Table of Contents ABSTRACT
1
1.0 INTRODUCTION
2-
5
2.0 EXPERIMENTAL DESIGN
6
2.1 Materials
7
2.2 Methods
8-
2.3 Procedure
10
9
3.0 RESULTS AND CALCULATIONS 11-14 4.0 DISCUSSIONS
15-16
5.0 CONCLUSION AND RECOMMENDATIONS
6.0 REFERENCES
17
18
Abstract
The aim of these experiments conducted is to study the effects of volume on the pressure of the gas at constant temperature which relates Boyle’s Law equation and the effects of temperature on the pressure of the gas at constant volume which relates Gay-Lussac’s Law equation.
An experimental set up was prepared to study the relationship between pressure and volume at constant temperature for Boyle’s law. In this experiment, the volume of the closed cylinder are manipulated to study the effect towards the pressure of the gas. Next, another experimental set up was prepared at the same time to study the relationship between pressure and temperature at constant volume. This time, the temperature of the gas was manipulated in order to study the effect on the pressure of the constant volume of gas contained in the hollow copper ball.
Based on the data obtained by conducting the experiment, a graph which relates pressure (kPa) with volume (m 3) and pressure (kPa) with temperature (K) were plotted. Then, using the graphs plotted, the Boyle’s law and Gay-Lussac’s law theory can be studied and verify. The results of these experiments clearly proven that both Boyle’s law and Gay-Lussac’s law are true and can be applied in ideal gas calculations.
1
1.0
Introduction
The objective of this experiment was conducted is mainly to study the effects of volume on the pressure of the gas at constant temperature which relates Boyle’s Law equation and the effects of temperature on the pressure of the gas at constant volume which relates Gay-Lussac’s Law equation.
The pressure of a gas is influences by both volume and temperature of the gas itself at which it is measured. The relationship between the volumes of a gas with it respective pressure at constant temperature are theorize by Boyle’s Law. On the other hand, the relationship between the temperatures of a gas with it respective pressure at constant volume are theorize by Gay-Lussac’s Law [1]. The equation of ideal gas is given as:
PV =nRT
[2]
1)
Where
P = pressure (kPa) V = volume (m3) n = no.of mol (mol) R = universal gas constant (J/mol K) T = temperature (K)
2
(equation
Boyle’s Law
Boyle’s Law states that the pressure of a gas is inversely proportional to its volume, and vice versa if only the temperature of the gas is kept constant [3]. This simply means that when the volume of the gas decreases, the pressure of the gas increases, and vice versa.
As the experiment is carried out in an enclosed container and the temperature is held constant at room temperature, the terms n, R, and T of the ideal gas equation will eventually remain constant. This can be simplified and detonate the terms nRT =C , where C is a constant. The ideal gas equation can be simplified as: PV =C
P∝
(equation 2)
C V , C is constant
The equation can be further simplified as pressure is inversely proportional to its volume at constant conditions: P∝
1 V
As the volume of the closed container decreases, the gas molecules in the container have lesser space to move around and therefore, it collides among themselves and against the wall more often. Thus, the rate of collision increase and as a results, the pressure of the gas increase due to the change of momentum between gas molecules [1]. The experiment was conducted at room temperature and the temperature in the closed syringe are assumed to be constant at room temperature throughout the whole experiment.
3
Gay-Lussac’s Law
Gay-Lussac’s Law states that the pressure of an ideal gas is directly proportional to its absolute temperature if only the volume of the gas are held constant [4].
As the experiment was carried out at a constant volume, the terms n, R, and V of the ideal gas equation will eventually remain constant. The ideal equation can be simplified as:
P nR =C ,C is T V
(equation 3)
P∝ T
From the derived equation, it states that pressure is directly proportional to temperature at constant volume. This statement could be explained whereas the temperature of a constant volume gas rises, the kinetic energy between molecules of the gas will increases rapidly, thus, the rate of collision between molecules increase. As a result of this phenomena, the pressure of the gas inside of the enclosed system increases.
