ConcentrationAbsorbance

0

0

0.00125

0.125

0.0025

0.279

0.005

0.552

Beer’s Law Plot

Standard

y = 111.36x – 0.0046

R² = 0.9992

0.6

0.5

Abosrbance

0.4

0.3

0.2

0.1

0

-0.1

0

0.001

0.002

0.003

0.004

Concentration of Bromine M

0.005

0.006

AbsorbanceTime

0.542

0.525

0.49

0.478

0.465

0.45

0.45

0.45

0.433

0.417

0.4

0.382

0.366

0.345

0.329

0.31

0.293

0.275

0.26

0.242

0.226

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

300

Concentration Time

Concentration

Time

0.004908405

0 -5.31681

0.004755747

15

-5.3484

0.004441451

30 -5.41677

0.004333693

45 -5.44134

0.004216954

60 -5.46864

0.004082256

75 -5.50111

0.004082256

90 -5.50111

0.004082256

105 -5.50111

0.003929598

120 -5.53922

0.00378592

135 -5.57647

0.003633261

150 -5.61762

0.003471624

165 -5.66313

0.003327945

180

-5.7054

0.003139368

195 -5.76373

0.00299569

210 -5.81058

0.002825072

225 -5.86922

0.002672414

240 -5.92477

0.002510776

255 -5.98716

0.002376078

270

-6.0423

0.00221444

285 -6.11276

0.002070761

300 -6.17984

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

300

second order

203.7322

210.2719

225.1516

230.7501

y = -8.43E-06x + 4.82E-03

R² = 9.77E-01

237.138

0.006

244.9626

244.9626 0.005

244.9626

254.479 0.004

264.1366 0.003

275.2348

0.002

288.0497

300.4857 0.001

318.5355

0

333.8129

0

50

353.9733

374.1935

398.2833

420.8617

451.5815

482.9141 p=0

2 1 21

time v 1/conc (second order)

y = 0.597x + 197.25

R² = 0.9398

400

Conc v Time (zero order)

350

300

250

200

150

100

50

0

100

150

200

250

0

50

y = -0.0022x – 5.3147

R² = 0.9648

100

150

lnConc/Time (first order)

-5.2

-5.3

Absorbance

06x + 4.82E-03

0

50

100

150

-5.4

-5.5

-5.6

-5.7

-5.8

-5.9

Time(s)

200

nd order)

200

200

250

250

AbsorbanceTime

0.555

0.519

0.472

0.370

0.331

0.281

0.230

0.180

0.130

0.070

0.021

0.002

0.002

0

15

30

45

60

75

90

105

120

135

150

165

180

Concentration

Time

0.005025

0.004702

0.00428

0.003364

0.003014

0.002565

0.002107

0.001658

0.001209

0.00067

0.00023

5.93E-05

5.93E-05

0

15

30

45

60

75

90

105

120

135

150

165

180

Concentration

Time

-5.2933

-5.3598

-5.45385

-5.69466

-5.8046

-5.96593

-6.16264

-6.40233

-6.71822

-7.30838

-8.37793

-9.73345

-9.73345

y = -3.00E-05x + 4.92E-03 conc

R² = 9.84E-01

0.006

0

15

30

45

60

75

90

105

120

135

150

165

180

second order

221

198.9993

212.6814

233.6551

297.2771 zero order

331.8236 p=0

389.916

474.6803

603.2503

827.3403

1492.761

4350

16872.73

16872.73

v time (Zero order)

0.005

0.004

0.003

0.002

0.001

0

0

-0.001

20

40

60

80

100

120

140

160

180

200

y = -0.0247x – 4.5509

R² = 0.8415

Time/ ln(Conc) (first order)

0

0

20

40

60

80

100

120

140

160

180

200

-2

-4

-6

-8

-10

-12

Time v 1/Con (seconder order)

