 7 (0 .050 ) k= 1. 1975 =26 .6 ( 0 .045 ) k= 1. 3408 =33 .52 ( 0 .040 ) k= 1. 5220 =43 . 5 (0 .035 ) k= 1. 7586 =58 .62 ( 0 .030 ) V = 0.055 mL P = 1.0853 atm V = 0.050 mL P = 1.1975 atm V = 0.045 mL P = 1.3408 atm V = 0.040 mL P = 1.5220 atm V = 0.035 mL P = 1.7586 atm V = 0.030 mL 18 .03+21. 7+26 . 6+33 .52+43 .5+58 . 62 =33 . 66 6 Standard Deviation: k = 33.66 m = 30.22 33.66 - 18.03 = 15.63 33.66 - 21.7 = 11.96 k = 18.03 33.66 - 26.6 = 7.06 k = 21.7 33.66 - 33.52 = 0.14 k = 26.6 33.66 - 43.5 = -9.84 k = 33.52 33.66 - 58.62 = -24.96 k = 43.5 k = 58.62 2 ( 2 2 2 2 2 15. 63 + 11. 96 +7 .06 + 0 . 14 +(− 9 . 84 ) +(−24 . 96 ) 1/2 ) =115 . 7 5 Experiment II: Gay Lussac’s Law n P=m(T ) describes the relationship between the dependent and independent variable. k= P (T )n is used to find proportionality constant, k. P = 0.9799 atm k= 0.9799 =3 .58 ×10−3 ( 273. 6 ) k= 1. 0269 =3. 54×10 −3 ( 289. 7 ) T = 273.6 K P = 1.0269 atm T = 289.7 K P = 1.0560 atm k= 1. 0560 =3. 54×10−3 (298. 5 ) k= 1.0935 =3 .51×10−3 (311. 2) k= 1 . 1214 =3 . 51×10−3 (319. 2) T = 298.5 K P = 1.0935 atm T = 311.2 K P = 1.1214 atm T = 319.2 K 3 . 58×10−3 +3 . 54×10−3 +3 . 54× 10−3 +3 . 51×10−3 +3 .51×10−3 =0 . 014872 5 k = 0.014872 m = 0.003093 Standard Deviation: −3 2 ( −3 2 −3 2 −3 2 −3 2 (3. 58×10 ) +(3 . 54×10 ) +(3. 54×10 ) +(3 .51×10 ) +(3 . 51×10 ) 1/2 ) =7 . 81×10−6 4 Experiment III: Charles’s Law V total=V bottle +V syringe +V tubing . V tubing is a constant of 4.0 mL. V syringe was recorded during the experiment. It was 0.0 mL V bottle is 67.1 mL. V total =67 . 1+0+4 V total=71.1 L n V total =m(T ) describes the relationship between the dependent and independent variable. k= V total (T )n is used to find the proportionality constant. V = 71.1 L k= 71. 1 =0. 260 (273. 5 ) k= 71. 1 =0 .256 ( 277 .5 ) k= 71. 1 =0 .251 (283. 8 ) k= 71. 1 =0 .245 (290. 6 ) k= 71. 1 =0. 237 (300. 3 ) T = 273.5 K V = 71.1 L T = 277.5 K V = 71.1 L T = 283.8 K V = 71.1 L T = 290.6 K V = 71.1 L T = 300.3 K 0. 260+0 . 256 + 0 . 251+ 0 .245+0. 237 =0 . 2498 5 Standard Deviation: 2 ( 2 2 2 2 (0 .260 ) +( 0. 256 ) +( 0. 251 ) +( 0 . 245 ) +( 0 . 237 ) 1/2 ) =0 . 039 4 Discussion Experiment I: Boyle’s Law In Experiment I, I predicted that as the volume increased, the pressure would increase. The graph from experiment I shows that my hypothesis is correct although the graph shows my hypothesis inversely. Experiment II: Gay Lussac’s Law In Experiment II, I predicted that as the temperature increased, the pressure would decrease. The graph from experiment II shows that my hypothesis is incorrect. After I reexamined my hypothesis, I understand why the pressure increases with the temperature. As the water becomes warmer, the pressure inside the flask expands therefore increasing. Experiment III: Charles’s Law In Experiment III, I predicted that as temperature increased, the volume would decrease. The graph from experiment III shows that my hypothesis is incorrect. After I re-examined my hypothesis I came to understand why the volume increased with the temperature. The volume we measured was not of water but of gas. As the water evaporates, it becomes a gas so the volume increases because of the change from liquid to gas. Conclusion I’ve learned a lot mainly about how the temperature affects the volume and pressure from performing the experiments. Even though my hypothesis from the second and third experiments involving temperature were wrong, I learned how to correct the hypothesis and come to the correct conclusion. When I think about the hypothesis after I’ve performed the experiment and gotten my results, the conclusion is easier to understand.