Allison Edwards-Thermodynamics (Gas Thermometry)
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Experiment #1: Gas Thermodynamics (Gas Thermometry)
Allison Edwards
CHM3411L
1/23/2024
Introduction
This experiment aims to utilize a gas thermometer apparatus to determine the
temperatures of two fixed points: the steam point and ice point. The gas thermometer is
calibrated to the ice point within the University of Central Florida Physical Chemistry lab using
helium gas. In order to accomplish the most accurate results, three measurements are taken for
both ice point and steam point. The idea is that once the temperature has been fixed at two or
more points, temperatures at other points can be defined within this thermometer range.
1
The perfect gas law, pV
=
nRT
, is taken into consideration for calculations and assembly
of the system used in this experiment. Temperatures will be read in Celsius but will be convert to
Kelvin by adding the ice point temperature of water to the temperature in Celsius:
t
(
℃
)
=
T
(
K
)
−
273.15
. The molar volume of the gas bulb will be determined using the equation
1
~
V
=
n
V
≅
p
0
RT
0
, where p
0
is the pressure at the ice point, V
is the volume of the gas bulb on the
gas thermometer, n is the number of moles in the gas, T
0
is the temperature in Kelvin of the ice
point, R
is the gas constant, and ~
V
is the molar volume of the gas bulb. For the purpose of this
lab, R
will be applied in the units of 62.36 L*Torr*K
-1
*mol
-1
. The proportionality factor used for
the accuracy achieved in this experiment will be A
A
0
=
1
+
p
−
p
0
p
r
v
V
+
3
∝
t
−
1
~
V
(
B
−
B
0
)
. B
is a
second virial coefficient, p
r
is the pressure measured in the lab, and
is given for Pyrex glass as
3.2x10
-6
K
-1
.
1
The equations used in the experiment will work in conjunction with the pressure
and temperature readings obtained within the lab atmosphere. Gas thermometry has been utilized in labs for decades to obtain thermodynamic
temperatures. National metrology institutes (NMIs) notably used similar helium-filled gas
thermometers.
3
The setup being utilized in this lab is similar to that of a typical research lab. The
apparatus is connected to a pressure gauge, via glass and plastic tubing, which will be accounted
for in calculations as a cumulative “dead space.” Results of gas thermometer readings are
expected to be accurate, and potentially less precise than other methods. Comparing data from
this experiment to commonly known theoretical values for the ice point and steam point of water,
273.15 K and 373.15 K, respectively, should support this claim.
2
Procedure
The procedure used followed the instructions found in the Gas Thermometry experiment
on pages 91-98 of the Experiments in Physical Chemistry textbook.
1
The pressure was adjust to
450 Torr instead of 600 Torr. Results
Table 1.
Calculated volumes of apparatus
Apparatus
Volume
Bulb (V)
48 cm
3
0.00007 cm
3
Dead Space (v)
247 cm
3
0.0001 cm
3
Table 2.
Measured pressures
Trial
Ice-Point Pressure (p
0
)
Steam-Point Pressure
Gas Bulb Pressure at Room
Temperature (p
r
)
1
420.5 Torr
0.05 Torr
536.7 Torr
0.05 Torr
449.1 Torr
0.01 Torr
2
420.5 Torr
0.05 Torr
535.8 Torr
0.05 Torr
3
419.2 Torr
0.05 Torr
533.7 Torr
0.05 Torr
Average
420.1 Torr
0.05 Torr
535.4 Torr
0.05 Torr
Table 3.
Temperatures
Temperature
T (K)
T (
C)
Ice-Point (T
0
)
273.1 K
0.005 K
-0.1
C
0.005
C
Steam-Point
348.07 K
0.0005 K
74.9
C
0.005
C
Room (T
r
)
295.15 K
0.0005 K
22
C
0.05
C
Discussion
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The ice-point temperature was found to be 273.1 K with a value of uncertainty of