20000

y = 74.945x – 3425.2

R² = 0.5122

15000

10000

5000

0

0

-5000

50

100

150

200

AbsorbanceTime

0.557

0.537

0.51

0.486

0.46

0.437

0.412

0.387

0.362

0.335

0.309

0.285

0.257

0.23

0.204

0.177

0.15

0.122

0.095

0.068

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

Concentration

Time

0.557041

0.537041

0.510041

0.486041

0.460041

0.437041

0.412041

0.387041

0.362041

0.335041

0.309041

0.285041

0.257041

0.230041

0.204041

0.177041

0.150041

0.122041

0.095041

0.068041

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

Concentration

Time

-0.58512

-0.62168

-0.67326

-0.72146

-0.77644

-0.82773

-0.88663

-0.94922

-1.016

-1.0935

-1.17428

-1.25512

-1.35852

-1.4695

-1.58943

-1.73137

-1.89684

-2.1034

-2.35344

-2.68764

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

second order

1.795199

1.862054

1.960626

2.057438

2.173718

2.288113

2.426941

2.583704

2.762116

2.984707

3.235813

3.508263

3.890425

4.347045

4.900968

5.648399

6.664831

8.193947

10.52174

14.69695

212

6

5

4

3

2

1

0

0

0

-0.2

Zero Order

0.6

y = -1.72E-03x + 5.65E-01

R² = 1.00E+00

-0.4

-0.6

-0.8

0.5

-1

0.4

-1.2

0.3

-1.4

-1.6

0.2

-1.8

0.1

0

0

50

100

150

200

250

300

0

time v 1/conc (seoncd order)

50

100

150

Time vs lnConc (first order)

50

100

150

y = 0.0136x + 1.4264

R² = 0.9165

200

250

y = -0.0047x – 0.5115

R² = 0.9764

200

250

AbsorbanceTime

0.456

0.42

0.412

0.404

0.394

0.386

0.373

0.36

0.344

0.333

0.32

0.3

0.289

0.27

0.25

0.228

0.203

0.183

0.155

0.147

0.107

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

300

Concentration

Time

0.004136

0.003813

0.003741

0.003669

0.003579

0.003508

0.003391

0.003274

0.00313

0.003032

0.002915

0.002735

0.002636

0.002466

0.002286

0.002089

0.001864

0.001685

0.001433

0.001361

0.001002

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

300

Concentration

Time

-5.48799

-5.56938

-5.5884

-5.60779

-5.63257

-5.65284

-5.68669

-5.72172

-5.7666

-5.79866

-5.83793

-5.90152

-5.93831

-6.00521

-6.08083

-6.1712

-6.28491

-6.38621

-6.54785

-6.59928

-6.9056

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

300

second order

cold 1 1 2

241.7716

262.2704

267.3068

272.5404

279.3778

285.0998

294.9153

305.4306

319.4492

329.8578

343.0684

365.5942

379.2916

405.5353

437.392

478.7618

536.4162

593.6034

697.7444

734.5646

997.8495

zero order

0.0045

0.004

0.0035

0.003

0.0025

0.002

0.0015

0.001

0.0005

0

0

50

100

150

200

y=

cold 1 1 2

time v lnconc (first order)

y = -0.004x – 5.3638

R² = 0.8991

0

0

50

100

150

200

250

300

-1

-2

-3

-4

-5

-6

-7

-8

Time v 1/conc (second order

y = -9.63E-06x + 4.19E-03

R² = 9.77E-01

1200

y = 1.8215x + 147.15

R² = 0.7615

1000

800

600

400

200

0

200

250

300

350

0

50

100

150

200

250

300

0.004x – 5.3638

R² = 0.8991

350

y = 1.8215x + 147.15

R² = 0.7615

300

350

AbsorbanceTime

0.095

0.06

0.022

0.008

0.006

0.006

0.006

0

0

0

0

0

0

0

0

Concentration

Time

0 0.000894

15 0.00058

30 0.000239

45 0.000113

60 9.52E-05

75 9.52E-05

90 9.52E-05

105 4.13E-05

120 4.13E-05

135 4.13E-05

150 4.13E-05

165 4.13E-05

180 4.13E-05

195 4.13E-05

210 4.13E-05

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

Concentration

Time

-7.01936

-7.45231

-8.33961

-9.08683

-9.25967

-9.25967

-9.25967

-10.0945

-10.0945

-10.0945

-10.0945

-10.0945

-10.0945

-10.0945

-10.0945

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

second order

1118.072

1723.839

4186.466

8838.095

10505.66

10505.66

10505.66

24208.7

24208.7

24208.7

24208.7

24208.7

24208.7

24208.7

24208.7

hot 1 1 2

Conc v Time Zero order

0.001

0.0008

0.0006

0.0004

0.0002

0

-0.0002

0

50

y = -0.0131x – 7.9824

R² = 0.7462

Time v lnConc (first order)

