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Nicole Christian
Hanna Chouinard
Maia Popova
Professor Jessa
Chemistry 144 D
4 December 2014
Testing the Physical Behaviors of Ideal Gases
Abstract:
The objective of this lab was to develop and test hypotheses involving the
pair-wise relationships of volume, temperature, and pressure. The first experiment
compressed gas volume to see how it affected the pressure. The second experiment
changed the temperature of the water around a gas to see how it affected the
pressure. The third experiment changed the temperature of the water to see how it
affected the volume. The results of these experiments were that as the volume
decreased the pressure increased, as the temperature increased the pressure
increased, and as the temperature increased the volume increased. From this it can
be concluded that volume and pressure have an inverse relationship, volume and
temperature have a directly proportional relationship, and pressure and
temperature have a directly proportional relationship.
Introduction:
For this lab, it’s crucial to understand some key concepts before attempting
it. Since this lab centers on gases, the background concepts include some laws about
gases. The physical behavior of a gas is determined by the four variables pressure
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(P), volume (V), temperature (T), and the number of moles (n). The difference with
an ideal gas is that all of these variables are interdependent, which means that one
variable can be found by measuring the other three variables. The relationships
between these variables are defined by Boyle’s, Charles’, and Avogadro’s laws.
(Silberberg, 2012) Boyle’s law states that at constant temperature, the volume
occupied by a fixed amount of gas is inversely proportional to the applied external
pressure. (Silberberg, 2012) Charles’ law states that at constant pressure, the
volume occupied by a fixed amount of gas is directly proportional to its absolute
Kelvin temperature. (Silberberg, 2012) Another relationship based on Charles’ and
Boyle’s laws is Gay-Lussac’s law, which states that at constant volume, the pressure
exerted by a fixed amount of gas is directly proportional to the absolute
temperature. (Silberberg, 2012) Avogadro’s law states that at fixed temperature and
pressure, equal volumes of any ideal gas contain equal numbers (moles) of particles.
(Silberberg, 2012) By taking into account all of these relationships, the ideal gas law
can be obtained: PV=nRT. Where P stands for pressure, V stands for volume, n
stands for the number of moles, T stands for temperature, and R stands for the
universal gas constant. The standard temperature of a gas is 273.15 K and the
standard pressure of a gas is 1 atm and the volume of 1 mole of an ideal gas within
these parameters is 22.4 liters, and if these are plugged into the ideal gas equation, R
can be calculated.
The scientific objectives of this experiment are to learn how to perform
simple gas phase experiments involving the measurement of volume, temperature,
and pressure, to develop hypotheses about the pair-wise relationships of three
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variables in the ideal gas law, and to experimentally test those hypotheses. The
overall purpose of this experiment is to conduct a series of experiments that will
examine the relationship between two of the four variables in the ideal gas law
while the other two are held constant.
For each of the 3 experiments done, and hypothesis was formed. For
experiment one, the hypothesis was that as pressure increases, volume decreases.
This was made based upon the ideal gas law proportion between pressure and
volume of P1V1=P2V2, assuming that temperature and moles are constant. The
reasoning behind this hypothesis was backed up with Boyle’s law that states that
volume and pressure are inversely proportional. The experimental method used to
test the first hypothesis is to compress the volume of the syringe by pushing down
the clamp and recording the pressure by the pressure sensor that is connected to it.
For experiment 2 the hypothesis was that as pressure increases, temperature
increases. This was made based upon the ideal gas law proportion between
pressure and temperature of P1/T1=P2/T2, assuming that volume is constant. The
reasoning behind this hypothesis was backed up with Gay-Lussac’s law that states
that pressure and temperature are directly proportional. The experimental method
used to test the second hypothesis is to place a flask filled with sealed air in a
container of water and to change the temperature of this water to record the
pressure changes of the flask using the pressure sensor that is connected to it.
