Sample AP Lab

Sealing the Deal with Real and Ideal:
Identifying Gases using the Principles of Real and Ideal Gas Equations
Lab Partners:
Two Students
~ AP Chem, Period 1 ~
Introduction:
This laboratory experiment essentially poses the question of how gases can be identified
when they do not have distinct odors, colors, or behaviors. While solids and liquids have physical
properties, like appearance and melting point, that help identify them, gases do not. Instead,
certain laws and equations have been designed to aid in distinguishing a gas. These include the
Ideal Gas Law, assuming that the Kinetic Molecular Theory is controlling, and van der Waals
equation, assuming that the real gas theory is controlling.
Ideal Gas Law:
PV = nRT
van der Waals equation:
2
(P + nV a2 )(Vnb) = nRT
There is a certain difference between the two equations. When put into practice, the Ideal
Gas Law, under the Kinetic Molecular Theory, presumes that volume and intermolecular forces
of a gas are negligible. However, van der Waals equation, under the real gas theory, presumes
that volume and intermolecular forces of a gas are existent and affect the properties of a gas. In
this experiment, both theories are utilized to find the molar mass and other characteristics of the
gas in a dust off can.
Procedure:
●
MATERIALS & EQUIPMENT
Throughout the experiment, a balance, a pneumatic trough, a eudiometer, a
thermometer, a dust off can [containing 1,1difluoroethane (C2H4F2)], sink water, a ring stand, a
utility clamp, and a graduated cylinder were utilized. The only notable safety precautions were to
be careful with the glass used throughout the experiment and to not inhale a large amount of air
from the dust off can. C2H4F2 can be toxic when one breathes it in directly for an extended period
of time.
SKETCH OF THE COMPLETE APPARATUS:
●
PROCEDURE
The gas identification lab began when the the dust off can was massed. This initial mass
was then recorded*. Next, the red tubing was stably attached to the nozzle. As the mass was
being recorded and tubing was being checked by one group member, the pneumatic trough was
being filled with sink water enough to be as level as possible with the 49.0 mL mark on the
eudiometer when the eudiometer would eventually be placed in the trough. by the other group
member. Then, the eudiometer was set up by both group members, meaning that the 50.00 mL
eudiometer was completely filled with water, was inverted using a group member’s finger, placed
inside the trough filled with water, and attached to a utility clamp which attached to a ring stand in
order to keep the eudiometer steady and vertical. At that point, the eudiometer was checked to
not contain any extra air bubbles by a group member. Next, the end of the red tubing on the dust
off can was placed directly under the opening on the eudiometer underwater. The level on the
nozzle of the dust off can was pressed down on by a group member, and gas began to collect at
the top of the eudiometer. Once the volume of gas in the eudiometer hit about 49.0 mL, the gas
stopped being let out. The tubing was taken off of the can, and the can was remassed. Then, in
order to find a more accurate and exact volume of the gas, the eudiometer was submerged in
the graduated cylinder up to the water line, allowing the pressures on the inside and outside to
equalize. At that point, the number at the water line was recorded. This entire process was then
repeated on a second run. Lastly, the temperature of the water was taken by a thermometer, the
pressure of water at the temperature recorded was found, and the barometric pressure was
found on the internet.
* Whenever procedure states that measurements were taken, they were put on a GoogleDoc.
Results:
●
DATA/TABLES
* We completed two runs of the experiment.
FIRST RUN
Initial Mass of Dust Off Can
133.57 g
Mass of Dust Off Can After Letting out Gas
133.41 g
Total Mass of Gas Let Out
0.1600 g
Exact Volume of Gas Collected
48.80 mL
Temperature of Water
294.0 K (21.0ºC)
Pressure of Water @ 21˚C
18.7 mmHg
Barometric Pressure
766.6 mmHg
Partial Pressure of the Gas
747.9 mmHg
SECOND RUN
Initial Mass of Dust Off Can
145.55 g
Mass of Dust Off Can After Letting out Gas
145.40 g
Total Mass of Gas Let Out
0.1500 g
Exact Volume of Gas Collected
49.10 mL
Temperature of Water
294.0 K (21.0ºC)
Pressure of Water @ 21˚C
18.7 mmHg
Barometric Pressure
766.6 mmHg
Partial Pressure of the Gas
747.9 mmHg
●
OBSERVATIONS
When we released the gas from the dust off can, the gas rose to the top of the eudiometer. When
we transferred the eudiometer to the large graduated cylinder, the pressures on the inside and outside
equalized, and we received an accurate volume of gas for each run.