0

0

50

100

150

-2

-4

-6

-8

-10

-12

Time V 1/Con (second order)

y = -2.57E-06x + 4.33E-04

R² = 4.91E-01

nc v Time Zero order

30000

25000

20000

15000

10000

100

150

200

250

5000

0

0

50

100

150

(first order)

200

250

on (second order)

150

200

250

Laboratory 5 and 6 Determination of the Rate of a

Reaction and its Temperature Dependence

This experiment will extend over two weeks. In the first week we will

collect the data, in the second week we will analyze the data.

Background

The rates of chemical reactions and the conditions, which control them,

are important for many aspects of chemistry. They help to determine the best

conditions to perform certain reactions and also give insight into the elementary

processes of reactions. Consider a general reaction:

aA + bBàcC + dD

We can monitor how fast this reaction happens by measuring the rate of

disappearance of A, -dA/dt or B, -dB/dt or the rate of appearance of C, dC/dt or D

dD/dt. The rate of the reaction is defined in terms of the stoichiometric

coefficients as:

Rate of reaction = –

1 dA

1 dB 1 dC 1 dD

==

=

a dt

b dt c dt d dt

This accounts for the fact that reactants are disappearing (the negative sign) and

products are appearing and also that the rate of disappearance or appearance

depends on how many of each substance are involved in the reaction.

The rate of the reaction at a particular temperature depends on the

concentration of the reactants so that:

rate of reaction = k[ A]n [ B]m

(1)

where k is the rate coefficient, and n and m are typically the 0, 1, or 2. This

expression is known as the rate law. The exponents, n and m, are determined

experimentally by measuring how the rate of the reaction changes with the

concentration of the reactants.

Picture the reaction of acetone with bromine.

50

O

H

H

O

H

C

H

C

C

H

H

+

Br

Br

H+

H

H

Br

C

H

C

C

H

H

H

Br

In this case, the concentration of one of the reactants, Br2, can be measured

using a SPEC 20. If we measure the concentration of Br2 versus time the rate of

change or slope of the line will give us:

− d [ Br2 ]

= k[acetone]n [ H + ]m [ Br2 ] p

dt

H+ is included because this reaction does not occur unless acid is present, and

this was indicated by the H+ over the reaction arrow. The goal is to find the

exponents n, m, o, and the rate coefficient, k. With that information, the reaction

is understood, and a mechanism can be proposed.

Here is the general theory.

If we start the reaction with a large excess of acetone and H+, compared to the

concentration of the bromine, their concentrations do not change measurably

over the first few minutes so we can assume they are constant. To determine

the exponent for Br2, p, first assume the concentrations of H+ and acetone are

constant. Then the rate is:

− d [ Br2 ]

= k ‘[ Br2 ] p

dt

where k ‘ = k[acetone]n [ H + ]m

Rearrange equation 2 to get

− d [ Br2 ] = k ‘ [ Br2 ] p dt

If p=0, integration gives

51

− d [ Br2 ] = ∫ k ‘ [ Br2 ] p dt

∫

∫

− d [ Br2 ] = ∫ k ‘ dt

[ Br2 ]t − [ Br2 ]0 = −k ‘ t

and the concentration of bromine will linearly decrease with time.

Figure 1

Zero order reaction

0.0045

0.004

y = -7E-06x + 0.004

2

R = 0.9996

Concentration Bromine

0.0035

0.003

0.0025

0.002

0.0015

0.001

0.0005

0

0

50

100

150

200

250

300

350

400

450

Time

If p= 1 the integrated rate equation is:

∫

− d [ Br2 ] = ∫ k ‘ [ Br2 ] p dt

∫

− d [ Br2 ]

1

= k ‘ dt

[ Br2 ] ∫

ln[ Br2 ]t − ln[ Br2 ]0 = −k ‘ t

and the natural log of the concentration of Br2 decreases linearly with time.