For experiment 3 the hypothesis was that as volume increases, temperature
increases. This was made based upon the ideal gas law proportion between
pressure and temperature of V1/T1=V2/T2, assuming that pressure is constant. The
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reasoning behind this hypothesis was backed up with Charles’ law that states that
volume and temperature are directly proportional. The experimental method used
to test the third hypothesis is to place a bottle filled with air and attached to a
pressure sensor within an ice bath. Then slowly heat up the water by adding hot
water and move the syringe to keep the pressure constant as recorded by the
pressure sensor and record the volume.
Methods:
Experiment 1:
For this experiment it is necessary to construct the syringe apparatus. To
construct this, a 60 ml syringe will need to be clamped to a stand, and the end of it
will need to be connected to a pressure sensor. A second clamp will be placed on the
top of the plunger so the syringe can be compressed. The syringe will need to have a
measured volume of air of 55 ml, use the handle to keep the syringe within this
range. Connect the gas pressure sensor to the LabQuest instrument and record the
initial volume and pressure of the syringe. Adjust the volume of the syringe by
turning the clamp handle attached to the plunger. Decrease the volume by 5 ml each
time for a total of 7 measurements and record the pressure at each time.
Experiment 2:
For this experiment it is necessary to construct an apparatus. To construct
this, put a 25 mL Erlenmeyer flask that is sealed with a one-holed rubber stopper.
Then fill up a 400 mL beaker with ice water that is approximately 273 K. Place the
flask and temperature probe in this beaker and connect the flask to the pressure
sensor after the flask has been submerged in the ice-water for 2 minutes. When the
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pressure has stabilized, record the pressure and temperature. Change the
temperature of the water bath by adding hot water. Create 4 more water baths that
vary in temperature by about 10 K. Record the pressure of each bath and make sure
that the temperature has a range of 40-50 K.
Experiment 3:
For this experiment it is necessary to construct an apparatus. To construct
this, put a rubber stopper into a bottle and place a tip of a completely depressed
syringe into one of the holes of the rubber stopper and a tube to the other hole.
Secure the syringe with a utility clamp. Make an ice-water bath with the cooler with
a uniform temperature. Adjust the utility clamp so the bottle is completely
submerged in the water, and the syringe is mostly submerged up to the 15ml mark.
After the bottle and syringe have been in the water for 2 minutes, connect the tube
to the pressure sensor and insert the temperature probe. When the pressure has
stabilized, record the pressure and volume of the gas in the notebook. Vary the
temperature of the water bath by adding hot water to create four additional water
baths that differ from each other by 10 K, make sure that the temperature has a
range of 40-50 K. With the apparatus submerged in the water bath, use the plunger
to adjust the pressure to within 0.001 of the initial temperature, and record the
temperature and volume. Do this for all four additional trials. Find the total volume
of the bottle by filling the bottle to the brim with tap water and re-inserting the
rubber stopper. Then remove the rubber stopper and pour the water into a 100 ml
graduated cylinder and record this volume.
Calculations:
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For the data in experiment 1, plot the data to make a graph using the
equation y=mx+b. Then from this find the proportionality constant (k) using the
equation K=P/(V^n). To make the linear regression line on the graph positive, it is
necessary to convert the n values to n^-1 before plugging them into the K=P/(V^n)
equation. The equation that describes the relationship between the dependent and
independent variables that has been modified for this graph is m=P/(V^n). Then the
mean of the K values was calculated using the equation E(xi)/n. The standard
deviation was also calculated using [Ed^2/n-1]^1/2. After all of these calculations
were done, the t-value needed to be calculated using the equation t-1, in order to use
the equation CI=xm +- t*sm. This equation was used in order to give a range for the
mean to fall into, in order to make sure the mean fell within the 95% confidence
level.