However, the gas bubbled over the side of the eudiometer about two times per run. Also, a little bit
of water might have been left on the can when we remassed it.
●
FIGURES
* See the labeled and complete apparatus diagram under “MATERIALS & EQUIPMENT.”
DISCUSSION AND PROCESSING:
*Note: All values used in calculations are referenced in the data tables above.*
In order to fully analyze and identify of the gas contained in the dustoff can, it is necessary to
utilize the equations associated with both ideal and real gas to solve for the molar mass of the
substance. To begin, the partial pressure of the gas through Dalton’s Law (subtracting the partial
pressure of the water vapor at its temperature of 21ºC from the barometric pressure) must be
calculated.
Pressure H2O at 21˚C: 18.7 mmHg
Barometric Pressure: 30.18 in. Hg = ( 30.18 in.
)( 25.4 mm
1
1 in. ) = 766.6 mmHg
766.6 mmHg 18.7 mmHg = 747.9 mmHg
After this, calculations can be made for the molar mass for both runs of the experiment based
upon the Ideal Gas Law.
RUN 1:
Molar Mass = mRT
PV
•mmHg
(0.1600g)(62.36 Lmol
•K )(294.0K)
(747.9mmHg)(0.04880L)
Molar Mass = Molar Mass = 80.37 g/mol

RUN 2:
Molar Mass = mRT
PV
•mmHg
(0.1500g)(62.36 Lmol
•K )(294.0K)
(747.9mmHg)(0.04910L)
Molar Mass = Molar Mass = 74.89 g/mol
Next, it is necessary to solve the molar mass for each run through a derivation of van der Waals
equation. This is done in order to acquire a more accurate answer.
EQUATION:
2
(P + nV a2 )(Vnb) = nRT
2
3
PV Pnb + nVa nVab2 nRT = 0
n3( Vab2 ) + n2( Va ) Pnb nRT + PV = 0
*Use calculator to find number of moles at xintercept*

RUN 1:
“a” = 7.201 and “b” = 0.07223
(7.201)
n3((7.201)(0.07223)
) + n2((0.04880 L)
) n(747.9mmHg)(0.07223) n(62.36 L•mmHg
mol•K )(294K) +
(0.04880 L)2
(747.9mmHg)(0.04880L) = 0
n3(10.66) + n2(147.6) n(18387.86) + 36.50 = 0
Value for n from calculator: 0.001985 moles
Molar Mass = mn
0.1600g
Molar Mass = 0.001985 moles
Molar Mass = 80.60 g/mol

RUN 2:
“a” = 7.201 and “b” = 0.07223
(7.201)
n3((7.201)(0.07223)
) + n2((0.04910 L)
) n(747.9mmHg)(0.07223) n(62.36 L•mmHg
mol•K )(294K) +
(0.04910 L)2
(747.9mmHg)(0.04910L) = 0
n3(10.59) + n2(146.7) n(18387.86) + 36.72 = 0
Value for n from calculator: 0.001997 moles
Molar Mass = mn
0.1500g
Molar Mass = 0.001997 moles
Molar Mass = 75.11 g/mol
Using each equation yields slightly different results. However, it can be deduced that van der
Waals equation provides a more accurate answer than the Ideal Gas Law. This is because in
addition to the values involved in the Ideal Gas Law equation, van der Waals equation accounts
for both intermolecular forces and the volume of real gas molecules (in Liters/mol), with
constants “a” and “b,” respectively. In this situation, the real gas values did not deviate far from
the ideal gas values, because the gas wasn’t under a high pressure or low temperature. When
there is a higher pressure, molecules are closer together and undergo more attraction and
repulsion. When there is a lower temperature, there is a lower kinetic energy within gas
molecules and slower movement. Both of these factors cause the intermolecular forces to have
a greater impact in the gas equation, and therefore would cause a value found through the van
der Waals (real gas) equation to deviate farther from a value found through the Ideal Gas Law.
Although this was not the case in this particular experiment, the answer found from van der
Waals equation is slightly more exact than that found using the Ideal Gas Law equation.
