Physical Chemistry Lab Guide

7/22/2019 Physical Chemistry Lab Guide

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Joule-Thomson Effect

Introduction:

The goal of this experiment is to calculate the Joule-Thomson coefficient for helium,

nitrogen, and carbon dioxide and understand their meanings. You will use experimental data to

calculate the coefficient for each gas and then calculate theoretical coefficient values using the

van der Waals equation, Beattie-Bridgeman equation, and virial equation. Shoemaker gives agood description of the Joule-Thomson effect, but if it does not make sense, your Physical

Chemistry textbook or numerous internet sites provide understandable descriptions.

Concepts to consider:

What does the Joule-Thomson coefficient represent? How is the Joule-Thomson effect isoenthalpic? What does the sign and magnitude of the Joule-Thomson coefficient tell you? How does the inversion temperature relate to the sign of the Joule-Thomson coefficient? Which of the theoretical equations should be most accurate? Which should be least? Based on the intermolecular forces felt for the three gases under study, what do you think

should be the sign/relative magnitude of the three Joule-Thomson coefficients?

Experimental:

The experimental diagram in Shoemaker is a bit confusing. What is important to

understand is that gas is being passed from high pressure to low pressure (atmospheric pressure)

across a frit, and the temperature change associated with this process measured by two

thermocouples. You will need to know the atmospheric pressure in the room, which can bemeasured from a barometer. You will also need to know the starting temperature of the gas as it

enters the Joule-Thomson cell (needed for calculating the Joule-Thomson coefficient using thetheoretical equations).

The pressure of the gas under study will be increased to a certain value (ex. 8 bar for

nitrogen), and the gas allowed to flow through the Joule-Thomson cell at this constant pressure.

As the gas flows, the temperature difference across the frit will be measured at 30 secondintervals (in actuality, you only need to know the steady, constant temperature difference across

the frit). The constant thermocouple reading correlates to the change in temperature at the

particular pressure difference used. After testing one pressure, the pressure will be lowered (ex.to 7 bar for nitrogen), and the temperature difference across the frit measured in the same way

again. The thermocouple readings along with the various pressure differences used will allow forthe calculation of the Joule-Thomson coefficient for all three gases.

Calculation Tips:

The thermocouples measure the temperature difference across the frit in mV, which can

be converted to temperature difference in Kelvin using the equation y = -0.755x2+ 26.03x +

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0.014, where x is the thermocouple reading in mV. This equation was obtained by plotting data

from -50C to 50C given at http://instrumentation-central.com/TechNotes/TypeTTableC.pdf.

To calculate the experimental values of the Joule-Thomson coefficient for each gas,simply plot the pressure difference used on the x-axis and the corresponding temperature

difference on the y-axis. The pressure difference can be obtained by subtracting the initial

pressure used from the atmospheric pressure in the room. Make sure both pressures are in bar.The slope of the line of best fit will be the Joule-Thomson coefficient in K/bar.

The theoretical value of the Joule-Thomson coefficient from the van der Waals

equation of state requires the use of equation 11. Shoemaker gives the constants needed, butremains somewhat ambiguous about the units of the constants. If you use the units listed in the

table below, you will get a Joule-Thomson coefficient in K/Pa, which is easily converted into

K/bar.

van der Waals Constant Helium Nitrogen Carbon Dioxide

a [ (Jm3)/mol

2] 3.457 10

-30.1408 0.3640

b (m3/mol) 2.370 10

-5 3.913 10

-5 4.267 10

-5

Cp,m [ J/(Kmol) ] 20.79 29.12 37.11

The theoretical value of the Joule-Thomson coefficient from the Beattie-Bridgeman

equation of state requires the use of equation 14. Using the constants given below will onceagain give a Joule-Thomson coefficient in K/Pa.

Beattie-Bridgeman Constant Helium Nitrogen Carbon Dioxide

A0[ (Jm3)/mol

2] 2.19 10

-3 0.13623 0.50728

a (m3/mol) 5.984 10

-5 2.617 10

-5 7.132 10

-5

B0(m3/mol) 1.400 10

-5 5.046 10

-5 1.0476 10

-4

b (m3/mol) 0.0 -6.91 10

-5 7.235 10

-5

c [ (m3

K3

)/mol ] 4.0 10-2

42.0 6.60 102

The pressure term at the end of the Beattie-Bridgeman equation needs to be in Pa and the molarheat capacity at constant pressure (Cp,m) is the same as used in the van der Waals equation.