52

500

Figure 2

First Order Reaction

0.001

y = -5E-06x + 0.0009

2

R = 0.9736

Concentration

0.0008

0.0006

0.0004

0.0002

0

0

20

40

60

80

100

120

140

160

Time

Figure 3

First Order Reaction

-6.8

-7

y = -0.008x – 6.905

2

R = 0.9995

Natural log Concentration

-7.2

-7.4

-7.6

-7.8

-8

-8.2

0

20

40

60

80

Time

53

100

120

140

160

It can be quite difficult to distinguish between the zero order reaction and the first

order reaction. However, if both concentration and the natural log of

concentration versus time are plotted, one graph will be straighter than the other.

It may be easier to determine this by adding a trendline in excel to both plots and

comparing the R value. R is a measure of how well the data fits to a straight line.

If R is 1.00, the line is exactly straight. In comparing two data sets, the one with

R closer to 1.00 is more accurately represented by a straight line.

If p = 2 the integrated rate equation is:

∫

− d [ Br2 ] = ∫ k ‘ [ Br2 ] p dt

∫

− d [ Br2 ]

1

= k ‘ dt

[ Br2 ]2 ∫

1

1

−

= −k ‘ t

[ Br2 ]t [ Br2 ]0

and the inverse of the concentration of Br2 increases linearly with time.

Figure 4

Second Order Reaction

0.0025

y = -4E-06x + 0.0016

2

R = 0.8558

Concentration

0.002

0.0015

0.001

0.0005

0

0

50

100

150

200

Time

54

250

300

350

Figure 5

Second Order Reaction

-6

-6.2

y = -0.0045x – 6.3875

2

R = 0.9635

-6.4

Natural log Concentration

-6.6

-6.8

-7

-7.2

-7.4

-7.6

-7.8

0

50

100

150

200

250

300

350

-8

Time

Figure 6

Second Order Reaction

2500

y = 5.1391x + 498.79

2

R = 0.9999

1/Concentration

2000

1500

1000

500

0

0

50

100

150

200

Time

55

250

300

350

To determine the reaction order for bromine, p in equation 2, we examine

how the concentration varies with time. If [Br2] versus time is a straight line, the

reaction is zero order in Br2. If ln [Br2] versus time is a straight line, it is first order

in Br2, and if 1/[Br2] versus time is a straight line, the reaction is second order in

Br2. For each case the slope of the straight line is k’, and in all cases C, the

constant of integration, depends on the initial concentration of bromine, and will

not need to be determined. As can be seen from the above plots, it is best to plot

concentration versus time, natural log of concentration versus time and the

inverse of concentration versus time, add a trendline to the data and compare the

values of R for these to make the final assessment. This will give the order with

respect to Br2.

To determine the reaction order for the acetone and the H+ vary the initial

concentrations of these reactants and see how they affect the reaction rate. If

we double the amount of acetone, and the rate does not change, the reaction if

zero order for acetone. If we double the acetone and the rate doubles, it is first

order in acetone, and if you double the acetone and the rate increases by a

factor of 4 the reaction is second order. The same will hold true for H+.

Procedure:

This experiment requires careful planning. Be sure you have assembled

everything you need and plan ahead. If you do not remember how to use the

SPEC 20 see the appendix.

First you will need to measure the absorbance of some known concentrations of

bromine and make a standard curve.

1. Turn on the spectrometer and let it warm-up for 15 minutes. Set the

wavelength to 395 nm and make sure it is zeroed. Take about 10 ml of each of

the three bromine standards. Measure the absorbance of the standards, and

record their concentrations. Make sure your standard curve is a straight line. Plot

absorbance versus concentration for Br2. This will allow you to convert

absorbance measured into concentration of Br2. You will use this later to

determine the concentration of bromine for your kinetics runs.

2. Label a small beaker and put about 15 mL of the 8M acetone solution in it.

Also take about 15mL of the 2M HCl solution, and about 50 mL of the 1x 10-3 M

bromine solution. Get 4, 10 mL volumetric flasks and label them one through

four. You will measure the rate for 4 different mixtures. To do this you must add

the following amounts of the reactants to the volumetric flasks and fill to the line

with distilled water. Each of these will be measured one at a time. Do not

prepare a sample until you are ready to take your readings.