With the values for the molar mass of the gas from both runs, the empirical and molecular
formulae can be found, knowing that the gas in the dustoff can consists of 36.3687% carbon,
6.1043% hydrogen, and 57.527% fluorine.
36.3687gC 1 moleC
( 12.01gC ) = 3.028 moleC / 3.028 = 1
1
6.1043gH
1 moleH
( 1.008gH
) = 6.056 moleH / 3.028 = 2
1
57.527gF 1 moleF
( 19.00gF ) = 3.028 moleF / 3.028 = 1
1
Empirical Formula: __CH2F__

RUN 1:
80.37
Ideal Gas Law: 33.026
≈ 2 →
Molecular Formula: __C2H4F2__
80.60
van der Waals Equation: 33.026
≈ 2 → Molecular Formula: __C2H4F2__
RUN 2:
74.89
Ideal Gas Law: 33.026
≈ 2 →
Molecular Formula: __C2H4F2__
75.11
van der Waals Equation: 33.026
≈ 2 →
Molecular Formula: __C2H4F2__
Although the ratio between the molar mass of the gas and the mass of the empirical formula is
approximately 2:1 (shown above), it is by no means exact. This would suggest that there was a
significant percent error. The percent (shown below) provided by the percent error equation
suggests the extent of the inaccuracy in the lab experiment.
alue − Experimental V alue
% error = |Theoretical VTheoretical V
| x 100
alue
RUN 1:
Ideal Gas Law: |66.052 − 80.37
66.052 | x 100
| 0.2168 | x 100
0.2168 x 100 = 21.68 % error
van der Waals Equation: |66.052 − 80.60
66.052 | x 100
| 0.2203 | x 100
0.2203 x 100 = 22.03 % error
RUN 2:
Ideal Gas Law: |66.052 − 74.89
66.052 | x 100
| 0.1338 | x 100
0.1338 x 100 = 13.38 % error
van der Waals Equation: |66.052 − 75.11
66.052 | x 100
| 0.1371 | x 100
0.1371 x 100 = 13.71 % error
If the molar mass were to have been, say, 10% less than expected, there may have been two
experimental sources of error within the experiment. For starters, when the dust off can was
taken out of water, there were still droplets of water on it. These droplets of water, if not wiped
off, would have added to the final mass of the can, causing the total mass of the gas in the
eudiometer to decrease. For example, using the conditions found in Run 1 of the experiment, if
the initial mass of the can was 133.57, and the final mass of the can was found to be 133.46,
and the mass of the residue of water still on the can was actually 0.05 g, then the found mass of
the gas in the eudiometer would really be 133.41 g rather than 133.46 g. (Although this example
isn’t an example of exactly 10% less, it is used to validate the reason.) Here are calculations to
show how this would be detrimental to the molar mass:
IDEAL GAS LAW
Without Water:
With Water:
Molar Mass = mRT
PV
Molar Mass = mRT
PV
•mmHg
(0.1600g)(62.36 Lmol
•K )(294.0K)
(747.9mmHg)(0.04880L)
•mmHg
(0.1100g)(62.36 Lmol
•K )(294.0K)
(747.9mmHg)(0.04880L)
Molar Mass = Molar Mass = Molar Mass = 80.37 g/mol
Molar Mass = 55.26 g/mol
*There would be a similar effect using van der Waals equation.*
^ This shows that with a greater mass, there is a greater molar mass. With a lower mass, there
is a lower molar mass. When water is left on the can after, it therefore makes the mass of gas
smaller than it actually is, according to the equation. A similar idea goes for volume. If the
graduated cylinder wasn’t used to find the exact volume of the gas, then the gas might be
smaller in volume than it actually seems. This can also be looked at through the Ideal Gas Law.
Using a larger volume, a larger denominator would be divided out of the numerator. Therefore,
the molar mass would seem smaller that if the graduated cylinder were used to find a more
exact volume.