Calculating the three Joule-Thomson coefficients from the virial equation is quite

difficult. To do this, software such as Mathcad 14 is required (trial version is available forfree). You should check with your TA about this calculation.

In addition, Lennard-Jones plots can be made athttp://www.oup.com/uk/orc/bin/9780199280957/01student/graphs/graphs/lg_11.32.html. To

copy the graph from the website to your lab report, simply hit the Print Screen button on your

keyboard, paste the image in Microsoft Paint, and cut out the graph to your liking.

References:

D.P. Shoemaker, C.W. Garland, and J.I. Steinfeld.Experiments in Physical Chemistry, 7th

ed.


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Low-Pressure Effusion of Gases

Introduction:

The goal of this experiment is to calculate the relaxation time and molar mass of

helium, nitrogen, and argon using low-pressure effusion. In low-pressure effusion, a gas stored at

low-pressure flows through a small pinhole into an evacuated chamber. The rate of pressure

decrease in the chamber the gas molecules were originally stored can be used to determine therelaxation time of the system. This value, along with the volume of the original chamber,

dimensions of the pinhole the gas passes through, and temperature of the system can be used to

calculate the molar mass of the gas under study.


What two variables affect the rate of effusion? How does the rate of effusion relate to the molar mass of the gas? Consider the equation

for the Maxwellian distribution (not given in Shoemaker). What is the mean free path length? How does the mean free path length relate to pure molecular flow versus viscous flow?

This should tell you why the experiment uses low pressure.

Experimental:

To determine the molar masses and the relaxation times of helium, nitrogen, and argon,

the drop in pressure over time is measured. To do this, a vacuum manifold is first evacuated andthe gas supply hose flushed out. After filling a short segment of the vacuum manifold with gas,

the valves leading to the bulb and capacitance monometer need to be opened and the valvesleading to other areas of the manifold including the pinhole closed, allowing the gas to expandonly into the bulb and capacitance monometer. Once the pressure inside the bulb reaches

between 0.14 to 0.15 torr (measured in volts by the capacitance monometer and then converted

into torr), the valve allowing gas to enter the system is closed. The valve leading to the pinhole isthen opened and the pressure inside the bulb measured every minute until only about 10% of the

original pressure remains inside the bulb. In addition to measuring the drop in pressure overtime, the length of the manifold tubing the gas initially occupies, the circumference of the bulb,

the dimensions of the pinhole, and the temperature need to be recorded.

Calculation Tips:

First, you need to convert the readings from the capacitance monometer into pressureusing the appropriate conversion factor (this should be listed on the device). To determine the

relaxation time , the following equation will come in handy.

lnp t

ln p

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All you need to do is plot the natural log of the pressure on the y-axis, and the time passed since

starting effusion on the x-axis. The slope of the corresponding line of best fit equals (-1/). Your

time should be in seconds, thus is also in seconds.

The molar mass of the gas can be determined from the following equation.

VA 2MRT K

Volume should be in m3, area in m

2, the gas constant R in (8.3143), and temperature

in Kelvin. The resulting molar mass will be in kg/mol.

In addition, error in volume and area measurements can be eliminated by calculating the

ratio of two values. The ratio of two values follows the relationship given below:

`

MM`

References:


ed.

D.P. Shoemaker, C.W. Garland, and J.I. Steinfeld.Experiments in Physical Chemistry, 3rd

ed.


5/13

Bomb Calorimetry

Introduction:

The goal of this experiment is to determine the molar heat of combustion and heat of

formation of a compound of your choice. In addition, the heat of combustion of 1,5,9-

trans,trans,cis-cyclododecatriene will be determined in order to calculate the resonance

stabilization of benzene.


How will benzoic acid be used in this experiment? How is the change in internal energy (U or E) related to the change in enthalpy (H)? How does the heat of combustion of 1,5,9-trans,trans,cis-cyclododecatriene allow for the

calculation of the resonance stabilization energy of benzene? Hint: Look at thenumber/type of bonds being broken in 1,5,9-trans,trans,cis-cyclododecatriene compared

to benzene + cyclohexane. Why does benzene release less energy upon combustion than theoretically expected? What does resonance stabilization mean in terms of the physics of the electrons?