4
Figure1. Idealize graph of pressure against volume. [5]
Figure2. Idealize graph of pressure against temperature. [6]
5
2.0
Experimental Design
Figure 3. Boyle’s Law experiment set up.
Figure 4. Gay-Lussac’s Law experiment set up.
6
2.1
Materials and Apparatus
Boyle’s Law Experiment
Syringe Bourdon pressure gauge with valve Retort stand with clamps
Gay-Lussac’s Experiment
2.2
Hollow copper ball Bourdon pressure gauge with valve Water bath Thermometer Retort stand with clamps
Methods
7
Boyle’s Law experiment
The experiment is set up as in Figure 1. A syringe which acts as a closed cylinder with a movable pistol is connected to the bourdon pressure gauge via a valve. The volume in the syringe is first adjusted to 60 cm 3 and the pressure of the gas was determined via the bourdon pressure gauge. The volume of the syringe is slowly compress to 50 cm3 followed by 40 cm3, 30 cm3, and 20 cm3. The pressure of the bounded gas was determined and recorded simultaneously after each compression. The compression stopped at 20 cm 3 as it is incompressible any further. The experiment was conducted for another two trials to minimize possible errors and to obtained an average values.
Based on the data obtained, the pressure displayed by bourdon gauge in bar was converted to Pascal. Next, a graph of pressure against its respective volume of gas and a graph of pressure against its respective reciprocal volume of gas were plotted separately. The relationship between pressure and volume of gas at constant temperature which relates Boyle’s Law could be able to be identified with the aids of the plotted graphs.
Gay-Lussac’s Law experiment 8
The experiment is set up as in Figure 2. A hollow copper ball which contains a fixed amount of gas (atmospheric air) was connected to a bourdon gauge via a needle valve. With the aid of the retort stand, the hollow copper ball is slowly placed into the water bath and water is filled into the water bath so that the hollow copper ball was immersed more than half of it. Next, the water bath was heated to 50 oC by adjusting the adjustment knob. Once the water bath reached 50 oC as indicated by the indicator light, the temperature of water bath was cross checked using a thermometer. The pressure of the bourdon gauge is now adjusted to 0 bar. This temperature and pressure was taken as initial value.
The experiment proceeded with heating the water bath to 55 oC, 60 oC, 65 oC, and 70 o
C. The pressure inside the hollow copper ball was determined and recorded
simultaneously after each heating. Based on the data obtained, the pressure which were displayed by bourdon gauge in bar was converted to Pascal. Next, a graph of pressure against its respective temperature was plotted. The relationship between pressure and temperature of gas at constant volume which relates Gay-Lussac’s Law could be able to be identified with the aid of the plotted graph.
2.3
Procedures
9
Boyle’s Law Experiment 1. 2. 3. 4.
The experiment was set-up as shown in Figure 3. A syringe was connected to a bourdon gauge. The initial volume of the syringe is set to 60 cm 3. The pressure of the gas in the syringe is determined via the bourdon gauge
and recorded. 5. The volume of the syringe is slowly compressed to 50 cm 3, 40 cm3, 30 cm3, and 20 cm3. 6. The pressure of the gas is determined simultaneously after each compression and recorded. 7. Steps 3 to 6 is repeated for two additional times to obtained an average data. 8. The results were tabulated as in Table 1.
Gay-Lussac’s Law Experiment. 1. The experiment was set-up as shown in Figure 4. 2. A closed metal with constant volume are placed into the water bath. 3. The temperature of the water bath was set to 50 o C using the heater and checked by using a thermometer. 4. After the temperature of the water bath is constant, the pressure of the gas was determine using the bourdon gauge and recorded. 5. Step 3 to 4 were repeated by setting the temperature of water bath to 55 oC, 60oC, 65oC, 70oC, 75oC, 80oC, and 85oC respectively. 6. The results were tabulated in Table 3.
3.0
Results and Calculations
Boyle’s Law Table 1: Table of tabulated data of Volume of gas (cm 3) with respective gauge Pressure (bar).