For the data in experiment 2, plot the data to make a graph using the
equation y=mx+b. Then from this find the proportionality constant (K) using the
equation K=P/(T^n). The equation that describes the relationship between the
dependent and independent variables that has been modified for this graph is
m=P/(T^n). Then the mean of the K values and the standard deviation were
calculated. Then the t-value was calculated in order to plug it into the confidence
interval equation.
For the data in experiment 3, plot the data to make a graph using the
equation y=mx+b. Find the total volume in the bottle using the equation
Vtotal=Vbottle+ Vsyringe+ Vtubing. Then from this find the proportionality constant
(K) using the equation K=Vtotal/(T^n). The equation that describes the relationship
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between the dependent and independent variables that has been modified for this
graph is m=Vtotal/(T^n). Then the mean of the K values and the standard deviation
were calculated. Then the t-value was calculated in order to plug it into the
confidence interval equation.
To form the hypotheses, use the ideal gas law equation PV=nRT.
Results:
Experiment 1:
Figure 1: The Relationship between Volume and Pressure at Constant Temperature
Figure 1 shows that at a constant temperature, volume and pressure share an
indirectly proportional relationship. Meaning, that as volume increases, pressure
decreases, and vice versa. The reason that this graph shows a positive linear regression is
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that the n value was changed to -1. The volume is in L units, and the pressure is in atm
units.
The slope of this graph is 0.04187, and it does not fall into the 95% confidence
interval of K. The slope of the graph is 0.0031% off of the proper range.
The equation that verifies this relationship between volume and pressure for this
graph is m=P/(V^n).
Trials
K
Initial
0.0546
1
0.0540
2
0.0538
3
0.0535
4
0.0529
5
0.0532
6
0.0524
7
0.0447
Average
0.0524
Standard
deviation
0.00317915
Confidence
Interval 95%
0.04490.0599
Table1: Calculations from data collected from Experiment 1
Table 1 shows the calculated proportionality constant (K) for each trial. The
average of these K values is shown in the third column, along with the Standard deviation
in the fourth column. In the fifth column, the confidence interval is given, and it is shown
that the average of the K values falls within that range.
Experiment 2:
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Figure 2: The relationship between temperature and pressure at constant volume.
Figure 2 shows that at constant volume, temperature and pressure share a directly
proportional relationship. Meaning, that as temperature increases so does pressure, and
vice versa. Temperature is in Kelvin units, and Pressure is in atm units.
The equation that verifies the relationship between temperature and pressure for
this graph is m=P/T^n.
The slope of this graph is 0.003223, it does not fall within the 95% confidence
interval range for K. The slope is 0.0028% off.
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Trials
K
Average
Initial
-0.000259
-0.0000224
1
-0.000132
2
-0.000000339
3
0.0000908
4
0.000188
Standard
Deviation
0.000177
Confidence
Interval 95%
-0.0005150.000470
Table 2: Calculations from data collected in experiment 2
Table 2 shows the calculated proportionality constant (K) for each trial. The
Average of these K values is shown in the third column, along with the Standard
deviation in the fourth column. In the fifth column, the confidence interval is shown, and
it is shown that the average of the K values falls within that range.
Experiment 3:
Figure 3: The relationship between Temperature and Volume at constant pressure.
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Figure 3 shows that at constant pressure, temperature and volume share a directly
proportional relationship. Meaning, that as temperature increases so does volume, and
vice versa. The temperature units are K and the volume units are L.
The equation that verifies the relationship between temperature and volume for
this graph is m=(T^n).
The slope of this graph is 0.0002422. This value does fall within the 95%
confidence interval range for K.
Trials
K
Average
Initial
0.0028
0.00028
1
0.00028
2
0.00028
3
0.00027
4
0.00028
Standard
Deviation
4.47x10^-6
Confidence
Interval 95%
0.000270.00029
Table 3: Calculations from data collected from Experiment 3
Table 3 shows the calculated proportionality constant (K) for each trial. The
Average of these K values is shown in the third column, along with the Standard
deviation in the fourth column. In the fifth column, the confidence interval is shown, and
it is shown that the average of the K values falls within that range.