0.0005 K. The known ice-point of water is 273.15 K.
2
The experimental temperature of the
ice-point was off by approximately 0.05 K. The discrepancy could be attributed to the degree
of uncertainty, but is indicative of a properly functioning gas thermometer in regards to the
ice-point procedure. The temperature of the steam-point was found to be 348.07 K with a value of uncertainty
of
0.0005 K. The known steam-point of water is 373 K. The experimental temperature was
found to be approximately 24.93 K lower than the theoretical temperature. In an effort to
establish a more accurate steam-point reading, a more enclosed system could potentially be
employed for use in the steam pressure portion of the procedure. The experiment utilized an
open system that was able to exchange heat in the form of the steam that escaped from
around the bulb being utilized to read the pressure. Proposal of a better fitting bulb, longer
duration spent reading the steam pressure, or longer period of cooldown for the bulb in
between readings for ice pressure and steam pressure could ideally yield data producing
calculated results aligning with the theoretical data. Conclusion
The experimental objective to find the temperature of the two fixed points, ice and steam
point, was successful. The calculated temperature of the ice point of water was off by a value that
could be attributed to uncertainty, while the steam point was off by a temperature value within 30
K of the expected temperature. The gas thermometer apparatus was designed with gas laws in
mind. The calculations used in this experiment are all derived from equations that represent these
laws mathematically. Through the pressures obtained, an almost exact value for the ice point of
water was found. The demonstrated functionality of a gas thermometer setup such as the one
used in this experiment effectively create a system that would prove useful in industrial settings
or continuation research laboratories. Improvements could be made in the steam collection
aspect of the apparatus used. A more enclosed system for measuring the pressure of the steam
could be utilized in the form of a tighter fitting bulb. Time and space allowing, the steam point
having a separate gas thermometer apparatus could yield undisturbed and more accurate results
without the necessity of switching a bulb pressure reader from an ice bath to a hot source in a
short timeframe.
References 1.
Garland, C. W.; Nibler, J. W.; Shoemaker, D. P. Experiments in Physical Chemistry
; McGraw-Hill Higher Education, 2009. 2.
Harvey, A. H.; McLinden, M. O.; and Tew, W. L. Thermodynamic Analysis and Experimental Study of the Effect of Atmospheric Pressure on the Ice Point
. https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=910516 (accessed 2024-01-22).
3.
Moldover, M.R.; Tew, W.L.; Yoon, H.W. Advances in thermometry
. Nat Phys. 2016 Jan;12:7-11. doi: 10.1038/nphys3618. Epub 2016 Jan 7. PMID: 27182278; PMCID: PMC4865254.
Appendix
Bulb Volume (V): Bulb diameter: 32 mm
External bulb radius (r
external
): 32
mm
2
=
16
mm
Interior bulb radius (r): 16
mm
−
2
mm
=
14
mm
(volume of hemispheres) + (volume of cylinder) = total bulb volume (V)
(
(
4
3
π r
3
)+
(
π r
2
h
)
=
¿
Propagation of Error for V: √
0.05
2
+
0.05
2
=
±
0.07
mm
Dead Space Volume (v): Dead space
1
: r = 6 mm, l = 40 mm, v
1
= π r
2
l
=
π
(
6
2
)
(
40
)
=
4524
mm
3
=
45
cm
3
Dead space
2
: r = 1.5 mm, l = 120 mm, v
2
= 848 mm
3 = 8.5 cm
3
Dead space
3
: r = 1.5 mm, l = 150 mm, v
3
= 1060 mm
3
= 11 cm
3
Dead space
4
: l = 520 mm, v = (
21
2
π
)
2
π
(
520
)
=
18249
mm
3
=
182
cm
3
Total volume of dead space (v): 247
cm
3
