Lab2 -Air: An Ideal Gas?
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dC
Darwin Constantino
J. McCullough
03/05112
Physics4C
Lab Partners:
Ari Kaplan
Eric Kaneshige
Paul Richter
D. Constantino1
Introduction:
In this lab, we verified the Ideal Gas Law and a.lsodetermined Absolute Zero and the
Universal Gas Constant. The Ideal Gas Law is an equationofa hypotheticalgasthat models
the behaviorof'real' gassesunder different conditions. It also describesthe relationship
betweeneachcondition. Equation [1] showsthe equationof the Ideal Gas Law;p is pressurein
Pascal(Pa),Zis volumein mr, z is the # molesof gas,rRis the ideal
ll] pV - nRZ (rdearcasLaw)
gasconstantin J/mol'K,and?is temperature
in Kelvin (K). This
ideal gasmodel refersto 'ideal' gassesthat have sufficiently low
densities,exert no long rangeforces on eachother and only interact during collisions (elastic).
In this experiment,we are verifying the Ideal Gas Law
(nRr=
constant) using the relationshipbetweenpressureand volume. By
rearrangingthe ideal gas law equation,Equation [2] showsus
PtVt = PzVz
that Pressureis inversely proportionalto Volume as long as nRZ
is kept constant. Theoretically,when volume increases,pressure
will decreaseexponentiallyas in Figure [1]. Therefore,you can
validatethe ideal gaslaw by experimentallyincreasingthe
volume and observingthe effect on pressure.
lZl p - jnAf
In the next part of this lab.we calculatedthe
Absolute Zero temperatureand the Ideal Gas Constant.
Absolute Zero is the theoreticaltemperaturewhere there is no
longer kinetic or thermal energy. It is the lowest possible
temperature;no substancecan be colder. Absolute Zero is
defined as 0 on the Kelvin scaleand -273.15" on the Celsius
scale. Scientistshave yet to fuliy reach absolutezero.
Volume(cm
AbsoiuteZero canbe
usingthe relationshipbetweenpressureandtemp
calculated
Equation[3] showsthat when nR/V is kept constant,
pressure
is directlyproportionalto temp.andwill
yield a lineargraphasin Figure[2]. On this pressure
graph,AbsoluteZerowill be the
vs. temperature
correspondingtemperatureat 0 pressure.
In orderto calculatethe Ideal GasConstant
R, we usethe slopeofthe curve. Equation[4]
illustratesthatR canbe calculateby dividingthe
slopewith n/V andinsteadof calculatingn/V, yort can
usethedensity(p) andmolarmass(M) of air Equation[5].
slope
... -nR
l+l -:-= stope ) ft =---
v
[5] R=
"/v
sLope
Pqtr t
I Mot
tZl p -Tr
(f =.on,t,nt)
("C)
Temperature
- -273.14.C
Figure 2
Theconceptspresented
in this modelrelateto ideal
gasses
andeventhoughthereis no perfectly'ideal' gas,we
canstill usethis modelasa suide.
D . C o n s t a n t i n o2
Equinment:
F
F
F
F
D
DataStudio
AbsolutePressure
Sensor
Temperature
Sensor
Syringe
Tubinp
F Quick-release
coupling
F Metalcanisterwith stopper
) Tubing-to-stopper
connectol
Procedure:
Part 1: Ideal GasLaw - Pressurevs. Volume
a) Usethe idealgasmodelto predictthepressureof air at 5 differentvolumesbelow20 mL
(temperature
constant).Equation[2]
b) Usinga syringe,tubingandan absolutepressuresensorin datastudio,measurean initial
volumeandpresswe- ptvt Initial volumeshouldbe about20mL.
c) Compress
the syringeto eachof the 5 voiumeschosenprior andrecordthe corresponding
pressue. Theseareyour experimental
values.
values.
d) Usea percentdifferenceto calculatethepredictedvalueswith the experimental
e) Plot pressure
vs. volumeto determinewhetheryour datasupportsthe idealgasmodel.
Analyzeandinterpretyour data.
\v.
Part 2: Ideal GasLaw - Pressurevs. Temperature
a) Submerge
a canisterwith air at constantvolumeinto a hot waterbath. Usingan absolute
pressuresensorandtemperature
sensor,recordpressureof theair andthetemperatueof
thewater(whichis ideallythe sametemperatueof theair).
b) With ice, slowlydecrease
thetemperature
of the waterandcarefullyrecordthepressure
andseveralpoint downto -10'C.
andtemperature
graphandapplya iinearfit to getthe
c) Plot yourpointson a pressure
vs. temperature
equationof the line andits slope.
d) Usethis equationto calculateAbsoluteZero(whenpressure: 0)
e) Usethe slopeto calculatethe IdealGasConstant- Equation[5].
f) Usea percentdifferenceto comparethe idealgasconstantandabsolutezerofrom your
measurement
to their acceoted
values.
