Viscosity of Liquids: Methanol and Water
Colin McGuire
January 24 and February 2, 2012
March 2, 2012
1
1
Abstract
This experiment was done in order to determine the viscosity of mixtures of methanol and water of concentrations 20, 40, 60, 80, and 100 % methanol by volume. An Otswald viscometer and a stop watch were used to
record the time of flow for the reference fluid, water, and each mixture. This time was then used in conjunction with the density of our reference liquid and mixture to in order to calculate the viscosity of the mixture
using equation 1. The viscosity of each solution was used to find the fluidity of the solution in equation 2. The
fluidity and viscosity of the ideal solutions were calculated. The viscosities of the methanol solutions were
g
1.36, 1.64, 1.55, 1.19, and 0.5656 centipoisse ( cms
2 ) for the solutions of 20, 40, 60, 80, and 100 % respectively.
2
Procedure
This procedure was performed from a handout that is labeled Transport Properties and Chemical Kinetics.
Experiment 17: Viscosity of Liquids, Part I: Low viscosities. The procedure we used was slightly different in
that we only used the methanol and water section and didnt use the toluene and p-xylene solution. A constant temperature bath was brought to 25 degrees Celsius and an Otswald viscometer was inserted. Water
was added and pipetted up past the start line. The time is took for the solution to flow from the top band
to the bottom band was recorded. Water was the reference sample and runs were conducted until the time
of flow agreed within 0.2 seconds. When switching samples the viscometer was washed with soap and water
and dried with acetone and suction. This same procedure was followed for each sample.
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Data Collected
The time of flow data was collected for water moving through the viscometer, which is our reference liquid,
and is presented in table A. The time of flow data for each methanol mixture, table B was used with the
water average time in equation 1 to calculate the viscostiy. For all of the tables the averages were calculated
using the three values that agreed within 0.2 seconds. The densities used were those at 25 degrees Celsius.
Within this equation is the viscometer constant, k, which is all of the data for the reference liquid. This value
mL
is 1.48e−4 cms
2 . It was obtained from running water. With this value equation 1 is reduced to equation 3.
The viscosities were used to find the fluidities using equation 4 . The mole fractions of methanol and water
and the viscosities of pure methanol and water were used to calculate the ideal viscosities of the solutions
using equation 5. Then the mole fractions and viscosities of pure water and methanol were used to calculate
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the ideal viscosities of the solutions. The mole fractions were calculated based on the volume of methanol
in 10 mL of solution with water. The density of methanol and water at 25 degrees Celsius was used. These
are presented in table C.
Run
1
2
3
4
5
6
7
8
Average
Table A:
20%
MeOH
Run
Water
Time (s)
11.22
61.97
57.38
62.36
62.38
61.96
62.02
62.12
61.98
Time of Flights for water
Time
(s)
1
98.04
2
91.24
3
94.59
4
94.78
5
94.17
Average 94.51
Table B: Time of
40%
MeOH
Run
1
2
3
4
Time
(s)
188.06
117.31
117.41
117.76
60 %
MeOH
Run
Time
(s)
114.56
115.05
115.04
115.06
1
2
3
4
80 %
MeOH
Run
1
2
3
4
Time
(s)
93.6
93.53
93.36
93.46
Average 117.49 Average 115.05
Average 93.45
Flights for methanol and water mixtures
Solution Measured
Viscosity
(cP)
20%
1.36
MeOH
40%
1.64
MeOH
60 % 1.55
MeOH
80 % 1.19
MeOH
100 % 0.5656
MeOH
Table C
Measured
Fluidity
(cP −1 )
0.7353
χM eOH χH2 O
0.1023
0.6098
100 %
MeOH
Run
1
2
3
4
Average 48.67
0.8977
Ideal
Fluidity
(cP −1 )
1.189
Ideal
Viscosity
(cP)
0.8410
0.2331
0.7669
1.27
0.7853
0.6452
0.4061
0.5939
1.385
0.7220
0.8403
0.6458
0.3542
1.540
0.6495
1.768
1.0
0
1.768
0.5656
3
Time
(s)
48.63
48.65
48.69
48.66
3.1
Calculations
η=(
ηr
)ρt
ρr tr
(1)
1
η
(2)
F =
η = kρt
(3)
Where k is the viscometer calibration constant, 1.48e−4
F = χA FA + χB FB
η=
4
χA
ηA
1
+
χB
ηB
(4)
(5)
Discussion
This experiment was successful in measuring the viscosities of pure liquids. This is known by the percent error
of the pure substances. The percent error of the calculation of pure methanol is 8.56 %. The calculations of
ideal fluidity were not accurate compared to the measured values. Tables D and E show the percent errors
for these calculations. These large percent errors show that these solutions do not behave ideally. In this
case the behavior of these solutions is not ideal making these equations not applicable. The effect of mixing
methanol and water is actually making the resulting solution more viscous than either of the two liquids
separately. This means that the intermolecular forces of the liquids are strongly interacting with each other.
This prevents sliding of the molecules past each other and results in a more viscous fluid. Because the fluidity
is very far off using the ideal case approximation it is valid to conclude that solutions of methanol and water
are not at all ideal. If the calculated and ideal fluidities were close their ratio would be close to 1. In this
case the ratio of the fluidities are much less than from 1 as shown in Table F. This experiment was not very
successful in measuring the viscosities of mixtures as seen in Table G. The percent differences of these values
is incredibly high indicating that this is not a good way to measure the viscosity of a solution.
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Solution Measured χM eOH χH2 O
Viscosity
(cP)
20%
1.36
0.1023
0.8977
MeOH
40%
1.64
0.2331
0.7669
MeOH
60 % 1.55
0.4061
0.5939
MeOH
80 % 1.193
0.6458
0.3542
MeOH
100 % 0.5656
1.0
0
MeOH
Table D: Percent Error in Ideal calculation
Solution Measured
Fluidity
(cP −1 )
20%
0.7353
MeOH
40%
0.6098
MeOH
60 % 0.6452
MeOH
80 % 0.8403
MeOH
100 % 0.5656
MeOH
Table E: Percent Error
χM eOH
χH2 O
0.1023
Ideal
Viscosity
(cP)
0.8410
Percent
Error
(%)
61.71
0.7853
108.84
0.7220
114.68
0.6495
83.21
0.5656
0
of viscosities.
0.8977
Ideal
Fluidity
(cP −1 )
1.189
Percent
Error
(%)
38.16
0.2331
0.7669
1.27
52.12
0.4061
0.5939
1.385
53.42
0.6458
0.3542
1.540
45.42
1.0
0
1.768
0
in Ideal calculation of fluidities.
Solution Measured CRC
Percent
Viscosity
Viscosity
Error
(cp)
(cp)
%
20%
1.36
0.822
65.4
MeOH
40%
1.64
0.753
117.8
MeOH
60 % 1.55
0.684
126.6
MeOH
80 % 1.19
0.616
93.2
MeOH
100 % 0.5656
0.547
3.40
MeOH
Table G: Measured viscosities versus the CRC handbook value and percentages of that value.
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