Matthew Neves
3-5-20\2
Physics4C Lab
Mccullough
Lab2: Air, An ldeal Gas?
Introduction:
The objective of this lab was to examine how the Ideal Gas Law applies to real
physicalexperiments.Usingthe Ideal GasLaw, we were able to find absolutezero
and the universalgasconstant.But first ofl an ideal gasis a gasthat is composedof
a set of randomly moving non-interactingpoint particles.The Ideal GasLaw was
first statedby EmileClapeyronin 1834 as a combinationof Boyle'sLaw and Charles'
Law It provides a good approximationto the behavior of many gasesunder many
conditions.The Ideal GasLaw is given by the equation:
pV = nRT
Where: p = pressure(Pa)
V = volume (m3)
n = numberof moles(mol)
R = UniversalGasConstant
T = temperature(K)
The universal gas constant (R), which is equivalentto the Boltzmannconstantbut
expressedin units of enerry per temperature increment per mole, has a value of
8.31 J/mol.K The second part of this experiment involved finding the value of
absolutezero. Absolute zero is the temperature in which the pressureis zero and
the thermal energr of matter vanishes.Absolutezero has a value of 0 degreesKelvin
or -273.L5oC.This experimentincorporatedthe ideal gaslaw, the ideal gasconstant
aswell as absolutezero to help further our knowledgeofair asan ideal gas.
L"'
Procedure:
PartL: IdealGasLaw- Pressure
vs.Volume
The goal of Part 1 was to veri8/ the ideal gas dependenceof the pressureon the
volume. We used a syringe,tubing and a DataStudioabsolute pressuresensor to
measurethe pressureof the air inside the syringe.We took the baselinepressureof
the air inside the syringeat the initial volume of 20 mL. We then proceededto take
the pressure of the air at 5 different volumes. Prior to aking the data using
Datastudio,we predictedthe pressureat every volume.We madeour predictionsby
looking at the ideal gaslaw, pV = nRT.But in this case,pV = constant,thereforep c ;
so we could predict the pressureby pluggingin the ratio of initial volume over the
measuredvolume multiplied by the initial pressure.After taking the pressureat the
5 different points,we plotted the graph of Pressurevs. Volume.We then examined
the graph and interpretedthe data.
Part 2: Ideal GasLaw - Pressurevs.Temperature
The goal of Part 2 was to determine the ideal gas constant and the centigrade
temperatureof absolutezero using the ideal gas model.We used a canisterof air, a
water bath and two sensors:absolutepressuresensorand temperaturesensor.We
put warm water in to a mug where we then placedthe air canister,pressuresensor
and thermometer.We then begantaking valuesofthe pressureand temperatureas
the temperature of the water decreasedas we added ice to the water. We took I
points of temperature and pressure.We then plotted the graph of Pressurevs.
Temperatureand applieda linear fit to get the equationof the line that represented
our values.From the equation of the line, we could solve for the value of absolute
zero and the ideal gas constant.We solved for the value of absolutezero by doing
the following:
P=mT+b
*Absolutezero
occursatp=0
t
t
0=mT+b
*Solvefor T
h
lexp=_-
,-/
Where:
T"*p= Absolute Zero
b = y-intercept
m = slopeofline
We then had to find the value of the ideal gasconstantwith the data we had.We did
so by doing the following:
p V = n R Tt
e = ( ; R ) r i s s i m i l a r t op = m T w h e r e , r n r ( | n )
*Wecanrewrite in termsof the densityof air (pa.Jand the molar massof air (M"i.)
I
Msam
lol=\=M
rns
V
n=Msam t
Matr
*Wecannow substitute
I
M att
!=
V
+.
Msam
_v_
M a,t
)2=Psir
v
Moi,
for I andsolvefor the idealgasconstant(R)
rn=f tnl + m=ffitn))
R=('")H
We looked up the valuesfor the molar massof air [M"i")and the density of air (p"i.)
at 25 'C. We got that M"i" = 28.966 x 10-3kg/mol and p"i" = 1.1839 kg/ms. After
getting valuesfor absolutezero and the ideal gasconstan! we comparedthem with
their theoreticalvaluesby using a percentdifference.
Data:
Part 1:
TableofData
SampleCalculation
of PredictedValues: &t**
pv=constant
+ p=#(p,l )
p=*(100) t
vi
+
o=fittoot
P= 133.3kPa
*ForV=15mL
SampleCalculationfor PercentDifferences:
t o/o= 0.98o/o
,,=l*#l1oo) t u"=lt:i1#lrloo)
*For V= 15 mL
Plot of P vs. V
450
400
350
$ aoo
! zso
h
fi zoo
$ rso
100
50
0
"+Experimental
+Prediction
Part2:'
DataTable
Plot of P vs. T
\a"
114000
112000
110000
3 108000
g lo6ooo
g 104000
d rozooo
p rooooo
E
98000
96000
94000
92000
NtP
Solvingfor AbsoluteZero:
b
^
l e x p =- - 2
o Seriesl
92372
l"*p=-ffi
P =299.6T+92372
* Equationofline in
(P)
termsof Preszure
(TJ
temperature
and
PercentDifferenceof AbsoluteZero:
Too = -308'32 oC
v"=lfflooot
Solvingfor UniversalGasConstant:
z.=lfflrrool
R= fmlMoit
' 'eab. )
ro-3
R= f299.6rzs's66x
r-;;3e-
o/o= f1.04 o/o
&*p = 7.33J/mol'K
PercentDifferenceof UniversalGasConstant:
t v"=
,"=lffil rtool
lffl rrool
o/o= lt.B o/o
DataAhalysis:
In part 1, we observedas the changingvolume effectedthe pressureofthe air inside
the syringe. We began to notice that as the volume of air in the syringe became
smaller, the percent error went up. At a volume of 5 mL, we had a 72.99 o/o
difference,where as,at a volume of 72 mL, we had a 1.01%o
difference.Overall,the
curve ofthe predictedvaluesand the curve ofthe experimentalvalueswere similar.