Data:
Part 1
Table 1: Results
Initial Volume Vt: 20 mL
pr: 101.0kPa
InitialPressure
Volume (mL
Predictions
Experimental o%
dffirence
(kPa)
(kPa)
Pressure
Pressure
18
112.2
111.6
l)
134.7
10
8
5
202.0
252.5
t32.0
tgl.4
232.9
342.8
404.0
0.55%
1.9%
5.0%
7.8%
t5%
D.Constantino
3
Relationship:
Graph1: Pressure/Volume
Predicted
vs.Experimental
Results
450.0
400.0
3s0.0
6' 300.0
9..^^
i zoo.o
o
100.0
50.0
0.0
o
L
2
3
4
5
6
7
8 9 70 77 12
Volume(cm3)
Relationship
Graph2: Pressure/Tempearture
Part 2
. ^. . , ]
ps;r: l.2l Kg/m-
102000
Mu;.:0.0289
kg/mol
100000
v
Table 2: Data
98000
96000
a!
94000
92000
90000
Table 3: Results
Theoretical/Accepted Experimental Percent
Value
Difference
Value
AbsoluteZero
IdealGasConstant
-273.15.C
8.31J/molK
-333.19'C
6.29llmol'K
22.0%
24.304
D.Constantino
4
Data Analysis:
Sample Calculations
Part 1 - predicting pressure
n,V.
p1l4
= n"V" -->D" = -:
V2
(2omL)(ro\.okPa)
li-i-lri-ilr-i-I
--J
llgmL)
'n"'
-
LTL.ZkPA
Part2 calculatingAbsoluteZero
equation:p -263547 +87809 (p:o)
0 - 263547* 87809--+
?"= -333.19'C
Part2 - calculatingIdealGasConstant
(PercentDifferencesin tablesabove)
\-,
Questions
thatmay contributesignificantlyto the
Part1 - Identifythe sourcesof errorin this experiment
percenterror.
In this experiment,
thereweremanypossiblecausesof error. A faulty s1'ringecould've
may
let air escapeandsothepressuresensorwouldreada smallervalue. A quick compression
increase
thetemperature
whichwill thenincreasethepressure.To preventthis,we triedto
because
asyou
increase
thevolumeslowly. Lastly,errorincreases
asvolumedecreases
andthe gasbehavelesslike an idealgas. In a modelfor
compress
the gas,the densityincreases
low-densitygases,decreasing
thevolumewill createmoreenor.
Part1 Interpretyour plotteddata;doesthe dataagreewith the IdealGasModel?
vaiueswereconsistent
At highervolumes,theplotteddatashowsthat our experimental
our vaiuesbecamelessaccurate.This agrees
with the IdealGasModel,but asvolumedecreases,
abovewheregasesbehavelesslike idealgassesastheyarecompressed.
with our hypothesis
Part2 Whatarethemostsignificantsourcesof errorin this experimentandhow do you expect
themto affect your resuits?
Oneimportantsourceof errorwasour approachin measuringthetemperatueof the gas.
We submergedthe canisterinto a water bath and assumedthat the temperatureof the water was
ofthe gas;this maynot be the case.Themetalcanisteris not a perfect
equalto thetemperature
thermalconductor,so the temperaturechangesin the watermay not be the sameasthe
changesin the gas. Energycanalsoescapeinto the surroundings.
temperature
Anothersourceof errorwasreadingthepressuregauge. Our methodrequiredus to wait
to equalizebeforerecordingits value. Theremay be someinaccuracywhen
for thepressure
we shouiduse.
determiningwhichpressure
D.Constantino
5
Discussion/Conclusion
:
In the first part oflab, we were able to validatethe Ideal Gas Law by testing the
gas. We predictedthe
relationshipbetweenpressureand volume on a temperature-constant
pressue valuesat certain volumes using the Ideal Gas Law and then experimentallytestedthose
values. Our resultswere fairly consistentwith the predictedvalues. As Table [1] shows,the
percentdifferencesrange from 0.55% to 15%. We noticed that the error increasesas the gas is
further compressed- Graph [1] illustratesthe deviation as volume decreases.We were able to
explain this using the definition of an ideal gas. An ideai gasis defined as a low-density gas..So
'idea]'. Our model became
as \ /e compressedthe gas,the density increasedand it becameiess
lessaccurateas the gasbecamedenser. However, the trend in our results still validatesthat
pressureis inversely proportionalto volume and the ideal gas1awholds true.
In the secondpart of the lab, we deviseda way to calculateAbsolute Zero and the Ideal
Gas Constantusing the relationshipbetweenpressureand temperature. The ideal gasmodel says
that pressue and temperatureare directly and linearly related. When we testedthis theory by
changingthe temperatureofa containedgas,our results generateda iinear curve - Graph [2].
We then calculatedthe Absolute Zero temperatureand Ideal Gas Constantusing the linear line './
and our resultsin Table [3] showsa22.0Vodifferencein our Absolute Zero value and24.3o/o
differencein our Gas Constantvalue. We were able to deducethat any error camefrom our
method and procedure. However, the generaltrendsin our resultsdo in fact agreewith the
theoriesoresented.