Experimental:

First, the constant volume heat capacity of the bomb calorimeter will be determined. To

determine this value, benzoic acid, with a known heat of combustion, will be weighed out and

smashed into a pellet. After placing the smashed sample of benzoic acid inside the sample holderon the bomb head, the bomb head will be closed, filled with oxygen, and lowered into the Dewar

flask filled with water. The temperature inside the bomb should be recorded every 10 seconds.After the rise in temperature (rate in change of temperature) reaches a steady pace, the fuse wire

can be ignited and the temperature recorded until it once again reaches a steady pace. Anyremaining wire should be massed and subtracted from the original weight of wire used. This

general procedure also applies to the other compounds under study.

Calculation Tips:

The constant volume heat capacity of the bomb calorimeter can be determined from the

following equation.

|U| CV T

The absolute value of the change in internal energy for benzoic acid is given as 26.41 103J/g.

By multiplying this value by the number of grams of benzoic acid combusted and subtracting the

energy released from the combustion of the wire (this factor should be listed on the packet of

wire), the internal energy of combustion can be calculated. To determine the change intemperature, you should be able to take the approximate difference between the initial steady

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state temperature and the final steady state temperature. The more accurate method for

calculating the temperature difference described in Shoemaker is a little more complex andrequires some calculus, but should not change the answer significantly if your obtained data is

accurate. You should check with your TA if you should use the calculus method.

The rest of the calculations are relatively straightforward, but note the following. When

converting the change in internal energy into change in enthalpy, the balanced chemical reactionof the respective combustion reaction will be required. In addition, do not forget to correct for

enthalpy of vaporization when calculating the heat of combustion for 1,5,9-trans,trans,cis-

cyclododecatriene and benzene + cyclohexane. Troutons Rule states that the enthalpy ofvaporization for many liquids equals the boiling temperature times 85 J/(mol K). Many of the

required literature values for this experiment can be found at http://www.hbcpnetbase.com/

References:

Atkins, Peter and Paula, Julio De. Atkins Physical Chemistry 8th

Edition. New York: W.H.

Freeman and Company, 2006


ed.

Polik, William F. Bomb Calorimetry. Hope College Chemistry Department. 3 Oct. 2007

.


7/13

Lattice Energy of Solid Argon

Introduction:

The goal of this experiment is to calculate the lattice energy of solid argon (LE). You will

use your experimental data to calculate the heat of sublimation of argon using two methods, and

use one of these values in the Debye theory of lattice energy to calculate LE. Then, you will

calculate a theoretical value for LE using the Lennard-Jones potential.


What is the lattice energy of a solid? What two energies contribute to total energy of argon at absolute zero? Note: The heat of

sublimation represents the total energy, and by subtracting one of the two contributing

energies, you will get the lattice energy (Equation 8).

How does the Lennard-Jones potential work? Note: You may remember this graph fromGeneral Chemistry or Biochemistry as a van der Waals attraction-repulsion curve.

Experimental:

The experiment you will carry out is a bit simpler than described in Shoemaker. In

essence, the pressure of argon is measured at various temperatures. To do this, a (one) chamber

is filled with gaseous argon and nitrogen and submersed in liquid nitrogen in order to achievelow temperatures. The pressure of argon is measured by a capacitance monometer and the

temperature inside the chamber measured by a U-tube mercury manometer (measures the

pressure of the gaseous nitrogen, which can be related to temperature). To decrease the

temperature, the liquid nitrogen is pumped on. As the temperature inside the chamber decreases,the pressure of argon is recorded versus the pressure of gaseous nitrogen. The pressure of argon

can also be measured as the temperature warms up when the liquid nitrogen is removed to ensureprecise data.

Calculation Tips:

First, use Equation 23 to obtain the corrected nitrogen pressures. Remember, for

example, if the mercury initially rested at 50 cm, and raised to 85 cm, the net change is 35 cm.Every change in one cm represents a change in 2 cm (the other side of the U-tube also changes)

so the initial, uncorrected pressure is 35.0 cm 2 10 mm/cm. The next pressure can beobtained by simply plugging in the new net change after the mercury has dropped one cm (34.0cm 2 10 mm/cm). Use the Equation 12b to convert pressure into temperature (Kelvin).

