Perfect Gas Laws
Zack st
1 November 2012 Lab Group-09
Summary Two experiments were carried out to test the laws of perfect gas. The first one was done by keeping the pressure of gas constant and investigating the changes in its volume by manipulating its temperature. Second experiment was done to see the relationship between pressure and temperature of the gas while its volume kept constant throughout the experiment. In both experiments, the results showed good agreement with the perfect gas laws where both the manipulating and responding variables are linearly proportional.
Contents
Item
Page No.
Title/Summary Contents Introduction Procedure Results Discussion Conclusion
1 2 3 4 6 8 9
Figure 1: Diagram of overview of experiment
1. Introduction Gas laws state that a specific physical quantity of gases cannot be altered without interference to the other physical quantities of gases. Thus, these experiments were carried out with the aim to study the relationship between two physical quantities of gases while keeping all the other quantities constant.
1.1 Objectives
To alter the temperature of the gas and measure its height and calculate its volume.
To alter the temperature of gas and measure its pressure using pressure pump.
To calculate the absolute zero temperature by extrapolation method.
To calculate the amount of gas used in the experiment.
1.2 Theories The experiments below were carried out based on theories made by scientist. These are the theories behind the perfect gas law : 1. Gay-Lussac’s Law states that volume of gas is directly proportional to temperature of gas when pressure of gas kept constant. 2. Amonton’s Law states that pressure of gas is directly proportional to temperature of gas when volume of gas kept constant.
2. Procedure During the experiment, simple procedures were done to carry the experiment out safely and successfully. All the fixed variables are carefully controlled to allow no changes done to it. The manipulated and responding variables in each experiment are measured and tabulated.
2.1 Experiment Based On Gay-Lussac’s Law Apparatus was set up as shown in Figure 1 below. The hand pump was then removed to keep the pressure of gas constant. Then, about 400 ml o f hot water poured into the large test tube using a kettle. The initial maximum temperature of water and the initial height of the mercury globule were recorded. The water is then allowed to cool down and readings of height of the mercury globule were taken at constant intervals. When the temperature reached about 55°C, cold water is added to the test tube to allow it to cool faster. As the water cooled down, the responding temperature and height of mercury globule were recorded. All the data were recorded as stated in Table 1 in the results section.
Figure 2 : Diagram showing experimental set up.
2.2 Experiment Based On Amonton’s Law All the apparatus was set up as shown earlier in Figure 1. Then, about 400 ml of hot water poured into the large test tube using a kettle. The initial maximum temperature of water and the initial height of the mercury globule, h 0 were recorded. The water is then allowed to cool down gradually and change in height of mercury globe is o bserved. At constant temperature intervals, the hand vacuum pump is used to reduce temperature until the height of the mercury globule reaches h 0. The reading on the hand vacuum pump is then recorded for every interval. When the temperature reached about 55°C, cold water is added to the test tube to allow it to cool faster. As the water cooled down, the responding temperature and the corresponding hand vacuum pump reading is recorded. All the data were recorded as on the Table 2 on the results section.
3. Results These recorded data are best to be analysed graphically. Hence, all the data we tabulated from each of the experiments. Necessary calculations were carried out to gain enough information to plot graphs. The plotted graphs are shown below for each experiment including the original tables of measured and calculated data.
3.1 Tabulated Data Tables are produced for each of the experiment to ease calculations and find appropriate quantities needed for plotting graphs. The original tables from each experiment are as below :
Temperature/°C 84.0 80.0 75.0 70.0 65.0 60.0 55.0 43.0 40.0
-7
Underpressure,∆P/102Pa
3
Volume/10 m
1.45 1.43 1.41 1.40 1.38 1.36 1.34 1.30 1.28 Table 1 : Data from experiment on Gay-Lussac’s Law
Temperature/°C 70.0 65.0 60.0 55.0 38.7 35.7
-1
Height/10 m
8.3 8.2 8.1 7.9 7.8 7.7 7.4 7.3 7.1
Total Pressure, P/104Pa
-50.0 -82.0 -100 -123 -158 -180 Table 2 : Data from experiment on Amonton’s Law
9.6 9.3 9.1 8.9 8.5 8.3
3.2 Plotted Graphs The graphs plotted explain well on the linear relations between the gas quantities which were tested in the experiment. From the graphs below, we can clearly see that the theories by Gay-Lussac and Amonton are true.
3
8.4
V = (0.0267x10-7) T + 6.0589x10-7
m8.2
7 -
0 8 1 / 7.8 e m7.6 u 7.4 l o V 7.2 7 0
20
40
60
80
100
Temperature/°C Figure 2 : Graph based on Gay-Lussac’s Law experiment
a 9.8 P 4 9.6 0 1 / 9.4 P 9.2 , e r 9 u s 8.8 s e r 8.6 P l 8.4 a t o 8.2 T
P = (0.0345x104) T + (7.0865 x 104)
0
20
40
60
Temperature/°C Figure 3 : Graph based on Amonton’s Law experiment
80
4. Discussions Figure 2 and 3 shows that both the pressure and volume of gas are related to temperature of gas with a linear relationship. In both the graphs, the points are slightly scattered out of the line of best fit indicating that there are errors present in these experiments. Main error was when the cold water was added to the hot water, stirring was not carried out which caused and uneven heat distribution in the water. Another source of error is that the height of mercury globule used is small which caused slightly high percentage of uncertainty.The calculated values of absolute zero in both of these experiments are much different compared to the actual data value which equals to -273°C . This gives about 17% error in experiment 1 and about 25% in experiment 2. Therefore, with a stirrer and using a greater height of mercury globule to measure the volume of gas would definitely increase the precision in the experiments and reduce the errors.
4.1 Sample Calculation Determining the amount of gas used in this experiment: When the temperature of gas, T= 80°C , then the volume of gas, V = 8.2 x 10
-7
3
m.
At that point, the pressure of the gas equals to the sum of atmospheric pressure and pressure due to mercury globule. Hence, the pressure of gas, P = P 0 + hρmerg Where 5
P0 = atmospheric pressure = 1.0 x 10 Pa h = height of mercury globule = 1.2 cm ρmer = density of mercury = 13.6 g cm
-3
g = acceleration due to gravity = 9.81 ms
-2
From above, the pressure of gas, 5
-2
5
P = 1.0 x 10 + (1.2 x 10 ) x (13600) x (9.81) = 1.016 x 10 Pa From,
PV = nRT n = PV / RT 5
-7
n = (1.016 x 10 ) (8.2 x 10 ) / (8.31) (80 +273) -5
n = 2.84 x 10 mole -5
Therefore, the amount of gas used in the experiment is 2.84 x 10 mole .
4.2 Percentage Error Calculation Error calculation in experiment 1 : % Error = l [(-227) - (-273)] / -273 l
% Error = 17 % Error calculation in experiment 2 : % Error = l [(-205) - (-273)] / -273 l
% Error = 25 %
Conclusion In both the experiments, the linear best fit line drawn on the graphs agree with the perfect gas laws where the volume and pressure of gas are directly proportional to the temperature in Kelvin scale. The slight error in the experiment might be caused by some external interference or human error. This confirms that the theories made by both Guy -Lussac and Amonton are very true.