Propagation of Error for v: √
0.05
2
+
0.05
2
+
0.05
2
+
0.05
2
=
±
0.1
mm
Room Pressure (p
r
): -287.7 Torr-(-733.3 Torr) (first & third zero) = 449.1 Torr
Instrument Error for p
r
:
0.01 Torr
[Trial 1] Measured Pressure of Ice Point (p
0
): −
313.2
Torr
−
(
−
733.7
Torr
)
=
420.5
Torr
Instrument Error for p
0
:
0.01 Torr
[Trial 1] Measured Pressure of Steam Point: −
197.0
Torr
−
(
−
733.7
Torr
)
=
536.7
Torr
Average Ice-Point Pressure (p
0
): 420.5
Torr
+
420.5
Torr
+
419.2
Torr
3
=
420.1
Torr
Average Steam-Point Pressure: 536.7
Torr
+
535.8
Torr
+
533.7
Torr
3
=
535.4
Torr
[Trials 1 & 2] Ice-Point Temperature Approximation:
T
=
273.15
p
0
p
=
273.15
420.1
Torr
(
420.5
Torr
)
=
273.4
K
Molar Volume of Bulb (
~
V
): ~
V
≅
RT
0
p
0
=
(
62.36
L
∗
Torr
∗
K
−
1
∗
mol
−
1
)
(
273.1
K
)
420.1
Torr
=
40.54
L
∗
mol
−
1
Propagation of Error for ~
V
: σ
~
V
=
|
40.54
L
∗
mol
−
1
|
∗
√
(
0.005
420.1
Torr
)
2
=
0.0005
~
V
=
40.54
L
∗
mol
−
1
±
0.0005
L
∗
mol
−
1
[Trials 1 & 2] Ice-Point Temperature (T
0
): B = T, 0
C = 11.8 for He
1
= 0.0118 L*mol
-1
A
A
0
=
1
+
p
−
p
0
p
r
v
V
+
3
∝
t
−
1
~
V
(
B
−
B
0
)=
1
+
420.5
Torr
−
420.1
Torr
4491.1
Torr
(
0.0247
L
0.048
L
)
¿
T
=
273.15
p
0
A
A
0
p
=
273.15
420.1
Torr
(
0.9997
) (
420.5
Torr
)
=
273.3
K
Propagation of Error for p [Trials 1 & 2]: √
(
0.05
420.5
)
2
+(
0.05
420.1
)
2
+
¿¿
Propagation of Error for p [Trial 3]: √
(
0.05
4 19
.
2
)
2
+(
0.05
420.1
)
2
+
¿¿
[Trial 1] Steam-Point Temperature: B = T, 100
C = 11.4 for He
1
= 0.0114 L*mol
-1
A
A
0
=
1
+
p
−
p
0
p
r
v
V
+
3
∝
t
−
1
~
V
(
B
−
B
0
)=
1
+
536.7
Torr
−
420.1
Torr
4491.1
Torr
(
0.0247
L
0.048
L
)
¿
T
=
273.15
p
0
A
A
0
p
=
273.15
420.1
Torr
(
0.9998
) (
536.7
Torr
)
=
348.9
K
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Propagation of Error for p [Trial 1]: √
(
0.05
536.7
)
2
+(
0.05
420.1
)
2
+
¿¿
Propagation of Error for p [Trial 2]: √
(
0.05
535.8
)
2
+(
0.05
420.1
)
2
+
¿¿
Propagation of Error for p [Trial 3]: √
(
0.05
533.7
)
2
+(
0.05
420.1
)
2
+
¿¿
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- 3arrow_forwardger Anna was asked to identify and explain if the equation CO2 (g) → CO2 (1) However she got it wrong. What is her error and what should the answer have been? was an endothermic or exothermic reaction. Anna's Statement: The equation is an endothermic reaction because the energy is absorbed by gaseous CO2 from the surroundings to become liquid CO2 causing the molecules to speed up. a 10 トII & -R T Parrow_forward▼ Part F telavancin, C80 H106 Cl2N11O27P Express your answer in percent to three significant figures. ΤΙ ΑΣΦΑ %0 24.6 Submit Previous Answers Request Answer X Incorrect; Try Again; 2 attempts remaining ? %arrow_forward
- Enter the balanced net ionic equation for HCl(aq)+K2CO3(aq)→H2O(l)+CO2(g)+KCl(aq)HCl(aq)+K2CO3(aq)→H2O(l)+CO2(g)+KCl(aq). Express your answer as a chemical equation. Identify all of the phases in your answer.arrow_forward← = Account Balance 1 substance Elanation 7 O STATES OF MATTER Predicting the relative boiling points of pure substances A 52°F Mostly cloudy B A Q Z Rank the elements or compounds in the table below in decreasing order of their boiling points. That is, choose 1 next to the substance with the highest boiling point, choose 2 next to the substance with the next highest boiling point, and so on. 2 https://www-awu.