Solving for the heat of sublimation using the approximate form of the Clapeyron equation

is relatively straightforward. The exact form is a bit more tricky. To obtain d(p)/d(T), plot thepressures obtained in Pa vs. temperature in K (it is important you use Pa, not torr, otherwise your

units for energy will not come out in Joules). Find an equation that fits the line well (it will not

be linear), take a derivative of this equation, and plug in the specific temperatures to find the

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value of d(p)/d(T) for that temperature. To calculate Vg,m, the following equation will come in

handy, which is simply the virial equation of state using one virial coefficient solved for Vg,m.

V, RT RT RT4pB2p

Remember to use an R value of 8.3145 J/(mol K) and pressure in Pa. The values of B listed in

Shoemaker are in cm3/mol, so you need to convert the necessary values into m

3/mol. Vs,mis

given in Shoemaker, but it also needs to be converted into m3/mol. You now have all the values

you need to calculate the heat of sublimation using the exact Clapeyron equation.

The third law calculation is most important since it will give you Hsub,m,0 K, which isneeded to calculate the lattice energy of solid argon. In the first expression needed (Equation 4),

G Tlnp B p V, 1 p

H,T

R

the first pressure should be in atm (this pressure is actually divided by p, which is standard state

1 atm and natural logarithms should be unitless). The other two pressures are in Pa andremember, use m

3/mol not cm

3/mol for B and Vs,m. You can now plug the values of Gm

obtained into Equation 5 and solve for H .,, K To use Equation 7, you need Hsub,m. To find this value for the individual temperaturesneeded, you can use the equation

H,, K

T X Y

, ,,

where X represents the value given in Shoemaker for the gas, and Yrepresents the same value for the solid/liquid (look at Table 2). The rest of the experimental

calculations are straightforward.

The theoretical Lennard-Jones equation might look daunting, but it is really just someplug and chug. You need to note that the variable k, which is needed to calculate , is theBoltzmann constant (1.38065 10

-23J/K), N0is Avogadros number, and needs to be in m, not

angstroms. The value of d can be calculated using the equation (1/2) a2, where a is equalto 5.30 10

-10m. This equation for d is just the nearest-neighbor distance calculated given the

face-centered cubic structure of solid argon.

References:

Atkins, Peter and Paula, Julio De. Atkins Physical Chemistry 8th

Edition. New York: W.H.

Freeman and Company, 2006


ed.

Lattice Energy. Wikipedia. 12 Oct. 2007. 20 Oct. 2007

.


9/13

Contact Angle

Introduction:

The goal of this experiment is to learn about the contact angle between a liquid and a

solid surface and determine the critical surface tension of Teflon. You will use the contact angles

of various liquids along with their respective surface tension to create a Zisman plot. The Zisman

plot will allow for the calculation of the critical surface tension of Teflon.


What is the contact angle and what three variables does it depend on? What is surface tension? What goes into making a Zisman plot and what information can be extracted from one? What does the magnitude of the contact angle tell you about the interaction between the

liquid and the surface?

How will increasing number of carbons in a hydrocarbon affect the contact anglebetween the liquid and Teflon? Hint: Consider the changing intermolecular forces upon

increasing number of carbons and its effect on surface tension.

Experimental:

The procedure for this experiment is fully detailed in the handout.

Calculation Tips:

The calculations for this experiment should be straightforward.

References:

Fairbrother, Howard. Contact Angle Experiment.

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Cyclic Voltammetry

Introduction:

The goal of this experiment is to understand how cyclic voltammetry works and use it to

determine the concentration of acetaminophen in Childrens Tylenol and study the mechanism of

acetaminophen oxidation. Kissinger and Heinemans article details the fundamentals of cyclic

voltammetry well, but it does not take much time explaining coupled chemical reactions, whichis what this experiment studies. What you need to consider is the presence of anodic peaks and

cathodic peaks during a scan. If an anodic peak is present, then an oxidation has occurred. If a

cathodic peak is present, a reduction has occurred. By interplaying pH and scan rate,acetaminophen oxidation (shown below) will proceed/stop at certain points.


