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2.a-b
2. Optical and electrical properties of molecules
2.a. Refraction measurement of methanol-ethanol mixtures
The measurement of the refractive index by immersion refractometer is based
on the determination of the limiting angle β𝑙𝑙𝑙𝑙 𝑙𝑙
of refraction to which the Snell
law applies:
sin β𝑙𝑙𝑙𝑙 𝑙𝑙
=
𝑛𝑛
𝑛𝑛𝑔𝑔
(1.1.)
where n is the refractive index of the measured environment and ng the refractive
index of the glass used for the refractometer prism. The limiting angle is given by the
position of the interface between the illuminated and the dark part of the field of view
read on the empirical scale of the instrument. The corresponding refractive index we
find a from the calibration table. The refractive index of the sample is dependent on
the wavelength of the passing light, and less on temperature and pressure.
The specific refraction is given by formula:
R
n
n
=
−
+
2
2
1
2
1
.
ρ
(1.2.)
where ρ is density of the environment. At given temperature and pressure, the
specific refraction depends on the wavelength only.
The dependence of the specific refraction of the mixture on volume fractions of
components φ𝑖𝑖
has an additive character. This dependence may be linear for similar
substances (Lorentz brothers' equations). For example, for a binary mixture:
R = R1φ1
+ R2φ2
(1.3.)
where R1 and R2 are specific refractions of pure components 1 and 2.
For pure substances, we define so-called molar refraction MR , which is given by the
product of the specific refraction R and the molar mass of the substance M.
The molar refraction is a constitutive property and it can be calculated theoretically as
the sum of the molar refractions of the atoms that we find in the molecule. Of course,
the atom refraction 𝑅𝑅𝐴𝐴
𝑖𝑖
has to be corrected for different binding types (see TABLE I).
∑ ⋅=
+
−
= i
AiM R
M
n
n
R n
ρ
.
2
1
2
2
(1.4.)
where iν is number of atoms with the same i-bond neighbourhood in the molecule.
This equation applies to both non-polar and polar substances, since the behaviour of
their atoms varies very little in the electromagnetic field or light.
The specific refraction n of the binary mixtures is often used in the practice of
refractometry for the determination of the composition of the minority component 𝑥𝑥1 if

TABLE I: The atom refractions of the elements in alcohols.
Atom i: C H O (v OH)
i
AR / cm3
mol-1 2,4 1,1 1,5
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2.a-b
the calibration function 𝑛𝑛 = 𝑓𝑓(𝑥𝑥1) is known. The calibration function is generally nonlinear
and temperature dependent.
Density measuring using glass pycnometer. First we weight an empty,
clean and dry pycnometer. We then fill it with a measured liquid at the
temperature slightly lower than the temperature of the thermostat bath into which the
pycnometer will be consequently inserted. After the temperature has stabilized and
according to the pycnometer design, the excess liquid either overflows spontaneously
or we remove a liquid to the volume marker level using the syringe. Dry the
pycnometer externally and weigh it. Thus we determine the weight of the pycnometer
with all the investigated liquids or their mixtures and finally with the water. We use the
distilled water to calibrate the actual volume of the pycnometer.
Next, we will find the tabulated water density for the bath temperature, and then
calculate the actual volume of the pycnometer occupied by the water at the
temperature inside the thermostat bath. Weighing can be further refined by correcting
the buoyancy of the pycnometer by air so that the density of the fluid under
investigation at temperature is calculated as follows:
( )ρ ρ ρ ρt
m
m
= − +
0
0
* *
(1.5.)
where ρ0 is the specific mass of pure water at the temperature of the thermostat bath
(we found it in tables), m is the mass of the fluid under investigation, and mo
is the
mass of water, ρ*
is specific mass of dry air (1,168 kg/m3
at 25°C and 100.0 kPa).
TASK: Find out the specific refraction of methanol and ethanol and their
mixtures at 25.0°C, test linear dependence of the specific refraction on the
composition, and verify the molar atom refraction additivity for pure alcohols.
LABORATORY AIDS AND CHEMICALS: Immersion refractometer, thermostatic bath,
7 refractometer cuvette, glass pycnometer (25 ml) for volatile liquids, methanol,
ethanol, and its binary mixtures with volume ratios (φ1
): 0.80; 0.60: 0; 40; and 0.20.
Methanol is a flammable toxic substance in ingestion, in contact with skin and
in inhalation. Same smelling and taste as ethanol. If swallowed, seek medical
advice immediately.
INSTRUCTIONS: Pour distilled water, ethanol, methanol, and alcohol mixtures
into refractometer cuvettes. Place the liquid samples in a thermostatic bath.
Clean the immerse refractometer with distilled water and place it in the cuvette
involving water.
After equilibration, we perform the calibration of the refractometer by measuring the
refractive index of the distilled water at bath temperature. Next, we proceed to
measure the refractive indexes of the samples. When transferring the refractometer
from one liquid to the other, carefully dry prism by filter paper.
The specific density of the monitored liquids can be measured by glass pycnometer
for example.
REPORT: Start and end temperature of measurement. Table 1: the masses of
the pycnometer with air, water, and with each mixture of alcohols, the masses
of the filling only; the specific masses of the samples according to the relationship
(1.5.). Table 2: for all measured liquids: composition (volume fraction of ethanol and
methanol), refractive index, specific mass, specific refraction calculated by eqn (1.2.).
Add also the value of the specific refractions of the mixtures obtained using the
relationship (1.3.) (use specific refraction of methanol R1 and ethanol R2 from the
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2.a-b
experiment as input), the differences between the experimental and calculated
specific refractions. Graph 1: the composition dependence of the refractive index.
Common graph 1: dependences of both experimental and calculated specific
refractions of alcohol mixtures on its compositions. Table 3: for pure methanol and
ethanol: comparing experimental values of molar refraction RM with values calculated
using atomic refractions i
AR (use TABLE I and eqn (1.4.)).