Unknown #2IR

Proton

MS

M+ 94

Chem 410A

Lab Quiz 8 – 1

Fall 2020

Lab 8: Lab Quiz

Part I. Testing the Value of the Intercept.

Put your work in Worksheet 1

A. According to Beerβs Law, the absorbance, A, of a solution of an absorbing species, B, is

proportional to its concentration [B]:

π΄ = ππΏ[π΅]

The molar absorptivity, ο₯, is a characteristic property of the solute and L is the path length of

the sample in the spectrometer. The slope of a graph of A vs [B] will be equal to ο₯L, and as

long as there are no absorbing impurities in the sample, the intercept will be zero (A = 0 when

[B] = 0). You will be given absorbance vs concentration data in class. Using this data,

calculate the slope, intercept, and uncertainties in both. Type the results with uncertainties and

units in a text box. From the slope and the path length (which you will be given), determine

the value of ο₯ with uncertainty. Type the result with units and uncertainty in the text box.

B. To test whether the intercept is actually zero, one computes the t-statistic,

π‘=

π β π0

ππ

b is the intercept, bo is the expected

(true) value for the intercept and ο³b

is the uncertainty in the intercept.

and compares it with the t distribution for f degrees of freedom (f = N-2 for a straight line).

The distribution for 95% probability is given in the table. If the calculated t-statistic is less

than that given in the table, then the intercept is considered to be equal to the true value at the

95% confidence level.

t-table for 95% probability

level. Compare the t-statistic

calculated for the intercept and

compare with this number.

df

1

2

3

4

5

6

7

t-statistic

12.7062

4.302653

3.182446

2.776445

2.570582

2.446912

2.364624

Using the results you obtained in part A, calculate t. Can you say that A = 0 when [B] = 0

with 95% confidence? Type your answer in the text box.

1

Chem 410A

Lab Quiz 8 – 2

Part II. Numerical Integration of a Spectral Band

Fall 2020

Put your work in Worksheet 2

Information about a compound can be obtained by measuring absorption spectra or emission

spectra. In each case, the peak wavelength of the spectral band is related to the energy

difference between the ground and excited electronic state. The area under the spectral band

is related to the strength of the transition in the absorption spectrum, and the quantum yield in

the emission spectrum. Both of these topics will be addressed in the lecture class. In this part

of the project you will be given data for either an absorption spectrum or emission spectrum.

Plot the data and determine the area under a spectral band using numerical integration. Type

the result with units in a text box.

Part III. Using Solver to Evaluate an Equation without an Analytical Solution.

We have used Solver to fit a calculated curve to data, but it can also be used to solve an

equation that is difficult to solve analytical. For example, it is straightforward to calculate the

pressure using the van der Waals equation when you know the molar volume, temperature,

and the constants a and b:

π=

π
π

π

β 2

ππ β π ππ

ππ =

π

π

On the other hand, calculating Vm when p, T, a, and b are known is more complicated, but

Solver will do this for you quite easily. Place the known pressure in one cell. Then type the

equation for p in the next cell (referring to the values for Vm, R, T, a, and b in other cells). In

the third cell, type the squared deviation of the known and calculated pressures. Use Solver to

minimize the squared deviation with Vm allowed to vary. Here is a problem to try before the

lab class class:

Practice: Find Vm for argon when p = 1 atm, T = 298 K, R = 0.08206 atm L/K

mol. The constants for argon are a = 1.337 atm L2/mol and b = 0.0320 L/mol.

You should get an answer of Vm = 24.43 L/mol.

You encountered one-dimensional tunneling in Chapter 7 of Atkins. The transmission

probability T of a particle of mass m with energy E through a rectangular barrier of energy Vo

and width W is given by the equation

(π π
π β π βπ
π )2

π = {1 +

}

16π(1 β π)

β1

π=

πΈ

ππ

π
=

{2π(ππ β πΈ)}1/2

β

In this project, you will be asked to find the energy E required to obtain a specific

transmission probability T. Values for T, Vo, W and m will be given. Place your final answer

with units in a text box.