What are the three electrodes used during cyclic voltammetry and what is eachelectrodes function?

What type of waveform does cyclic voltammetry use and why? How does pH affect the oxidation of acetaminophen? What kind of information can be extracted from varying the scan rate of cyclic

voltammetry? Consider the competition between a chemical reaction and the speed atwhich the electrode is able to reverse its scan.

Experimental:

The procedure for this experiment is fully detailed in the handout.

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Calculation Tips:

The calculations for this experiment should be straightforward. Do not forget that

molarity has the units mol/liter, and can be converted into g/mL by using molecular weight

(g/mol).

References:

Fairbrother, Howard. Study of Electrode Mechanism by Cyclic Voltammetry.


12/13

Atomic Force Microscopy

Introduction:

The goal of this experiment is to learn about atomic force microscopy (AFM) and how it

works. You will collect images of a diffraction grating, ceramic surface (alumina), and silicon.

The force-approach measurements made for alumina and silicon will allow you to calculate the

relative stiffness of one material compared to the other.An AFM is made up of four basic components: a piezoelectric actuator, cantilever, tip,

and photodiode detector. A tip is attached to a cantilever, which is in essence a small coil spring.

The cantilever and attached tip hover over a sample that is placed on piezoelectric material(PZT). Since AFM measures height variations of a sample, the sample has to be moved with

respect to the tip. To do this, the PZT moves the sample in the X and Y direction. Various

interactions such as electrostatic, magnetic, capillary, and Van der Waals forces between thesample and tip cause movement of the tip and thus movement of the cantilever. As the cantilever

moves up or down based on the tip interaction with the sample, a laser that shines on the end of

the cantilever illuminates different parts of the photodiode detector because the reflection angleof the laser beam between the moving cantilever and detector changes. The change in laserreflection causes the photodiode to output a different voltage, which varies from an initial preset

voltage. Changes in voltage are translated by the photodiode as changes in cantilever deflection.

An AFM attempts to keep the voltage in the photodiode constant and thus the deflection of thecantilever constant (total force applied to the sample is also constant) through a feedback

mechanism. The changes in deflection angle of the cantilever received by the photodiode are

forwarded to the PZT. The PZT changes the orientation of the sample in the Z direction so thatthe initial deflection of the cantilever is restored and thus the initial preset voltage of the

photodiode restored. A computer translates the movement of the PZT required to keep the

cantilever deflection constant in the Z direction and from this, it creates a topographic image of

the sample under study. An AFM can also measure the force on the cantilever from the changesin reflection angle of the laser.

If you are having trouble understanding the interplay between the four components, many

websites on the internet explain how atomic force microscopy works.


What are the four main components of an AFM? What does an AFM measure? What kinds of forces occur between the tip and the sample? What benefits does AFM offer over other types of high-resolution microscopes?

Experimental:

This experiment mostly involves operating computer software. The other handout details

how the software is setup to take images.

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Calculation Tips:

The calculations required for the diffraction grating and ceramic surface should be

straightforward. When trying to count the particle density for alumina, make your best guess for

how many particles are in the image produced by the AFM and dont forget to take note of the

dimensions of the image you are looking at (you need to calculate particles/area).The relative material stiffness is approximated by the following equation

k~ kL S

S 1

where ksrepresents the sample spring constant (material stiffness), kLthe cantilever spring

constant (should be 0.15 N/m, check this with your TA), Scal

systhe slope of the force approachcurve for a calibrating sample, and Ssysthe slope of the force approach curve for the sample of

interest. To determine the slope of the force approach curves obtained, you need to graph force in

volts (y-axis) versus distance in nanometers (x-axis). The data you obtained will also include the

retrace of the tip (the tip approaches the sample, and then retracts), and you only need one of thetwo. So graph only the data up to the point where the tip approaches the sample and reaches a

very close distance. Remove the data for when the distance starts to increase again. The graphbelow is an example of what your graph should look like.

To calculate Scal

sysand Ssys, only take the slope of the slanted portion of the force-approach curve(red line in the graph above). The calibrating sample should be the sample with the larger slope.

References:

Fairbrother, Howard. Atomic Force Microscopy.

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