Ross Rybakowicz
Lauren Roy
Justin Pratt, Professor Jessa
CHM 144 A
November 24th 2014
Exploration of Different Gas Relationships
Abstract
The three experiments that were observed in this lab in order to understand gas laws
were: Boyle’s Law, Gay-Lussac’s Law, and Charles’ Law. Boyle’s Law was determined by
adjusting the volume of an enclosed gas sample and recorded the following pressure, all while
the temperature was held constant. Gay-Lussac’s Law was studied by placing an enclosed gas
sample into various baths with different temperatures. The pressure was then recorded at each
point all while volume was being held constant. Charles’ Law was observed changing the
temperature of a closed gas sample then recording the new volume that resulted, all while
keeping the pressure. By completing these three experiment, it was determined that the
relationship between volume and pressure was inverse, the relationship between pressure and
temperature was direct, and the relationship between volume and temperature was direct.
Introduction
In order for the human population to survive on earth, gases are needed. Our atmosphere
is full of vital gases such as Oxygen (O2), Carbon dioxide (CO2), Nitrogen (N2) etc., without
gases, we could not survive. It is crucial to understand this form of matter, as it is so important to
our daily life. There are four variables that gases possess to help develop the knowledge of their
physical attributes. The four variables are pressure, volume, temperature, and the number of
moles in the specific substance. These four variables then combine to form the ideal gas law,
which is described as PV=nRT; pressure being P, volume being V, the number of moles being
n, the gas constant being R, and temperature being T. This equation provides information on a
gas’ ideal state of existence. The standard conditions of a gas would be at one atmosphere (atm)
of pressure, 22.4L of volume, one mole of the specific gas, the temperature being 273.15K, and
𝑎𝑡𝑚 × 𝐿
the gas constant always being equal to 0.0821 𝑚𝑜𝑙 × 𝑘.
Relationships of variables are able to be experimentally determined. By isolating two
variables while holding the other two constant, the relationship between them can be calculated
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by altering one of them and seeing how the other is affected. In this experiment, two variables
were tested at a time holding moles of gas, due to the enclosed air sample, and the third variable
constant. One of the variables being tested was manipulated and the other was then observed to
experimentally determine the relationship between the two.
Before this experiment occurred, three hypotheses were formed in order to predict the
outcomes of the relationships of gases. For the first experiment, the relationship between
pressure and volume, or Boyle’s Law, was observed. The hypothesis was that pressure and
volume were inversely related meaning that as pressure increased, volume decreased, or vice
versa. Boyle’s Law relates to the equation: P1V1 = P2V2. This was derived from P=
𝐧𝐑𝐓
𝐕
, since the
gas constant is always the same, temperature, and number of moles were held constant, this
equation was then able to be formed. Pressure and Volume are inversely related in this
experiment meaning that what happened to the first variable, the opposite happened to the other.
In order to test this, a syringe was used to change the amount of volume in the container, thus
affecting the amount of pressure at a constant temperature.
For the second experiment, Gay-Lussac’s Law, or the relationship between pressure and
temperature were examined. The hypothesis for this relationship was that pressure and
temperature are directly related meaning that as the pressure increased or decreased, the
temperature did as well. Gay-Lussac’s Law refers to the equation P1/T1 = P2/T2, this again was
derived from the equation P=
𝐧𝐑𝐓
𝐕
. Since the gas constant is always the same, volume and the
number of moles is held constant, the equation was able to be determined experimentally. To test
this relationship, an enclosed gas sample was placed into a beaker of water with varying
temperature; the pressure was documented due to the change in temperature.
The third and final experiment looked at Charles’ Law, or the relationship between
volume and temperature. The hypothesis for this relationship was that temperature and volume
are directly related, meaning that as one variable increased or decreased, the other did the same.
Charles’ Law referred to the relationship V1T1 = V2T2, which again was derived from the ideal
gas law PV=nRT; since the gas constant was the same, the number of moles and pressure were
held constant, the relationship was able to be experimentally determined. To test this, an
enclosed gas sample was submerged in a cooler of varying water temperatures, the pressure was
allowed to equalize and the new volume was then recorded, thus determining the relationship.
