Experiment 9

CHEM 3493 - Experiment # 2 -Molecular theories

Heat capacity ratios for gases- sound velocity method: measurement of the speed of sound, modeling of g, Cv and Cp -for atoms and molecules with different molecular structures and degrees of freedom

LIST:

1. Notebook: pre-lab report, all results from lab notebook, all work done in the notebook written in lab notebook

BEFORE THE EXPERIMENT: Read EXPERIMENT 3 (B) and related material from the textbook. In this experiment we measure speed of sound using Kundt's tube. You will need to prepare the instrumental configuration, identify the instrumentation and characterize each part and its function, draw your own diagram or take a picture (see handouts or texbook). OBSERVE ALL SAFETY RULES IN THE LAB! You will also read and become familiar with the wavelike observables and principles as well as with the basic physico -chemical principles on which the models for cv, cp, c etc. are based (see textbooks and manuals. You should calculate all theoretical and experimental values for ideal gas and real gas (w/and w/out vibrational contributions) using the expressions in the book . Particularly focus on degrees of freedom, gamma-cp-cv relations (1,3), ideal (24) and real (35) gas relations. You will need to find the experimental values for van der Waals constants a and b, (this book, or PChem p466) and the experimental (real gas) literature cp and cv values for the studied gases: He, Ne, N2, Ar, CO2 . You will report all uncertainties as well as the comparative % difference between your measurements and experimental values obtained from real Cv and Cp.

2. Mathematica (or similar ): all calculations and uncertainty calculations

* You will write all needed expressions - see textbook and this page to find what you need to calculate and model in Mathematica - and do the calculations before submission of results to this webpage. In the Mathematica program assign the values to the standard physical constants first (example: a, b,R, etc). Make sure that all input values are in real number format ("with decimal point"). USE THE CORRECT and CONSISTENT SET of UNITS The dimensional equations could be calculated the same way as numerical-but be careful.

Use Mathematica for the calculation of the propagation of uncertainties expressions. You can practice the model calculations and uncertainty calculation using available literature data for sound velocity. Make a MathematicaSoundVelocitymethod example file from your in-class work to see how to do the modeling and calculations (in class). You can calculate Vmol (tilda) using ideal gas approx. and report it with its own uncertainty for future calculations.

3.This web submission

Fill in the blank fields below with your measured data, results of (Mathematica) modeling, simulations and calculations. After you have re-checked that all of your values are entered correctly, print out a hard copy of confirmation page for your record to be submitted with your pre-lab and the copies of lab-notebook sheets. You are allowed to submit data more than once-if you make entry error; so make sure your last entries are correct. Then click on the submit button.

4. Report in .doc format (abstract, intro, results&discussion, conclusions, references)

You can use the calculations from Mathematica and cut-paste copy into report.

*You can attach/submitt by e-mail with CHEM3493-experiment#-YOUR NAME all on that list, except the copies from notebook. Also ,when needed, computer generated work (acquired data in files, images, including all instrument-software, LabView, Mathematica, Excel files, Gaussian03 or PeakFit files etc. ).

5. Show using Mathematica Plot how the waves are formed in a cavity/tube. (attach the file to e-mail)

Additional post-experiment work (calculation assignment ) will include QM software based (Gaussian) modeling of the thermodynamic properties of these molecules. You will read about these calculations and will be shown how to perform the calculations on the GaussView or/and LSU parallel computer system Use Gaussian 03 example file for the additional report.

Additional post-experiment work (instrumentation) will include instrumentation study and development using LabView.

Name:

Group:

Instrument (s) used

Chemicals used

TA:

Pre-lab information: (Use commas when needed. Ask questions if not sure!)