10
V(cm 20 30 40 50 60
Set 1 ) Pgauge(bar) 1.00 0.60 0.25 0.05 0.00
3
V(cm 20 30 40 50 60
Set 2 ) Pgauge(bar) 1.05 0.65 0.30 0.08 0.00
3
V(cm 20 30 40 50 60
Set 3 ) Pgauge(bar) 1.00 0.60 0.25 0.05 0.00
3
Average Data V(cm3) Pgauge(bar) 20 1.02 30 0.62 40 0.27 50 0.06 60 0.00
Table 2: Table of Volume of gas (m3) with respective absolute Pressure (kPa). Average Data 3
V(m ) 0.00002 0.00003 0.00004 0.00005 0.00006
Pabsolute(kPa) 205.97 165.45 129.99 108.72 102.64
Table 3: Table of reciprocal Volume of gas (m -3) with respective absolute Pressure (kPa). V(m3) 0.00002 0.00003 0.00004 0.00005 0.00006
Average Data 1/V (m-3) 50000.00 33333.33 25000.00 20000.00 16666.67
11
Pabsolute(kPa) 205.97 165.45 129.99 108.72 102.64
Pressure against Volume
Gr aph 1. Graph of absolute pressure (kPa) against volume (m3).
Pressure against reciprocal of Volume
f(x) = 0x + 49.36
Gr aph 2. Graph of absolute pressure (kPa) against reciprocal of volume (m-3).
Gay-Lussac’s Law 12
Table 4: Table of tabulated data of Temperature of gas ( oC) with respective gauge Pressure (bar). T (oC) 50 55 60 65 70
Pgauge(bar) 0.000 0.025 0.050 0.075 0.080
Table 5: Table of Temperature of gas (K) with respective absolute Pressure (kPa). T (K) 323 328 333 338 343
Pabsolute(kPa) 102.64 105.17 107.71 110.24 110.75
Pressure against Temperature f(x) = 0.43x - 34.49
Gr aph 3. Graph of absolute pressure (kPa) against temperature (K). Sample calculations Boyle’s Law Pabsolute =P gauge + Patmosphere
13
Given Patmosphere (bar)
= 1.01325 bar
1 bar = 101.3 kPa = 101 300 Pa 1 cm3 = 0.000001 m3
Average Data at Pgauge = 1.02bar, 20 cm3 Pabsolute = Pgauge + Patmosphere = 1.02 bar + 1.01325 bar = 2.0333 bar = 205.97 kPa 20 cm3
= 20 x 0.000001 = 0.00002 m3
Gay-Lussac Law Given T (K) = T (oC) + 273K At 50 oC, 0 bar T (K) = 50 + 273 = 323K Pabsolute = Pgauge + Patmosphere = 0 bar + 1.01325 bar = 1.01325 bar = 102.64 kPa 4.0
Discussion
Boyle’s Law
14
Based on the results plotted from graph 1, it is clearly observed that as the volume of the gas increases, the pressure eventually decreases. Thus, the equation that states pressure is inversely proportional to its volume are verified. P∝
C V
The shape graph also assembles the theoretical graph as shown in Figure 1 where it is an inversely proportional graph. The imperfect shape of the graph might due to some minor errors which occurred during the experiment was conducted and in this experiment, the gas is assumed to be ideal and constant at room temperature. Based on the results obtained from graph 2, it is able to conclude that absolute pressure is direction proportional to reciprocal of volume where: P∝
1 V
The linear line of graph 2 did not touches or intercept at 0 kPa and 0 m -3 compared to theoretical graph are due to the fact that the experiment was carried out starting at an initial volume fixed at 20 cm 3 instead of starting at volume of 0 cm 3. Besides, based on the equation of the linear line provided in graph 2, the y-intercept obtained is 49.362. Suppose that the y-intercept of an ideal experiment should intercept at 0, however, errors might have occurred in this experiment which caused an imprecise data of experiment results.
