PARTIAL MOLAR VOLUMES
HYDROCARBON PRODUCTS
AND
A
CASE
INVOLVING
MIXTURES
OF
Authors: Kim Lian Kuah, BSc, Chin Chin Lim, MSc, Michael MK Tay, PhD
SUMMARY
This forensic investigation was based on the concept of partial molar volumes and how this
physical phenomenon affected the resultant volume when two petroleum products were mixed.
Experimentally, through the precise and accurate determination of densities in a temperate-stabilized
environment, we were able to easily determine to a high precision, small deviations in volumes from
the simple additive value when two petroleum products were mixed.
Key-words: partial molar volumes, density, petroleum products
INTRODUCTION
Our Laboratory was requested to provide expert opinion for a dispute between a buyer and a
supplier concerning an alleged shortfall in the quantity of naphtha delivered by the supplier’s oil tanker
to the buyer’s bunking terminal. After delivery, the buyer refused to pay the supplier, claiming that the
quantity of naphtha stipulated in the contract was not delivered.
This dispute arose because at the time the tanker berthed at the receiving terminal, the storage
tank already had a known significant quantity of mogas. Without prior emptying of this mogas, naphtha
was transferred from the tanker to this storage tank, resulting in a combined volume that did not match
the simple addition of the original volumes of mogas and naphtha. The supplier denied the purchaser’s
charges of shortfall, claiming a contraction of volume when mogas and naphtha were mixed. The
arbiter in this dispute was the Customs and Excise Department. Samples of mogas and naphtha were
taken by officials of this department for testing. Approximately a litre each of mogas and naphtha in
metal tins were submitted to the Laboratory for the investigation.
Non-ideal solutions and partial molar volumes
Molar volumes are a measure of molecular volume plus any free space between molecules.
When a solution is formed from its components, unless this solution is ideal (no heat or volume
changes on mixing), the final volume is not simply the sum of the constituent volumes. Volume
changes nearly always occur on mixing. For instance, in binary mixtures, it is rare to find a mixture
with V = n1 V1 + n2 V2 where V is the total volume of the mixture, n1 and n2 are the number of moles of
components 1 and 2, and V1 and V2 are the molar volumes of the components 1 and 2.
For non-ideal binary mixtures, V = n1 v 1 + n2 v2 where v1 and v2 are the partial molar volumes
of the two components. The partial molar volume of a substance in a mixture of some general
composition is defined as the increase of volume that occurs when a mole of the substance is added to
an indefinitely large sample of the solution.
Although molar volumes are definitely positive, partial molar volumes need not be. In nonideal solutions, expansion or contraction of volume may occur when components are mixed. Mixing of
introduces new intermolecular forces (attractive and repulsive) and disrupts the structures, solvation
effects and intermolecular forces of the original constituent liquids resulting in either a collapse or
dilation.
Theoretical calculations required for partial molar volumes are complicated even for binary
mixtures and would not be practical for mogas and naphtha which are multi-component petroleum
products each containing hundreds of hydrocarbons. It is similarly not practical to determine the molar
fractions of the many components in these complex products.
We adopted a simple approach of mixing different weight/weight proportions o f mogas and
naphtha and calculating the resultant volume of the mixture. Deviations from the expected ideal
addition of the two original volumes were easily and accurately obtained.
MATERIALS & INSTRUMENTATION
·
·
·
·
·
·
Shimadzu QP5050 GC/MS with DB-1 capillary column
A&D electronic weighing balance
Anton Paar DMA 48 density meter
DI water for calibrating the density meter
Hexane and acetone for rinsing
Borosilicate glassware
METHODS
1) GC/MS Analysis
The mogas and naphtha samples were first analyzed by GC/MS to determine their individual
compositions. Mogas appeared as a slightly yellowish oil, and naphtha as a colorless oil. These samples
were diluted in carbon disulfide solvent prior to injection.
GC/MS operating conditions:
· Column:
· Linear velocity:
· Injection:
· Injector temperature:
· Temperature programming:
v Initial temperature:
v Ramp rate:
v Final temperature:
· Detector temperature
· Mass range :
DB-1, 30 m, i.d. 0.25 mm, 0.25 mm film thickness,
35 cm/s, helium
Split ratio 100
o
270 C
o
40 C, hold 2 min
o
10 C/min
o
290 C, hold 3 min
o
230 C
35-350 amu
2) Preparation of mixtures
Approximately 10-g mixtures of mogas and naphtha were prepared in mass ratios of
approximately 20:80, 40:60, 50:50, 60:40 and 80:20.
Evaporation effects during preparation were reduced by using a syringe with volumetric
graduations to sample the two liquids directly from the tins, introducing them one at a time into a
mixing vessel of minimum headspace, and stoppering in between transfers. The quantity of liquid
drawn up in the syringe was estimated by calculating volumes based on the desired mass and the
measured densities of the mogas and naphtha. At all proportions, the mogas and naphtha were found to
be completely miscible as expected.