56

Table 1.

Sample

1

2

3

mL Bromine

2.0

2.0

2.0

mL HCl

1.0

2.0

1.0

mL Acetone

1.0

1.0

2.0

distilled water

to the 10 mL line

to the 10 mL line

to the 10 mL line

3. Quickly mix together sample #1 in a 10 mL volumetric flask, by placing 2.0 mL

of the Br2 solution, 1.0 mL of the H+ solution, 1.0 mL of Acetone solution and

then adding distilled water to the 10.0 mL line. Cover it with a small amount of

parafilm and mix it thoroughly. Transfer the solution to a cuvette, place in the

spectrometer and measure the absorbance every 15 seconds for about 5

minutes or until the absorbance goes to zero.

4. Quickly mix together sample #2 in a 10 mL volumetric flask, by placing 2.0 mL

of the Br2 solution, 2.0 mL of the H+ solution, 1.0 mL of Acetone solution and

then adding distilled water to the 10.0 mL line. Cover it with a small amount of

parafilm and mix it thoroughly. Transfer the solution to a cuvette, place in the

spectrometer and measure the absorbance every 15 seconds for about 5

minutes or until the absorbance goes to zero.

5. Quickly mix together sample #1 in a 10 mL volumetric flask, by placing 2.0 mL

of the Br2 solution, 1.0 mL of the H+ solution, 2.0 mL of Acetone solution and

then adding distilled water to the 10.0 mL line. Cover it with a small amount of

parafilm and mix it thoroughly. Transfer the solution to a cuvette, place in the

spectrometer and measure the absorbance every 15 seconds for about 5

minutes or until the absorbance goes to zero.

6. Repeat step 3, that is sample 1, using solutions which are at 0oC.

7. Repeat step 3, using solutions which are at 40oC.

Analysis of data using EXCEL:

First start the program, in a windows system usually you use a double click.

The program opens to a fresh sheet. To move between sheets click on the tabs

on the bottom of the page.

57

The first step is to input some of your data. The easiest method to keep

everything straight is to use different sheets for your different kinetic runs. Use

the first sheet to analyze your standard curve. In the first column enter the

concentration of your standards. These were labeled on the container. Just type

in the number, and hit return. In the second column, type in the absorbances.

Now plot the line.

To make a graph in Excel 97, I have found the easiest method is to make sure

your x values are in one column and your y values are in the next column. Using

the mouse highlight your data, x and y for your standard curve. Then click on the

insert icon, then the chart icon, then select the scatter plot, and finally pick the

upper left plot.

This is your Beer’s Law Plot. You can make it look nicer. Remove the legend by

clicking on it and deleting it. Give your axis labels by clicking on the graph to

outline it. Then the chart tools menu should appear. Click on layout, then

58

Axis titles and insert the proper titles. Now your chart will appear like this:

0.4

A

b

s

o

r

b

a

n

c

e

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

Concentration of Bromine M

To fit the data with a straight line, click on the graph, then click the

layout menu again, then analysis, then click on trendline. A window will ask

what type-click on linear. After the trendline has been added right click on it. Go

to format trendline and display equation. To determine the goodness of the fit

also check display R-squared value on chart. The closer R2 is to 1.0 the

straighter the line. Click on okay. Now you have a plot of your standards and the

equation of the straight line, which fits it.

0.4

A

b

s

o

r

b

a

n

c

e

y = 121x + 0.001

R² = 0.99904

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

0

0.0005

0.001

0.0015

0.002

0.0025

Concentration of Bromine M

59

0.003

0.0035

This will give you the values you need to convert absorbance to concentration.

To analyze the first kinetic run: move the mouse to the bottom of the

page and click on sheet 2. Enter the absorbance in column A and your times in

column B. Use the top row of the column to label them: absorbance in a1, time

in b1 and concentration in c1. Now in column C you will change your

absorbance values into concentration. To do this you will use the values from

your standard curve on sheet 1. The fit to the data, your trendline, gives you the

slope and intercept to convert absorbance to concentration. Go to cell C2 and

type in it: =(A2-intercept)/slope, using the values of your Beer’s Law Plot. (This

takes the absorbance, subtracts the intercept, and divides by the slope of your

standard curve.)