The results obtained for Boyle’s law experiment could be explained. As the experiment was carry on, the volume of the closed syringe was compressed. By doing so, the volume of the closed syringe eventually decreases, leaving the gas molecules in the container have lesser and lesser space to move around. The gas particles in the syringe now collides among themselves and against the wall more frequently. Thus, the rate of collision increase and resulting in an increase of gas pressure due to the change of momentum between gas molecules.
Gay-Lussac’s Law 15
Based on the graph plotted from graph 3, it is clearly seen that the absolute pressure of the gas is directly proportional to its temperature at constant volume. Thus, GayLussac’s Law are verified. P∝ T The shape of the graph also assembles the shape of the theoretical graph as shown in Figure 2 where it shows a directly proportional graph. The reason for the linear line that it does not touches or intercept at 0 kPa and 0 oC it due to the fact that the experiment was started initially at 50 oC instead of 0 oC. The initial temperature of the experiment was set to 50 oC and the pressure at that particular temperature was set initially to 0 bar using the bourdon pressure gauge.
The results obtained for Gay-Lussac law could also be explained. The temperature of the constant gas in the hollow copper ball was manipulated and increased as the experiment was carried on. As the temperature of the constant gas rises, the kinetic energy between the gas particles will eventually increases. Since the experiment was carried out in an enclosed system, the gas molecules will not escaped but it will collide against the wall of the copper ball more frequently. Thus, the rate of collision between the gases molecules increase. As a result of this phenomena, the pressure of the gas inside of the enclosed system increases.
5.0
Conclusion 16
By conducting the experiment, we are able to study and verify two of the ideal gas law which includes Boyle’s law and Gay-Lussac law which relates pressure and volume at constant temperature as well as pressure and temperature at constant volume respectively. In order to prove that both of the equations are true, different graph are required to be plotted based on the data obtained by conducting the experiment. To prove Boyle’s law equation, two graph are plotted by using pressure against its respective volume and pressure against its reciprocal volume. For Boyle’s law experiment, the volume of gas were manipulated at constant temperature to investigate it effects towards pressure. On the other hand, to prove Gay-Lussac law equation, a graph of pressure against its temperature are plotted. In Gay-Lussac’s law experiment, the temperature of the gas were manipulated at constant volume in order to study the effect towards its respective pressure. In conclusion, the results obtained by conducting the experiment have shown that the pressure of the gas is inversely proportional to the volume of gas at constant temperature or pressure of gas is directly proportional to the reciprocal of its volume. Boyle’s law explains and theorize that an inverse relationship between the pressure and volume of a gas at constant temperature. Besides, Gay-Lussac law was also verified since the results shown that pressure is directly proportional to its temperature at constant volume.
6.0
Refferences 17
[1] G. R. Delpierre and B. T. Sewell, “BOYLE'S LAW,” Boyle's law. [Online]. Available: http://www.physchem.co.za/ob11-mat/kinetic2.htm. [Accessed: 01-Oct-2016]. [2] R. N., “Ideal Gas Law,” Ideal Gas Law. [Online]. Available: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html. [Accessed: 01-Oct2016]. [3] “Boyle's law,” , Boyle's Law Formula, What is Boyle's Law? [Online]. Available: http://chemistry.tutorvista.com/physical-chemistry/boyles-law.html. [Accessed: 01Oct-2016]. [4] L. M. A., “Gay Lussac's Law,” Gay Lussac's Law, 2009. [Online]. Available: http://abetterchemtext.com/gases/g_lussac.htm. [Accessed: 01-Oct-2016]. [5] C. K.-12 Foundation, “CK-12 Foundation,” CK-12 Foundation, Nov-2016. [Online]. Available: http://www.ck12.org/book/ck-12-chemistry-intermediate/section/14.2/. [Accessed: 01-Oct-2016]. [6] F., “Frazer does Physics,” : November 2011, 2011. [Online]. Available: http://frazerphysics.blogspot.my/2011_11_01_archive.html. [Accessed: 01-Oct-2016]. [7] Smith, J. M., Van Ness, H.C., ‘’Introduction to Chemical Engineering Thermodynamics’’, McGraw Hill, New York, 7th Edition, 2005.
18