ο Save your project as lastname_8.xlsx and send your file to kpeterson@sdsu.edu

2

Lab 8, Part 1

[dye]/mM

0.23

0.76

1.25

1.86

2.68

A

0.0252

0.112

0.208

0.289

0.431

L = 10.00 Β± 0.02 cm

Lab 8, part 2

wavenumber (cm-1)

16025.50465

16052.00442

16078.59828

16101.46913

16128.24157

16155.11115

16182.07681

16209.14226

16232.41843

16259.66559

16287.01247

16314.45962

16338.06553

16365.69824

16393.43278

16421.26971

16449.2096

16473.23883

16501.37095

16529.60599

16557.94619

16582.32125

16610.85612

16639.49782

16668.24695

16692.97359

16721.92161

16750.97877

16780.14568

16805.23153

16834.60341

16864.08335

16893.67543

16919.13009

16948.93162

16978.84536

17008.8737

17034.70353

17064.94417

17095.3013

17121.41417

17151.98708

17182.67838

e (M-1cm-1)

8.40001868

36.709867

19.3525531

47.5509964

48.9978388

39.4259574

-33.551587

22.9460519

24.9406664

6.76992557

75.9071806

41.935649

22.8630925

56.5388233

36.1465464

59.403418

47.3955399

46.741923

67.0672591

90.1113943

62.6588947

38.7018779

117.614186

33.3883813

59.5200599

108.096201

146.016347

124.687373

119.271643

157.449043

155.427751

103.784372

207.014005

160.598292

204.767322

288.790214

255.38654

285.101963

314.316077

352.48196

364.239322

404.60988

466.476759

17213.48695

17239.98962

17271.02062

17302.17084

17328.96584

17360.34217

17391.83972

17423.45918

17450.65934

17482.51002

17514.48467

17541.99066

17574.19854

17606.53247

17638.9951

17666.92244

17699.62365

17732.45381

17760.69929

17793.77209

17826.97799

17855.54511

17888.99781

17922.58393

17951.48016

17985.31733

18019.29221

18048.52126

18082.74955

18117.11792

18146.68757

18181.31377

18216.0825

18245.99666

18281.02977

18316.20586

18346.47059

18381.91571

18417.50634

18448.12989

18483.99432

18520.00684

18550.99349

18587.28257

18623.72449

18655.08285

18691.80629

512.237396

558.300745

639.865442

731.031306

775.790975

810.046831

945.148401

1072.94606

1133.17996

1331.43772

1427.71678

1544.35888

1757.87246

1929.89505

2155.92434

2433.45055

2632.68285

2970.65744

3175.41158

3527.34776

3929.8854

4420.42656

4829.81402

5416.4223

5872.08867

6514.08086

7219.699

8006.41093

8879.71187

9828.46469

10697.9253

11716.1607

12921.7982

14192.0986

15697.7994

17116.7934

18440.7645

20103.8263

21968.4309

23899.5057

25728.5065

27914.3815

29680.5488

31836.8122

34026.1757

36560.9449

39118.3894

18728.68532

18760.41776

18797.58339

18834.90739

18867.02284

18904.63865

18937.00787

18974.92112

19012.99531

19045.75911

19084.13396

19122.67269

19155.83831

19194.68547

19228.11511

19267.27213

19306.60034

19340.44411

19380.08566

19419.90156

19454.16718

19494.3046

19528.84748

19569.31151

19609.95296

19644.93083

19685.90386

19721.16768

19762.47755

19803.97043

19839.68171

19881.51785

19917.52414

19959.70659

20002.07785

20038.54583

20081.27007

20118.0437

20161.12534

20204.40186

20241.65202

20285.29288

20322.85606

20366.86588

20411.0769

20449.13331

20493.71927

41390.1305

43099.1681

45525.5564

47612.2611

49843.98

51513.5842

52854.3521

54252.8568

55246.1803

55936.8698

56433.8118

56313.1236

56059.5478

55442.5919

54676.8937

53376.7532

51598.9609

50083.8658

47958.1703

46429.0603

44826.6797

42988.718

41126.1826

39490.976

38069.7454

37166.3714

36118.4097

35261.8481

34548.2215

34022.0172

33770.2283

33560.8434

33520.9085

33631.1047

33804.0268

34040.3307

34475.3733

34722.033

