Introduction
Thepurposeof this lab is to experimentally
determineif dry air follows the idealgasmodel.
Theidealgasmodelstatesthat for anyrealgas(singleor a mixtue), at low densities(the
moleculesdo not interact,or havevery little interactionwith eachother):
pV - nRT
Wherep ([p] : Pa)is the absolutepressure,V \U4: ^') is thevoiumethe gasis confinedto, n is
thenumberof molesin the sample,R is the idealgasconstant(8.31J/molK),andZ([fl : K) is
provenby confining1 mol samplesof
thetemperature.
This modelhasbeenexperimentally
pressures
differentgasesto the samevolumeat the sametemperature.
Themeasured
ofeachgas
pg 508).
werefoundto be approximately
the same(Halliday-Resnick,
In Part 1, we will determineif air followsthe abovemodelby_testing
the relationshipbetween
pressure
andvolumeif n andT archeldconstant.Thatis p c<:, usinga syringehookedup to an
absolutepressuresensor.We makethe assumptions
is constant,andthatno air
thattemperature
is leakingfrom the syringe,sothe numberof molesis alsoconstant.
In Part 2, we attemptto verify the idealrelationshipbetweenpressureandtemperatveif n andV
insulated
areheldconstant.Thatis p x I , usinga sealedcanistersubmerged
in a semi-thermally
the canister
container,waterard ice, andabsolutetemperature
andpressuresensors.
We assume
are
andthewaterarein thermalequilibriumwhenmeasurements
of pressureandtemperature
recorded.
We alsoassumethatthevolumeofthe canisteris constant,andthatno air is leaking,
we can
the
number
of molesremainsconstant.By graphingTemperature
vs. Pressure,
so
in Celsius
experimentally
determinethe idealgasconstantR, andAbsoluteZeromeasured
degrees.
We prediotthatair will follow the idealgasmodel,with somecaveats:
p =! ,we Vedictthat air followsthe idealgasmodelfor certainvaluesof V.As V
Because
p increases,
decreases,
andthe greaterthe densitythe lessaccwatethe idealgasmodelbecomes.
Thereareseveralsourcesof enorIn Part 2 that couldcontradictthe idealgasmodel,they will be
discussed
in the conclusion.
Procedure
Part l
With tubingandquick-release
coupling,we hookedup a syringefilled with 20 mL of air to
anabsolutepressure
sensor.Thepressuresensorwaspluggedinto DataStudio,whichdisplayed
thepressure
measurements.
At20 mL, thepressureinsidethe syringewascloseto atmospheric
pressnre
at 100.5kPa.UsingpZ - nRT-+ (100.5)(20)- 201,0andp =ry -. p -4f,.w"
predictedwhatthepressureshouldbe for a givenvolume.
We decreased
thevolumeto 18mL, andthenin 3 mL increments
until we reached6 mL, taking
pressure
readingseachtime.
Part 2
Usingtubing,quick-release
couplinganda tubing-to-stopper
connector,we hookedup a
metalcanistersealedwith a rubberstopperto the absolutepressuresensor.We thensubmerged
pluggedinto DataStudio,we
thecanisterin waterinsidean insulatedmug.Usinga thermometer
measured
thetemperature
of the water*.Theinitial temperature
of the waterwas57 "C. We
decreased
thetemperature
of the waterin increments
by adding3 smallice cubesat a time,
makingsureto constantlystir with thethermometer,
until we reacheda temperature
of 9.4 "C.
Adding3 cubesat a time yielded13datapairs.
*Thetemperature
we needis thetemperatueinsidethe canister,but because
we cannotmeasure
thatwe makethe assumption
thatthe water,canisterandair in the canisterarein thermal
equilibrium.For thatassumption
to be useful,measurements
must
of pressureandtemperature
betakenonly whenthe readingsdisplayedby DataStudioarechangingby no morethan0.10.
Thetemperature
will level offfirst, but the measurements
shouldnot be recordeduntil the
pressure
hasalsoleveledoff Fromthe idealgaslaw, in this experiment,if Ap = 0 -+ A? : 0.
Data
Part l
Predicted
Actual
Volume(mL) Pressure(kPa) Pressure (kPa) 7o DiIT
20
100.5
100.5
0
-1.164
l8
tlt.7
113
. 15
t2
134
167.5
133.1
0.6716
t66.2
0.7761
9
6
223.3
218.1
2.328',7
335
314.5
6.1194
r
Pr6ssurevs.Volume
t,
Pressurevs.Volums-l(m['1)
350
350
300
300
6 2s0
o
J(, zoo
$ roo
e
i 100
; 1so
; lso
50
50
0
0
0.05
0.1
0.15
Volume-l(mL'1)
Part 2
Temperature
vs. Pressure
IY
I
I
Pressure
109.6
Temperature
(in C")
r07.4
57
52
48.5
106.3
43.6
10E.4
104.8
103.5
38.1
33.1
50
I
40
o
(, 30
102.2
l0t.l
29.3
100.1
22.5
10
99.4
98.6
20
t7.4
0
n.2
12.8
96.7
9.4
25.4
y=3.562x-334.4
R'?= 0.998
o
F
20
o/oDiff
Theoretical
Ideal Css Constant R
AbsoluteZero ('C)
8.31J/nnlK
-273.15
6.74J/nnK
-334.4
18.9
0.2
Data Analvsis
-
To find our experimental
valuefor R.