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Methods
Experiment I: Relationship between Pressure and Volume (Boyle’s Law)
An apparatus to test this relationship was constructed with a ring stand, a clamp handle,
clamp foot, clamp a syringe holder, plunger, pressure sensor, and a 60 mL syringe. The
temperature was held constant at room temperature. To collect the data, a LabQuest was used to
track the pressure inside the enclosed sample. The syringe was initially placed at 55mL. A table
was set up in the lab manual to record our observations. The volume was decreased in 5mL
increments by tightening the handle to push down the plunger. For each new volume the pressure
was recorded. Seven individual measurements were noted and used for calculations.
Experiment 1 Calculations
LoggerPro was used to determine this relationship of pressure and volume. Pressure,
being the dependent variable, was plotted on the Y-axis while volume, being the independent
variable, was plotted on the X-axis. A positive linear slope meant that the two variables were
directly related while a negative slope with a curve meant that the two variables inversely
related. Once the correct n value was determined and a linear slope was determined, the linear fit
was analyzed displayed the equation of the line in P=m(V)n format. The proportionality
constant, k=P/(V)n was calculated for each of the data pairs acquired throughout the
experimental trials. The average of the k (proportionality constant) values was equivalent to m
(the slope of the line). The standard deviation and the confidence interval at 95% were calculated
as well.
Experiment II: Relationship between Pressure and Temperature (Gay-Lussac’s Law)
To test this relationship, an apparatus was used with a LabQuest device, temperature
probe, pressure sensor, breaker, and a 25mL flask. The 25mL flask was sealed with a rubber
stopper to assure the constant value of moles in the sample, which was then attached to a
pressure sensor. The initial bath that the sample was placed in was 273K, which was made by
cold water and crushed ice provided in the laboratory. Four additional baths of temperatures
increasing in 10K increments were created for the sample of gas in which to be placed, making
sure the temperature of the entire experiment varied between 40-50K. Each time the sample was
submerged completely into the bath, the pressure was recorded and writing down in a lab
manual.
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Experiment II Calculations
A graph was established in LoggerPro, displaying pressure, the dependent variable, on
the Y-axis, and temperature, the independent variable, on the X-axis. Once the correct n value
was determined, the linear fit was calculated showing the equation in P=m(T)n format. The
proportionality constant was found for each individual pair of data points using k=P/(T)n. The
average k value was equivalent to the m value in equation of the line. The standard deviation and
confidence interval at 95% were also calculated.
Experiment III: Relationship between Volume and Temperature (Charles’ Law)
In this experiment, an apparatus was put together with a temperature probe, clamp, ring
stand, a cooler, pressure sensor, bottle, stopper, stopcock, syringe, a ring stand and the LabQuest.
An ice bath was made in the cooler for the initial trial. The utility clamp was used to place the
temperature probe at the top of the cooler ensuring that the enclosed gas sample was fully
submerged in the bath. Once the gas sample was submerged, the pressure was allowed to
stabilize, which was recorded in the lab manual as the initial pressure. The volume was set to
read 0.0mL. After the initial readings were documented, four additional baths with temperature
increases of 10K, making sure there was a range between 40-50K, the syringe with the gas
sample was submerged. The plunger was then pushed down until the pressure was the same as
the initial pressure. A table was set up in the lab manual documenting each data pair of
temperature and volume of the gas. Vbottle was acquired by filling up the bottle completely with
water, then pouring the contents of the bottle into a graduated cylinder and recording the volume.
Experiment III Calculations
The total volume used in this experiment (Vtotal) was found by the equation:
Vtotal = Vbottle + Vsyringe + Vtubing
A graph was created on LoggerPro placing Vtotal, the dependent variable on the Y-axis, and
temperature, the independent variable, on the X-axis. The correct n value was found, following
by the equation of the line in Vtotal=m(T)n format using the linear fit. The proportionality
constant for each set of data points was found using the equation k=Vtotal/(T)n. The average of
the k values was equivalent to the m value in the equation of the line. The standard deviation and
confidence interval at the 95% level were also calculated.