Another property of the gas in the dust off can that can be concluded from the given information
is its rootmeansquare speed.
urms = RUN 1:
Ideal Gas Law:
urms = van der Waals Equation:
√
√
3RT
MM
J
3(8.314 mol•K
)(294.0K)
= 302.0 m/s
0.0804 kg/mol
urms = √
J
3(8.314 mol•K
)(294.0K)
= 301.6 m/s
0.0806 kg/mol
RUN 2:
Ideal Gas Law:
urms = van der Waals Equation:
√
J
3(8.314 mol•K
)(294.0K)
= 312.9 m/s
0.0749 kg/mol
urms = √
J
3(8.314 mol•K
)(294.0K)
= 312.5 m/s
0.0751 kg/mol
AIR:
*Chemical compositions found at http://chemistry.about.com/od/chemistryfaqs/f/aircomposition.htm*
Find molar mass of air by adding up the percents (of air composition) of their own molar
masses.
Nitrogen (N2) ~ 78.084% of 28.0134 g/mol = 21.8740
Oxygen (O2) ~ 20.946%of 31.9989 g/mol = 6.7025
Argon (Ar) ~ 0.9340% of 39.9481 g/mol= 0.3731
Carbon Dioxide (CO2) ~ 0.0387% of 44.0096 g/mol = 0.0170
*Other gases are extremely trace.*
21.8740 + 6.7025 + 0.3731 + 0.0170 ≈ 28.9666 g/mol ≈ Molar Mass
*Room temperature was also 21ºC (294K).*
urms = √
J
3(8.314 mol•K
)(294.0K)
= 503.1 m/s
0.0289666 kg/mol
When compared to the average rootmeansquare speed of air, the speed of the gas in the dust
off can is considerably lower than that of air. This can be explained by the fact that the molar
mass of the gas in the dust off can is larger than the molar mass of air. Because this makes the
denominator larger in the equation for the speed of the gas, it ultimately causes the quotient to
be a smaller number than the quotient in the equation for the speed of air.
The kinetic energy of the gas can also be compared with the kinetic energy of air. The water
used in the experiment was measured to be at room temperature, about 21ºC. Therefore, the
temperature of the air was equal to that of the gas. Because kinetic energy is directly related to
temperature, this would suggest that the average kinetic energy of the gas from the dust off can
was the same as the average kinetic energy of the air.
CONCLUSION:
Overall, the purpose of this laboratory experiment was to compel students to identify
gases through the Ideal Gas Law and van der Waals equation. Lab groups individually analyzed
the similarities and differences between using both equations and how accomodating for volume
an intermolecular forces in the real gas theory provides a slightly different, more exact answer
than when using the Kinetic Molecular Theory. The procedure enabled students to meet these
stated objectives because it called students to actively find the measurements necessary in the
real and ideal gas equations. That information could then be applied when discussing values of
molar mass and more for each run.
In this lab, the results for the real values for molar mass didn’t stray far from the ideal
values for molar mass because it wasn’t a high pressure or low temperature situation, as
explained in the discussion portion. Higher pressure would indicate that molecules are nearer to
each other and going through constant attraction and repulsion, and a lower temperature would
stipulate that there is a lower kinetic energy and slower movement. However, these factors did
not play a major role in this experiment, which demonstrates the reason for the closeness
between the real and ideal values. The values calculated for molar mass were utilized all
throughout the lab, ultimately permitting the computation of the empirical and molecular formula
of the gas in the dust off can, the calculation of the percent error in the experiment, as well as the
comparison of the gas’s rootmeansquare speed and kinetic energy to that of air.
Although the endeavor was successful in general, there might have been some
experimental mistakes throughout the process. One notable error in the data was the fact that
the runs came out with about a 20% greater molar mass than expected. This occurrence was
likely due to an observation taken down during the experiment, which noted that gas bubbled
over the lip of the eudiometer about two times per run. This meant that some of the gas was let
out into the water of the trough rather than floating through the opening of the eudiometer,
perhaps because the red tubing jiggles a little bit in the water when the group member that was
holding the dust off can moved their hand. Even though it was only a few bubbles of gas that
didn’t go up the eudiometer, that difference probably affected the molar mass considerably in the
long run. This mistake could have been avoided or fixed simply by holding the can more carefully
and steadily. Also, if the group member saw the gas bubble over the side of the eudiometer, he
or she could have even decided to redo the run. In addition to the escaped gas, the eudiometer
could have been submerged in the graduated cylinder too far over the water line inside. This
could have caused an inaccurate measurement for volume to be read from the eudiometer in the
graduated cylinder, because the pressures on the inside and the outside would not have been
equalized. Ultimately, this imprecision could have affected the values in all of the calculations. To
prevent this, two group members could have checked the water line rather than one.

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