Discussion:
In experiment 1, prior to the conversion of n to n^-1, the graph was negative. This
means that there is an inverse relationship between volume and pressure. This data is
supported by Boyle’s law that states that as volume increases, the pressure decreases.
This makes sense because as the volume increases it gives the gas particles more room to
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move around so they aren’t so pressed for space and banging on the walls of the container
and increasing the pressure. The graph reflected this, but in order to get a positive linear
regression line, it had to be inversed, changing n to n^-1. The slope of the graph was
0.0031% off of the 95% confidence interval range of K because the intercepts from the
graphical analysis were not exactly zero. This would have put the slope of the graph
slightly off its actual value, which would explain why it was slightly off of the confidence
interval. Human error also could have been responsible for the less than accurate data, for
example the plunger could have been pushed down to the wrong line on the syringe,
causing an error in data.
In Experiment 2, the graph shows a positive regression line. This means that the
relationship between temperature and pressure is directly proportional. This data is
backed up by the Gay-Lussac law that states that as temperature increases so will
pressure increase. This makes sense because higher temperatures make gas particles
moves faster, and the faster a particle moves, the harder it will hit the side of the
container that increases the pressure. The slope of the graph was 0.0028% off of the 95%
confidence interval range of K because the intercepts from the graphical analysis were
not exactly zero. This would have put the slope of the graph slightly off its actual value,
which would explain why it was slightly off of the confidence interval. Human error also
could have been responsible for the less than accurate data, for example the apparatus
could have not been sufficiently sealed, letting air escape.
In Experiment 3, the graph shows a positive regression line. This means that the
relationship between temperature and volume is directly proportional. This data is backed
up by the Charles’ law that states that as temperature increases so will volume increase.
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This makes sense because as volume decreases it gives the gas particles less room to
move around, and less movement makes their temperature decrease. The slope of the
graph was within the 95% confidence interval range of K. This means that the slope of
the graph and the proportionality constant were similar to the 95 percentile. This could be
because minimal human errors were committed within this experiment, to allow for the
most accurate results.
The experimental results do support the hypotheses that were summarized in the
introduction. Each graph reflected the trend listed by each hypothesis. For experiment 1,
the original regression showed the inverse relationship between volume and pressure
outlined in the first hypothesis. For experiment 2, the graph shows the positive, directly
proportional relationship between pressure and temperature outlined in the second
hypothesis. For experiment 3, the graph shows the positive, directly proportional
relationship between volume and temperature outlined in the third hypothesis.
Conclusion:
From completing this experiment, I have learned the fundamental behaviors of
gases, and how to think logically about how best to complete a task. From each of the
three experiments, I observed how the gases reacted to the multiple situations they were
put in, and I have committed it to memory. As pressure increases temperature increases
and volume decreases. As Volume increases temperature increases and pressure
decreases. And as temperature increases both volume and pressure increase. This
experiment also taught me to think logically and quickly, since there was limited stations
for people to work at, I could not afford to waste time thinking of what to do since there
was a time limit for each station, so it was very important for me to work efficiently.
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With the ice-water baths we had to change the temperature in order to record the data. I
chose to add hot water instead of cold water, because it would take so much longer to
make the water colder rather than warmer. This decision helped my partner and I to finish
on time. From the experience of writing the hypotheses and performing the experiments,
I learned that doing some background research really helps when going into an unknown.
Since I had done some background research on my hypotheses before making them, I
knew better what the behavior of gases were and because of this my hypotheses were
correct. Having correct hypotheses was an amazing help because it prepared me for what
data I should be collecting, and let me know what to expect.
References:
Silberberg, Martin S. Chemistry: The Molecular Nature of Matter and Change,
7e.; McGraw-Hill: New York, 2012.
Jessa, Yasmin. General Chemistry: Laboratory Manual.; Hayden-McNeil: Plymouth,
2014.