How many vibrational degrees of freedom are in atoms, linear, nonlinear molecules, respectively
Write down the ideal gas equation ?
Convert 27C to K
What is the Cv (in "R" units) of the gases : CO2, N2, He, based on the internal energy partition, respectively (in the approximation of ideal gas model)?
Calculate gamma and s(g) using the data for Ar given in the textbook exercise (in class , p57) Try also to calculate g using expression (35) for real gas using Mathematica with values for and a and b (McQuarrie p. 644)
What are the experimental( literature ) values for Cv and Cp for He, Ne, Ar, N2, CO2 in J/mol, respectively (Use literature and/or web search)
Write down the relation between gamma, Cv and Cp (ideal gas)
What is the frequency range you use in this experiment
Calculate c+-s(c), speed of sound for Ar, using the data from the textbook exercise( in class, p 57)

A) Measured values and standard uncertainty - speed of sound-c

He -literature value speed c	+_ m/s
He-Trial 1 Temp (K)	+_ K
Pressure	+_ units
Frequency (signal generator)	+_ kHz
Wavelength (average all (n) measurements in this group)	+_ units
Speed (measured in this experiment)	+_ m/s
% c difference (literature value -measured value)/literature value	%
N2-literature value speed c	+_ m/s
N2-Trial 1 Temp (K)	+_ K
Pressure	+_ units
Frequency	+_ kHz
Wavelength (all n=5)	+_ units
Speed (measured)	+_ units
% c difference (literature-measured)/literature	+_ %
CO2-Trial 1 Temp (K)	+_ K
Pressure	+_ units
Frequency	+_ kHz
Wavelength (all n=5)	+_ units
Speed (measured)	+_ units
% c difference (literature-measured)/literature	%

Air-Trial 1 Temp (K)	+_ K
Pressure	+_ units
Frequency	+-kHz
Wavelength (all n=5)	+_ units
Speed (measured)	+_m/s
% c difference (literature-measured)/literature	%

B - no van der Walls : ideal gas g

Gas/Calculated g from your measured speed c values
(equation 24, use Mathematica to speed the calculations)
+-s(g)
uncertainty
Calculated g - with vibration for molecules
(internal energy with partition to translational rotational and vibrational)

OPTION 1
Calculated g without vibration form molecules
(internal energy with partition to translational rotational)

OPTION 2
Literature value for g calculate form literature/experimental values for Cv and Cp("true" if you have them available
OPTION 3
Choose either literature value for gamma or one of the calculated values based on the partition energy that is closer to your measured gamma and use it as the "true" value
s(g)-true

from this table option 1, 2 or 3
% difference: (measuered-"true")/"true")

He

Second - He

N2

Second -N2

CO2

Second- CO2

CO2(p 2)

CO2 (p 2)

C real gas -van der Waals g

Gas/Calculated g from your measured speed c values

(equation 35, use Mathematica to speed the calculations)
+-s(g)
uncertainty
Calculated g - with vibration for molecules
(internal energy with partition to translational rotational and vibrational)

OPTION 1
Calculated g without vibration form molecules
(internal energy with partition to translational rotational)

OPTION 2
Literature value for g calculate form literature/experimental values for Cv and Cp("true" if you have them available
OPTION 3
Choose either literature value for gamma or one of the calculated values based on the partition energy that is closer to your measured gamma and use it as the "true" value
s(g)-true

from this table option 1, 2 or 3
% difference: (measuered-"true")/"true")

He

Second-He

N2

Second-N2

CO2

Second-CO2

CO2(p 2)

CO2 (p 2)

Air

Air

Air

Air

Additional information for C.

Literature value/Gas	He	N2	CO2	UNITS
cv
cp
a (McQuarrie p. 644)
b (McQuarrie p. 644)

Print and save a hard copy of this page and save the confirmation page, for your records.

Gas/Calculated g from your measured speed c values (equation 24, use Mathematica to speed the calculations)	+-s(g) uncertainty	Calculated g - with vibration for molecules (internal energy with partition to translational rotational and vibrational) OPTION 1	Calculated g without vibration form molecules (internal energy with partition to translational rotational) OPTION 2	Literature value for g calculate form literature/experimental values for Cv and Cp("true" if you have them available OPTION 3	Choose either literature value for gamma or one of the calculated values based on the partition energy that is closer to your measured gamma and use it as the "true" value s(g)-true from this table option 1, 2 or 3	% difference: (measuered-"true")/"true")
He
Second - He
N2
Second -N2
CO2
Second- CO2
CO2(p 2)
CO2 (p 2)