pv = nlr - r = ({)r + or
*d
(*)
is the slopefrom the Temperaturevs. Pressuregraph,
*--(k)--=(:)(*)
^,
A n d i'fpvM-nMprt o
. Z \ 4atngdmno=L, t 1 *
-
y_M
^^^^ kg
_ v ' u z d Y r ! 6 i_ 0 . 0 2 4 y
-'-- m3
ttPa
And -= --------V;-1bp.
m
z c.a't !-
"''"'
- -i!i!-
- 280.7
r"L
kPa^ 1-000
Pa
(o.oz+)
P= Qa0.7)
+#tK
! = 6.7
*Yx
To find percentdifferences,
percent Dif f erence= (T
\
lrcor e-tical- Actual)
I neoretlcal
/
r 100y0
Theexperimental
valuefor AbsoluteZeroin degreesCelsiusis givenby they-interceptof the .
graph.
vs. Pressure
Temperature
vs. Volume,it is
Basedon our resultsfrom Part.1,andthe linearizedgraphof Pressure
(1.c),
reasonable
to saythatair followsthe idealgasmodel
aslong asthe densityis low. This is
aswe predicted.Furthererroranalysiscanbe foundin the conclusion.
Therearetwo significantsowcesof errorin Part 2: Thevolumeto whichthe air is confinedis
/rol constant.
As thewateris cooled,the canisterwill contract,decreasing
the volume.The
assumptionsmadeaboutthermalequilibrium alsocauseddiscrepanciesin the data. Despite
thesesourcesofenor, our percentenorswerestill muchlowerthanis expectedfor this
experiment.
Furthererroranalysiscanbe foundin the conclusion.
Conclusion
In Part I of this experimentwe useda pressuesensorhookedup to a syringeanddecreased
thevolumeby 3 mL increments
to measure5 differentvaluesfor the corresponding
pressure.
our predictionwasthat air followsthe idealgaslaw, aslong asthe densityof theair is low. our
experimental
resultscloselymatchedourpredictedresults,with our greatestpereenterrorbeing
6.12%,conesponding
to the greatestmeasurement
of pressure.
we speculate
thatthis is dueto
the increase
in density.As thevolumedecreased,
thepercenterrorbetweenpredictedandactual
valuesincreased.
Therefore,the mainsourceoferror in this experimentis the increasein density
thatcorresponds
to the decrease
in volume,causingthe idealgasmodelto be lessaccuate(-/.b).
Theambienttemperature
of the air, assumingthe air in the syringeis in thermalequilibriumwith
theroom,alsoplaysa factor.with thetemperature
sensor,we measured
the temperature
of the
roomto be 296.5K. However,a 3 K discrepancy
betweenour measured
valueundrootemperatueshouldnot be enoughto causesignificanterror.Fromour results,we concludethat
air followstheidealgasmodel.
Usingthis conclusion,\ryewereableto conductPart 2 of theexperiment.By submergrng
a
stoppered
canisterin wateranddecreasing
thetemperature
of thewaterby -5 degreeincrements,
we wereableto collecttemperatueandcorresponding
pressuredatafor the air insidethe
canister.Theassumption
thatthe air insidethe canisteris in thermalequilibriumwith thewater
thatsurrounds
it is a significantsourceoferror. Thewateris alsoin contactwith the air in the
room,whichmeansthatit will be exchanging
energyasheatwith theroom throughoutmostof
theexperiment.
Only whenthetemperature
of the wateris equalto thetemperature
ofthe room
will this not bethe case.
In anattemptto makethis assumption
reasonable,
eachtime we addedice cubeswe waited
until all of theice hadmeltedandthen, waitedfor thetemperatueandpressurereadingfrom
Datastudioto leveloff. Whenneithermeasurement
waschangingby morethan0.10,we took
our readings.we alsostinedthe water-icemixtureconstantly,
to decrease
the likelihoodof
pocketsof waterbeingcooleror warmerthanthe restof themixture.
Thesecondsignificantsourceoferror is the fact thatvolumeof the canisteris not constant
throughoutthe experiment.
As thetemperature
of thewaterdecreases,
so doesthetemperature
of
the canister,causingit to contract.with this decrease
in volume,we expectour experimental
Rvalueto be smallerthanthe theoreticalvalueof 8.31J/molK.This is theresultwe found,with
our experimental
valuebeing6.74JlmolK,with a percentdifferenceof lB.9 %.
We cameacrossan interestingcalculationduringour dataanalysis,which supportstheabove
statement
concerningthe volume.
*-
=
*,r"",r,"ondRspeciytc
o =(*)*r.+
#ft specific=;:
wnere
tP
v
i
(zlo.7)(0n2s1-e.ra+
shouLdbe the tnverseof m.
F
;
tr
M
-- o,o28g!+ -- 0.024 m3 If we assumethenumberof molesin the sampleto be
Recall.
. :n = =p ------g:!!
;.r.
7.2o#
constant,thanthe only factor that causesV/nto deqease,is the decreasein volume asthe
temperaturedecreases.
Therefore,we proposethat in future experiments,a canisterwith a high
fr-valueanda low B-valuebe used.
Despitethesesourcesof error, our experimentalvaluesweremore accuratethan is usually
expectedfor this type of experiment.We found AbsohfieZero to be -334.4K, with a percent
differcnceof -22.4Vo,wfuchis20-30% lessthanexpected.
From both experiments,we concludethat air follows the ideal gasmodel given -ideal
circumstances.
If it werepossibleto diminishthe effectof the conkactingcanisterandincrease
thermalequilibrium betweenthe water andair in the cuister, Part 2 would yield resultswith an
enor < lo %o'
,a'