60

Before you hit return, move the mouse to the lower right corner of the cell.

When you get a solid plus sign for the cursor, push down on the mouse button

and include as many cells as you have absorbance versus concentration data

sets. Now hit return. You should now have in column C the concentrations of

Br2 at each time.

Now plot concentration of Br2 versus time, (Outline column B and C, click

on the insert chart etc. ) Is the data a straight line? If it is a straight line the

reaction is zero order with respect to Br2. Because this is very important for the

analysis of all our data, we need to be certain of the order with respect to Br2. So

for the first run you will check the other orders too.

To determine if it is first order in Br2: Plot ln concentration Br2 versus

time. The easiest way to do this is to copy the times into column D. (Move the

cursor with the mouse to the top of column B. Click until the column is

61

highlighted. Go to the edit menu and hit copy. Go to cell D1 click, back to the

edit menu and hit paste. Put ln Br2 concentration in column E. To do this go to

cell E2 and type in it:

=ln(C2)

Before you hit return expand the cell to accommodate your entire data set. Hit

return. Plot column D versus column E. Is it a straight line?

Is it second order? To plot 1/[Br2] versus time, copy the times into

column F. In cell G2 type =1/C2, expanding so all the data is calculated. Plot

column F versus column G. Is it a straight line?

Examine the three graphs. If the first graph gives the best straight line,

the reaction is zero order in Br2, which means p=0, and the rate is simply equal to

the slope of line which fits the data. If the plot of lnBr2 versus time is the

straightest, the reaction is first order in Br2, and p=1. The rate of the reaction is

then equal to the slope of the line lnBr2 versus time. If the plot of 1/Br2 versus

time gives the straightest line, p=2 and the slope of the line 1/Br2 versus time

gives the rate of the reaction.

− d [ Br2 ]

Remember the rate law is:

= k[acetone]n [ H + ]m [ Br2 ] p

dt

Now we know p, to find n and m:

If p=0, plot concentration of Br2 for your other kinetic runs. If p=1 plot ln

concentration Br2 versus time, and if p=2 plot 1/concentration of Br2 versus time.

Using the trendline find the slope of the line, which is the straight line for each

kinetic run. This is k’. Calculate the initial concentrations of all species for all the

different runs. Construct a table similar to those in your textbook. Compare the

rates and concentrations for the different runs and determine the rest of the rate

law: that is determine n and m. Using the rate law and the rates find the rate

constant, k.

Sample

1

2

3

4

[Br2]

[Acetone]

[H+]

Reaction rate

For your report include printouts of all the work done on Excel and the final rate

law and value for the rate coefficient, k.

k is determined using the rate equation and substituting the known values of

concentration and rate and the determined values of n, m and p.

− d [ Br2 ]

= k[acetone]n [ H + ]m [ Br2 ] p

dt

62

Temperature dependence

The rate coefficient also depends on the temperature.

The rate coefficient depends on the temperature as:

k = Ae-Ea/RT

(10)

If k is measured at two different temperatures EA can be determined by

solving,

EA = – R(ln(

k2

1 1

)) (

– )

k1

T2 T1

(11)

If more than two temperatures are measured plot ln k versus 1/T in Kelvin

and the slope of the line = -EA/R.

Analyze your cold and warm sample runs assuming the rate law determined at

room temperature. Solve each for k.

Determine Ea and then A can be determined by equation 11 or from intercept of

the plot of ln k versus 1/T.

For your report give the rate law for the reaction, EA and A.

Safety and Disposal:

Bromine and HCl are irritating. Acetone is absorbed by skin. Contact should be

avoided with all solutions. All solutions should be disposed of in the receptacles

provided.

63

Measurement of Physical Properties

In any measurement it is important to know the precision of the

measurement and also its accuracy. All physical measurements should be made

as precisely and accurately as possible. Maximizing the precision of a

measurement is accomplished by using the most precise equipment available,

and using it properly. If possible it is also wise to compare your result with either

a known or theoretical value.