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Results
Experiment I: Relationship between Pressure and Volume (Boyle’s Law)
Table 1-1 For Graph 1
Volume
.055
.050
.045
.040
.035
.030
.025
(L)
Pressure .9285
1.0090
1.1028
1.2270
1.3915
1.6147
1.8925
(atm)
Table 1-1 displays each volume and pressure data point for each specific trial from the first
experiment.
Graph 1. Pressure and Volume Relationship
Graph 1 shows the relationship between pressure and volume while the temperature was held
constant. This was first a curve with a negative slope, which indicated that it was inversely
related. The graph had to be manipulated by making the n value (-1) in order to get the correct
linear fit and equation of the line. The correlation of the line was .9998, the Y-intercept was
.1169, and the m value (slope) of the line was .04457. This was checked using the derived
equation from the data points P= .04457(V)-1.
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Table 1-2, Calculations for Experiment 1
Trial
1
2
3
4
5
6
7
k-value
.0511
.0505
.0496
.0491
.0487
.0484
.0473
Average k-value:
Standard Deviation:
Confidence Interval at 95%:
𝒂𝒕𝒎
.0492
𝑳
1.3×10-3
.0492 ± 1.2×10-3
Table 1-2 shows each k-value, average k-value, standard deviation, and confidence interval at
95% calculated.
These calculations depict the average k-value, standard deviation, and confidence interval at
95%. The m value (slope) was determined from the graph being .04457 and from the average kvalue being .0492. The m value from the graph does not fall into the range of appropriate kvalues (.0504-.0480) at the 95% confidence interval. It would fit if the confidence interval was
changed to a lower percentage.
Experiment II: Relationship between Pressure and Temperature (Gay-Lussac’s Law)
Table 2-1 for Graph 2
Pressure
.9285
.9685
.9923
1.0240
1.0533
(atm)
Temperature 276.5
287.8
296.2
306.9
318.2
(K)
Table 2-1 shows each data point that was recorded from each specific trial in the second
experiment.
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Graph 2. Pressure and Temperature Relationship
Graph 2 illustrates the relationship between Temperature and Pressure while volume was held
constant. When this graph was first plotted, the point made a straight line with a positive slope
indicated the two variables were directly related. The n value was determined to be (1) since they
were directly related. The correlation of this graph was .9982, the Y-intercept was .1091, and the
m value was 2.976 × 10-3. This was checked with the derived equation being P=.002976(T).
Table 2-2 Calculations
Trial
k-value
1
.003358
Average k-value:
2
.003365
3
.003350
4
.003337
.003344
Standard Deviation:
2.2 ×10-5
Confidence Interval at 95% level:
.003344 ± 2.7 × 10-5
5
.003310
Table 2-2 shows the calculated values for each k-value, the average k-value, standard deviation,
and confidence interval at 95%.
These calculations show the k-values, the average of those values, the standard deviation, and the
confidence interval at 95%. The m value was determined on the graph to be .002976 and through
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the average k-value, which was .003344. The m value from the graph does not fall into the
appropriate range (.003371-.003317) of the 95% confidence interval. If the percentage were to be
lowered then the slope might fit.
Experiment 3: Relationship between Temperature and Volume
Table 3-1 for Graph 3
Volumetotal
.0759
.0767
.0789
(L)
Temperature
279.0
290.2
300.9
(K)
Table 3-1 shows each individual volume and temperature data point
.0809
.0837
311.4
321.4
Graph 3 Volume and Temperature
Graph 3 illustrates the relationship between temperature and volume using the data points from
experiment 3.
Graph 3 is the relationship between temperature and volume while pressure was held constant.
When this was first graphed, it had a positive linear slope indicating a direct relationship
meaning as one of the variables increased or decreased, the other variable did the same. The
correlation was .9818, the Y-intercept was .02329, and the m value (slope of the line) was
1.861 ×10-4.
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Table 3-2 Calculations
Trial
1
2
3
4
5
k-value
2.72 ×10-4
2.64 ×10-4
2.62 ×10-4
2.60 ×10-4
2.60 ×10-4
Average k-value:
2.64 ×10-4
Standard Deviation:
5.0 ×10-6
Confidence Interval at 95%:
2.64 ×10-4 ± 6.1 ×10-6
Table 3-2 shows each calculated k-value, the average k-value, the standard deviation, and the
confidence interval at 95%.