35180.6625

35708.3227

36062.3663

36401.6519

36597.8807

36706.7795

36645.9927

36384.25

36027.786

20532.10021

20577.06717

20615.77679

20661.12967

20706.6943

20745.91596

20791.8729

20831.43543

20877.79108

20917.69626

20964.45581

21011.43298

21051.87687

21099.2661

21140.06415

21187.87225

21229.02914

21277.25889

21318.78077

21367.43777

21416.32858

21458.42084

21507.74631

21550.21605

21599.98486

21642.83575

21693.05244

21736.28962

21786.96171

21830.59041

21881.72264

21933.10523

21977.34834

22029.20079

22073.84918

22126.17796

22171.23722

22224.0474

22269.52473

22322.8245

22368.7242

22422.5204

22468.84683

22523.14795

22569.90865

22624.71869

22671.91979

35451.4289

34599.956

33731.3269

32439.9949

31169.3868

29819.9383

28510.6847

27215.6408

25730.269

24387.4299

23075.5731

21659.4127

20782.5436

19709.005

18713.6266

17902.9597

17222.5448

16685.7745

16109.9951

15618.957

15108.1758

14797.4794

14471.9052

14230.4741

13966.3262

13696.9141

13435.011

13237.1821

12924.7871

12700.0574

12352.3806

11772.3746

11326.489

10814.8559

10459.1584

9910.08898

9271.49644

8686.8182

8203.26825

7712.29153

7308.38048

6800.52426

6306.06971

5915.06183

5608.75248

5258.82325

5005.70635

22727.24751

22782.85543

22830.7464

22886.88336

22935.23079

22991.90273

23040.71318

23097.92943

23147.20792

23204.97468

23254.72963

23313.05488

23363.29155

23422.18677

23472.91221

23532.38238

23583.60542

23643.6573

23695.38529

23756.02917

23808.26788

23869.51429

23922.27131

23984.1275

24037.41057

24099.88567

24153.70448

24216.80604

24271.16689

24334.90798

24389.81728

24454.20583

24509.67559

24565.40494

24630.75663

24687.0572

24753.0792

24809.96166

24876.66434

24934.13585

25001.53169

4676.61011

4444.70236

4248.24812

4060.25089

3902.94322

3728.02099

3550.33645

3431.78194

3287.61908

3148.82957

3016.77517

2842.7738

2688.41298

2531.75585

2429.45061

2246.72597

2100.33331

1969.89687

1832.62013

1689.45593

1596.79951

1475.46783

1354.98976

1253.32681

1193.00052

1116.08154

1018.69742

939.254523

920.981361

868.448789

847.335196

774.480123

744.985666

698.473882

650.864963

651.780871

638.329961

587.122073

597.007834

554.621885

553.822227

Lab 3, Part 3. Use Solver to find the solution to this problem. Show all of your work in Worksheet 3.

In class, you may have encountered the one-dimensional tunnelling of a particle of mass m with energy

E through a rectangular barrier of energy Vo and width W. The equation for the transmission probability

T through this barrier is given by the equation

β1

π π
π β π βπ
π 2

πΈ

2π(ππ β πΈ) 1/2

π = 1+

π=

π
=

16π(1 β π)

ππ

β

Find the energy E required to obtain a transmission probability of 0.75 when Vo = 2.0 eV, W = 1.5 x 10

m), and the mass of the particle is 9.109 x 10-31 kg. Recall that Δ§ = h/2p = 1.055 x 10-34 J-s. Be sure to

include the eVβ joules conversion constant in the equation to make sure the units work out (1 eV =

1.6022 x 10-19 J). Solver does not do well varying a very small number, so have it vary the energy before

the conversion to joules. To check your calculations, note that kW should be between about 0.1 and 1.

work in Worksheet 3.

e of mass m with energy

e transmission probability

= 2.0 eV, W = 1.5 x 10-10

s. Be sure to

units work out (1 eV =

it vary the energy before

etween about 0.1 and 1.

Format Shape

2.

1

7:01

10:30

1x

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