Mixture
1
2
Mogas (g)
8.0364
6.1837
Naphtha (g)
2.0083
4.1427
Total mass (g)
10.0447
10.3264
3
4
5
5.0138
4.1624
2.1072
5.1811
5.9940
8.0155
10.1949
10.1564
10.1227
3 Density measurements
o
The DMA 48 density meter was set at a thermostating temperature of 20 C and allowed to
warm up for 30 minutes. It was then calibrated using a two-point calibration with air and DI water. At
o
20 C, the densities of air and water are 0.001204 g/mL and 0.9982 g/mL respectively.
A b o u t 2 mL of the mogas-naphtha mixture was drawn into a 10 mL syringe and
approximately 0.7 mL was injected into the U-tube of the density meter. Sample introduction was
carried out slowly and carefully to avoid introducing bubbles into the U-tube. The density reading was
taken after two minutes when the temperature of the sample had stabilized. The liquid was then
expelled from the U-tube, which was rinsed several times using hexane, followed by acetone, and air.
Care was taken to ensure that the U-tube was completely dry by flushing with air until the measured
density corresponded to the density of air.
RESULTS
1) Composition of mogas and naphtha
GC/MS analysis indicated that mogas was a petroleum product of the C5 to C11 range mainly
straight-chained aliphatic and alicyclic hydrocarbons. Naphtha was a petroleum product of the C5 t o
C10 range containing mainly aromatic hydrocarbons (toluene and pseudo-cumene).
2) Density measurements and calculations of volumes
The introduction of a fluid into the oscillating sample tube alters the mass of the tube,
resulting in a change in oscillating frequency. This change is used by the meter to calculate the density
of the fluid.
As mass is conserved when the two liquids are combined, the resultant volume can be easily
calculated from the total mass divided by resultant density of the mixture. The densities of mogas and
naphtha were also individually determined. These obtained values were used in combination with each
known weighing of mogas and naphtha to determine the expected ideal-case final volume of each
mixture, based on the simple addition of the original volumes.
Expected
volume of
mixture
(ideal solution)
Difference in
volume
(between
actual and
ideal
solution)
Total
mass of
mixture
Density of
mixture
(measured)
Volume
of
mixture
Volume of
mogas
Volume
of
naphtha
M
r mix
Vmix
(M/rmix)
Vm
( Mm /rm )
Vm
( Mm /rm )
Vm + Vn
DV
Vmix(Vm +Vn)
% DV
1
10.0447
0.7685
13.0705
10.2270
2.7132
12.9402
0.1303
1.00
2
10.3264
0.7517
13.7374
7.8693
5.5967
13.4660
0.2714
1.98
3
10.1949
0.7434
13.7139
6.3805
6.9996
13.3801
0.3338
2.43
4
10.1564
0.7448
13.6364
5.2970
8.0978
13.3948
0.2416
1.77
5
10.1227
0.7436
13.6131
2.6816
10.8288
13.5104
0.1027
0.75
Mixture
%
Volume
deviation
Table showing the % difference between the actual volume and the expected volume of the mogas-naphtha
mixtures.
Density of mogas: 0.7858 g/mL
Density of naphtha: 0.7402 g/mL
The results are presented in a plot below:
Graph showing % deviation in volume from ideality of each mogas-naptha mixture
3
2.5
% Deviation in volume
2
1.5
1
0.5
0
0
10
20
30
40
50
Ratio of naphtha to mogas
60
70
80
90
100
DISCUSSION
Mixtures of mogas and naphtha were found to have lower densities than the individual
unadulterated mogas and naphtha, indicating an increase in volume when the two liquids were mixed.
This increase in volume was non-linear from one end of the mass ratio to the other, and peaked in an
approximate maximum of 2.43 % for the 50:50 (w/w) mixture. These results indicate that there was
indeed a shortfall in the amount of naphtha delivered by the supplier’s tanker.
Since petroleum products contain mainly neutral non-polar hydrocarbons, intermolecular
forces are mainly of the van der Waals type. When molecules in a liquid are brought close together, the
van der Waals.attraction that holds them together in the liquid are rapidly replaced by van der Waals
repulsion (steric repulsion). Mogas contains mainly straight-chained aliphatic and alicyclic
hydrocarbons while naphtha contains mainly aromatic hydrocarbons rich in delocalised p electrons.
The expansion of volume in mixtures of mogas and naphtha can be explained by differences in
compactness, surface area and electron density of the molecules resulting in a poorer fit of molecules in
the new liquid structure, increased steric effects and intermolecular distances.
CONCLUSIONS
Minute changes in volumes of fairly large amounts (approx 10 g) of liquids are difficult to
determine with the required accuracy and precision by direct measurements. In addition, it is difficult
to ensure that the large volume of liquid is equilibrated at a fixed temperature and thermal expansion
effects of both the liquid and vessel need to be accounted for. It is well known that temperature
fluctuations and inconsistencies induce errors in determination of densities of liquids by means of the
traditional glass pyknometer with a capillary bore.
In contrast, density is an intensive parameter that can be accurately determined to five
significant figures by a temperature-stabilized oscillating tube density meter with built-in thermostat.
The sample volume required is small, and its fixed temperature easily achieved and maintained for very
stable and reliable readings.
When confronted with these findings, the supplier settled the case out of court, and made
restitution for the shortfall in the amount of naphtha delivered.
REFERENCES
1
Physical Chemistry by PW Atkins, pp.204-208 (1977)
th
15 Triennial meeting of IAFS, abstract no: G5