This table shows all of the calculated values for Experiment 3. The m value was determined
from the graph as 1.861 ×10-4, however the average k-value was determined to be 2.64 ×10-4.
The m value from the graph does not fit into the range of appropriate numbers from the 95%
confidence interval, which were 2.70 ×10-4 to 2.58 ×10-4. If the percentage for the confidence
interval were lowered then the m value from the graph would have fit.
Discussion
For the first experiment regarding pressure and volume, the hypothesis was that these two
variables are inversely related meaning that as one variable increased or decreased, the other did
the opposite. This hypothesis, known as Boyle’s Law, was supported due to the calculations. The
experiment displayed correct results to show the inverse relationship. A negative curved slope
was formed on the pressure and volume initial graph and the n value was determined to be (-1).
The graph was then flipped to create a proper linear graph to attain the equation of the line.
The second experiment pertained to pressure and temperature; the hypothesis was that
these two variables were directly related meaning that if one increased or decreased, the other did
the same. This hypothesis, derived from Gay-Lussac’s Law, was support from multiple
calculations from the experiment. The data points collected created a positive line graph the first
time it was plotted indicating a direct relationship. The n value was determined to be (1) since
the graph was already linear.
The third experiment was observing the relationship between volume and temperature;
the hypothesis for this was that these two variables are directly related. This hypothesis was
derived from Charles’ Law, was supported by the data collected and the results achieved. Once
the data points were graphed, it displayed a straight line with a positive slope indicating a direct
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relationship. Therefore, the n value was determined to be (1) since it was initially a positive
linear graph.
There were numerous areas in this experiment where an error could have occurred and
skewed the data that was collected. A great source of error could have been the change in
temperature for experiments two and three. Since the temperature of the water needed to
stabilize, the temperature could have been recorded before the actual temperature was reached.
Since the room temperature was much different than the water in the cooler that the experiments
were been done in, the water was either always cooling down or heating up slightly. If this
incorrect temperature were taken down, it would create a chain reaction of incorrect data,
throwing off the other variable, which would then cause an inaccurate graph to be created. Since
the graph would have been inaccurate, the line of best would be created incorrectly leading to
very inaccurate calculations. Since the temperature was supposed to differ 10K each trial in those
two experiments and there was suppose to be an overall difference of 40-50K, the change in
temperature could greatly affect the ending results. Another outlet of error could be in the third
experiment when observing Charles’ Law. In this experiment, the plunger was required to be
adjusted to maintain the original pressure. If the original pressure were not reached in the
specific trials then data would be incorrect. If the pressure for this experiment was not held
constant, then the data would be inaccurate, potentially causing the experiment to not support
Charles’ Law. As well as the other experiments, if one of the variables was not help constant that
was suppose to be, the data would be skewed due to a third variable altering the effect of one of
the variables being tested on the other.
Conclusion
This lab has given me a large spectrum of information. From the beginning of this lab, we
were asked to create hypotheses about the three experiments that described the relationships
between two variables. This taught me the skill of inferring because I had to predict the
relationships between the variables based on the equation PV=nRT. The lab manual came in
handy when I had to create these hypotheses and it made me feel much more confident in my
abilities to predict and infer. This also provided an incentive to accomplish the lab accurately in
order to see if my hypotheses were correct.
Another major insight of information was the three gas laws, Charles’ Law, Gay-Lussac’s
Law, and Boyle’s Law. Rather than just reading about these laws and concepts, I was able to test
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them experimentally and accumulate my own understandings of how they worked. Experiencing
a direct and inversely related relationship, in my opinion, is much better than reading about them
in a lab manual. Watching three variables change and seeing how they affected the other variable
in the experiment helped me understand the relationships very effectively.
References
Novak, Michael. "Chapter 11." General Chemistry Laboratory Manual. By Yasmin
Jessa. N.p.: n.p., n.d. 127-36. Print.
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