It was until the lower volumeswhere the curvesbeganto noticeablyseparate.Our
plotted data did agreewith the Ideal GasModel becausefor an ideal gas,the curve
looks like a 1/x curve. Our plots did the sameshapeand properties of a 1/x curve.
This is becausewe were comparingthe pressureto 1/V.
ln part 2, we found the experimental values for the Universal Gas Constantand
AbsoluteZero.Our experimentalvalue for absolutezero had an 11.04 7odifference
to the theoretical.We could tell that our data wasn't absolutelyaccuratebecauseof
our percent differencewhich therefore meant that there we errors that could have
arose during the experiment (See Discussion).Our experimental value for the
Universal GasConstanthad an 11.8 7o difference to the theoretical value. Again,
there were more areasfor error (SeeDiscussion).
Drscussron.'
This entire lab revolved around the Ideal GasLaw.We usedthe Ideal GasLaw to do
both parts of this experiment.Part 1 we were askedto measurethe pressureof air
inside of a syringe as we decreasedthe volume. Usingthe Ideal GasLaw, we were
able to show that p a 1/V. We predictedwhat the pressurewould be using this and
the comparedour predictionsto the experimentalresults.We beganto notice that
as the volume of the air inside the syringe decreased,the error of our predicted to
experimentaldata increased.We believethat there were various sourcesof error in
this part of the experiment.The first sourcecould havebeenfrom assumingthat AT
was zero. Evenif we decreasedthe volume at slow ratg it doesn'tnecessarilymean
that no enerry went to AT. Another sourceof error could have camefrom assuming
that n (# of moles) did not change.There could have been some gas that escaped
during the compression,therefore changingr1 and making the model of p u l/V
invalid becausen is no longer a constant.But we believe that the largest sourceof
error came from disregardingthe extra volume of air inside the tubing that was
connectedto the syringetip. The volume marked on the syringewas not the volume
of air enclosedwithin the syringe and tubing. So by neglectingthat extra volume of
air, our volume valueswere not completelyaccurate.We noticed it most when the
volume was smallest.When speakingwith other groups, they also had the same
increasein error when the volume was small. But overall, when looking at the big
picture ofthe data result,they did confirm the ideal gaslaw. For our data to be valid,
our plot of P vs. V must look like the plot of y = 1/x. Our data did look like a 1/x
curvewhich thereforeconfirmsthe ideal gasmodel.
"/
Part 2 was a bit different than part 1 in that this time we weren't measurethe
volume but rather we were measuringthe temperature.This part of the experiment
required us to placean air canisterinside a warm water bath.We then proceededto
placeice cubesinto the water bath to lower the temperatureof the water. We took B
points of the temperature and pressure.We were taking the temperature of the
water and assumingthat the temperature ofthe air in the canisterwas equalto the
temperature of the water. We watchedthe pressureof the air and waited until the
pressurebeganto equilibrateto take a measurementAfter taking 8 data points,we
graphedthe plot of P vs. T. We then got the equationof the line of points. From that
equation,we got the experimentalvalue for absolute zero and the Universal Gas
Constant.But we had some error becausewe had an I'J,.04o/odifferencewith the
absolutezero value and an l1.B o/odifferencewith the UniversalGasConstantValue.
After completingthe experiment,we beganto think of the different sourcesof error /
for this part ofthe experiment Onesourceof error could havebeen from the wate/
over flowing. Our amount of water in our water bath increasedas we added more
ice and inevitably,the water beganto over flow and spill out. That spilling of water
may have causedsome sort of error with our data.Another sourceof error could
have been from not being able to get a proper gap in temperature between each
data point. Sometimes it was difficult to get exactlya 1o-degreedifference.Instead
of adding ice to the water to cool it down, maybe it would have been better use a
metal container that sat on a heating/cooling reservoir so we could control the
water temperaturemore precisely.But we believedthat probablythe biggestsource
of error camefrom assumingthat the temperatureof the air inside the air canister
was the same temperature of the water. This assumptioncould have causedbad
data values to be taken. The water might have actually been colder than the air
temperaturebecauseit might have taken longer for the air to reachthe equilibrium
temperature.Looking past all the sourcesof error and percent differences,our job
was to find the value of absolutezero and the value of the UniversalGasConstant.
The theory behind this experimentwas that we could use the equationof line from
the pressureand temperaturedata taken to find the value of absolutezero and the
Universal Gas Constant. We indeed did get value that were with reasonable
uncertainty.With the given equipmentand conditionswe had,our valueswere quite
similar to the theoreticalvalues.But the overall objectivewas to examinethe Ideal
GasLaw and to seewhether or not air is an ideal gas.After this experiment,we can
concludethat air is physicallyan ideal gas.