Significant Figures

When calculating a result from more than one measurement it important to

retain the uncertainty information from all the measurements. There is an entire

field of mathematics devoted to this topic. In this course we use the relatively

simple method of significant figures. A summary of the rules with examples:

Addition and subtraction: line up the numbers to be added or subtracted;

the answer is truncated to the decimal place of the least precise number.

Ex. 12.1 + 2.345 = 14.4

15.678 – 2.2 = 13.5 (notice I rounded up)

Multiplication and Division: Significant Figures in the answer are equal to

the number of significant figures in the least precise number.

15.6 x 2.1 = 31

16.789 ⎟ 25.67432 = 0.65392

25.1 x 3.00 = 75.0

Note zeroes before another number as in 0.65392 do not count. In the

middle and the end they count.

Laboratory Notebooks

In this course you will be required to keep a laboratory notebook. A good

laboratory notebook is an accurate record of everything, which occurred in the

lab. In patent disputes a good lab book versus an inaccurate lab book can mean

millions of dollars. In this course it may mean hundreds of points. Before the lab

you will be required to prepare a lab report outline to be completed during the lab

session. Each lab report will contain:

7

Title and Purpose

1. Procedure and Observations

2. Data and Calculations

3. Results and Conclusions

4. Answers to questions in manual

An example of a lab report is shown below:

1. Title: Density of liquid and a solid.

Purpose to measure the density of a liquid and an unknown solid.

2. Procedure:

Observations

Part 1 Liquid

Unknown # 5 smells like gasoline

Weigh an empty 10.0 mL volumetric flask

Fill with unknown liquid.

Weigh filled volumetric flask

Mass of empty flask = 12.032 grams

Mass of full flask = 18.685 grams

Part 2 Solid

Part 2 Unknown #12 Shiny orange color

Fill a graduated cylinder with about 25 mL of

water

Measure precisely volume of water.

Volume of water = 24.83 mL

Volume of water + metal = 28.53 mL

Mass of Dry metal = 46.409 grams

weigh dry solid sample

Data and Calculations:

Part 1 Liquid:

Density = Mass / volume

Mass of liquid = mass of liquid + flask – mass of flask = 18.685 grams – 12.032 grams = 6.652

grams.

Density = 6.652 grams / 10.000 mL = 0.6652 g/mL

Part 2 solid

volume of solid = volume of solid + water – volume water = 28.53 mL – 24.83 mL = 3.70 mL

density = 46.409 g/3.70 mL = 12.5 g/mL

Results and Conclusions:

The density of the liquid was determined to be 0.6652 g/mL by comparison with the

density table in the CRC it appears the sample could be hexane, which has a density of 0.660

g/mL

The density of solid was 12.5 grams / mL. The solid looked like copper, but the density of

copper from the CRC is: 8.94 g/mL, which is significantly less than my unknown sample.

Therefore although the sample looks like copper it must be something else.

8

In this example, the data is recorded in the section with the observations,

and the procedure is recorded in one column and the observations are recorded

in an adjoining column. This allows you to record your observations with the

correct section of the procedure. In some experiments, the type and volume of

data is better recorded in a table. In this case it should follow the procedure

section. You should still leave room in the procedure section for observations.

One of the objectives of this course is for students to learn how to determine

what data they need to collect, and how to organize it. For some experiments

explicit instructions for organizing the data and calculations will be given, but for

other experiments you will need to determine this for yourself before class. In the

case of repetitive calculations tables are necessary. A spreadsheet such as

Excel can be used, and instructions are included for the Reaction Rate

experiment. All your calculations must follow the rules for significant figures and

every value must have a correct unit. A spreadsheet or calculator will not

determine the correct number of significant figures; it is up to you.

When determining the results and conclusions, there are some things to

keep in mind. The results should relate back to the purpose. Address directly if

the purpose was fulfilled. If the result is a number clearly restate what it is and

the unit for the number. If possible compare your result with a literature value. If

you received no result or an unexpected result, give some scientific explanation

of this. Human error is not a good explanation, because the experiment or

section, which was in error, should be repeated. Thoroughness is important but it

is not necessary to write everything you know about density or volume etc.

To be ready to use all the lab time efficiently, before lab class you should

have completed the purpose, procedure and arranged the data table or written

down what you need to measure.

Lab Instructors may have additional report requirements.

9

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