GMU Determination of the Rate of a Reaction and its Temperature Dependence Lab Report

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