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNslkr7j8P3jH-IBMBkpcnaFu0F7Uj... X chemical symbol, chemical formula or Lewis structure S .. : Cl: W CaCl₂ 0=N-CI: .. : Cl: / C=C Check Schedule Builder CL₂ **** # 3 E D .. : Cl: : Cl: .. H 14 td-jolch. $ 4 R X boiling point (Choose one) ✓ (Choose one) v (Choose one) ✓ F (Choose one) ✓ 1 do % 5 V Give to Queensborough X T G 6 L B & 27 H N * Announcements-2022 F. X All 10 ✔ 8 J DE ( || M 9 K ho ) ALEKS - Chisom Obidieg X + ——— O Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibil Ⓒ 40 D 12:42 PM 11/3/2022 O D…arrow_forwardConstants: • c = 2.9979 x 108 m/s h = 6.626 x 10-34 J s per one photon • R = 8.314 J/(K mol) = 0.08206 L atm/(K mol) NA = 6.022 x 1023 particles/mol RH = 1.097 x 107 m1 = 2.178 x 10-18 J . . You have an aqueous Glucose solution that is 12.0% Glucose by mass. What is the molality of Glucose in the solution? Molar Mass of Water = 18.015 g/mol Molar Mass of Glucose 180.16 g/mol =arrow_forward
- Please helparrow_forwardA chemist fills a reaction vessel with 3.61 atm nitrogen (N,) gas, 8.64 atm oxygen (0,) gas, and 6.55 atm nitrogen monoxide (NO) gas at a temperature of 25.0° C. Under these conditions, calculate the reaction free energy AG for the following chemical reaction: N,(g) + O,(g) = 2NO (g) Use the thermodynamic information in the ALEKS Data tab. Round your answer to the nearest kilojoule. do Data HNO3 (1) -174.1 HNO3 (g) -133.9 Oxygen OH (aq) H20 (1) -285.8 H20 (g) -241.8 02 (9) H202 (1) -187.8 H202 (9) -136.3 Phosphorus Explanation Check P4 (s) 2021 McCarrow_forwardUse Hess’s Law to determineDH for the reaction C3H4 (g) + 2 H2 (g) ® C3H8 (g), given that H2 (g) + ½ O2 (g) ® H2O (l)DH = -285.8 kJ C3H4 (g) + 4 O2 (g) ® 3 CO2 (g) + 2 H2O (l) DH = -1941 kJ C3H8 (g) + 5 O2 (g) ® 3 CO2 (g) + 4 H2O (l) DH = -2219.9 kJarrow_forward
- CC, (g) can also be produced by reacting CHCI, (g) with Cl, at 400°C, as represented by the equation below. CHCI, (g) + Cl, (g) z C, (g) + HCI (g) i. A student injects CHCI, (g) and CI, (g) into a previously evacuated, rigid vessel and raises the temperature of the vessel to 400°C. At this temperature the initial partial pressures of CHCI, (g) and Cl, (g) are 5.250 atm and 1.150 atm, respectively. The system is allowed to reach equilibrium. The partial pressure of CCI, (g) at equilibrium is 0.1050 atm. The partial pressure of HCI (g) at equilibrium is also 0.1050 atm. Calculate the value of K,.arrow_forwardYou have substance X which is very flammable and substance Y which is very combustible in your garage in containers right in front of where you park your car. It is a hot July afternoon, 119Fand you just come home from work where your car was parked outside in the sun for 8 hrs and you were running the air conditioning the entire way home (hence, the car is very hot and is giving off a lot of heat). Which substance would you be more worried about and why ?arrow_forwardIn an effort to moderate the interior temperature of their home during a heat wave in July, Shakir turns on the air conditioner. As the interior temperature of the home cools from 29°C to 21°C, the molecules in the air would primarily undergo Select one: O a decrease in kinetic energy O an increase in potential energy O an increase in kinetic energy O a decrease in potential energy In addition to catalyzing the depletion of the ozone layer, CFC molecules that are utilized in air conditioning units also contribute to the enhanced greenhouse effect. Which of the following processes also affects global climate change by releasing a gas that enhances the greenhouse effect? Select one: O Photosynthesis by releasing oxygen O Photosynthesis by releasing carbon dioxide O Hydrocarbon combustion by releasing oxygen O Hydrocarbon combustion by releasing carbon dioxide Enthalpy represents the total kinetic and potential energy in a chemical system. Select one: O True O False If the reactants and…arrow_forward
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