Determination of molecular's refraction of liquids.
L. Lorenz & H. Lorentz introduced to the physics and chemistry the parameter connecting the refractive index of the substance and the polarizability of the molecules. This parameter is called molecular (or molar) refraction and is given by:
where M is the molecular weight of the substance, r is the density .
For non-polar dielectrics molar refraction is related to the induced polarizability of the molecules - the ability to move electrons in the atom under the influence of an electric field - with the following formula:
where a is the induced polarizability of the molecules, NA is Avogadro's number and eo is the vacuum permittivity.
In polar dielectrics there is also orientational polarizability of molecules, connected with orientation of their permanent electric dipoles in the electric field. According to the Debye's theory the following equation is correct then:
where e is the dielectric permittivity of the test substance , m - permanent dipole moment of the molecules, k - Boltzmann constant and T - the absolute temperature. Based on the formula (3) we can determine the dipole moment of molecules, if there aren’t molecular interactions dipole- dipole, and there are no associations. If these conditions are not fulfilled, the dipole moments obtained by the formula (3) are generally underestimated.
If the electron clouds of individual bonds in the molecule are independent of each other, it means that the molecule’s refraction is equal to the sum of refractions of individual bonds. Such a property is called refraction additivity. Compatibility of refraction calculated for a proposed structural pattern and refraction determined experimentally is an important confirmation of the proposed structure . If the molar refraction obtained from the principle of additivity disagrees with the refraction obtained by the formula (1), then this indicates the dependence of bonds in the molecule. The difference of refraction obtained by these two methods is called exaltation of refraction, and is a measure of the strength of the interaction between electrons of different bonds.
The principle of additivity of refraction is also valid in the case of a mixture of several substances. Refraction of mixture R is:
where Ri is the refraction of i-th component of the mixture and Xi represents the mole fraction of the i-th component. For example - for an aqueous solution of alcohol - refraction of the solution is:
wherein RA and Rw are, respectively, the molar refraction of alcohol and water, and XA and Xw respective mole fractions. If the mA and mw denote the mass of alcohol and water in solution, then the weight concentration of alcohol in the solution can be expressed either in percentage: p% = mA/(mA + mw) ×100% or in fraction: p = mA/ (mA + mw). Using the definition of the mole fraction (e.g. molar fraction of alcohol XA = NA/(NA + Nw), where NA and Nw are, respectively, the number of moles of alcohol and water) can easily be shown that the mole fraction of alcohol is related to the concentration expressed as a fraction by relationship:
where MA and Mw are, respectively, molecular weights of alcohol and water. Since the sum of the mole fractions of all components of the solution is equal to one, so the molar fraction of water: Xw = 1 – XA.
I. Course of the exercise.
Measurement of the refractive index we perform by using the Abbe’s refractometer. Before measurements, rinse the walls of the prism by ethanol. Liquid apply using a pipette and spread with a glass rod. After application of the liquid close cube consisting of two prisms.
1. Measure the refractive index of distilled water.
2. Measure the refractive index of ethyl alcohol solutions, starting with the smallest concentration. The results of the measurement include in the table:
n
3. Measure the refractive index of glycerol
II. Computational informations.
1. Basis on the formula (1) calculate the molar refraction of water Rw.
2. On the basis of measurements of the refractive index for ethanol plot a graph of n = f (c).
3. Determine the refractive index of pure ethanol by extrapolation of the graph n = f (c) to a concentration of 100%.
4. Basis on the formula (1) calculate the molar refraction of ethanol Rexp, using a value obtained from extrapolation of refractive index, and assuming that for pure ethanol (at 20˚ C) ρ = 789.5 [kg/m3].
5. Using the table of refraction and additivity principle - calculate Rcomp for the two structures of ethanol proposed below:
H H H H
ê ê | |
H - C - C - O - H H – C – O – C - H
ê ê | |
H H H H
C2H5OH ( CH3 )2O
Compare the obtained values with Rexp and draw appropriate conclusions.
Table of molar refraction of some bonds:
Bond / Refraction ´ 10-6 [m3 mol-1]C - H
C - C
C - O
O - H / 1,68
1,30
1,54
1,66
6. Calculate the refraction of the selected solution of ethanol Rcomp, using the formula (5).
7. Calculate refraction Rexp of the same solution of ethanol using equation (1), wherein M should be replaced by:
8. Compare the results.
9. Calculate the molar refraction Rexp for glycerol using the formula (1) and with a density of glycerol (at 20˚C) ρ = 1233 [kg/m3].
10. Using the table of refraction and additivity principle - calculate Rcomp for the two structures of glycerol proposed below:
H
|
H H O H H H
| | | | | |
H – C – C – C – O – H H – C – C – O - C – O – H
| | | | | |
H O H H O H
| |
H H
CH3(CHOH)2OH CH3CHOHOCH2OH
11. Compare the values obtained from Rexp and draw appropriate conclusions.
12. From the transformation of Debye’s formula you can get the following formula for the dipole moment of the molecule:
or, after substituting the values of physical constants (for T = 293 K)
On the basis of the above formula calculate the dipole moment of a molecule of: water, ethanol and glycerol using dielectric permittivity values given in the following table:
Substance / e / Dipole momentmtabl (D)
Water
Ethanol
Glycerol / 81
25,8
40 / 1,84
1,7
2,8
The values of the dipole moment of molecules give - as in the table - in debye:
13. Compare the results with the table’s values and draw conclusions.
The densities of aqueous solutions of ethanol at 20°C.
c [%] / Density [g/cm3]0 / 1,0000
3 / 0,9948
4 / 0,9938
5 / 0,9918
7 / 0,9908
10 / 0,9958
15 / 0,9803
20 / 0,9717
25 / 0,9637
30 / 0,9557
40 / 0,9368
50 / 0,9156
60 / 0,8926
70 / 0,8694
80 / 0,8425
90 / 0,8185
96 / 0,8040
:
Measurement of the twisting angle of polarization plane of the light and the specific rotation of solutions.
Measurements of the twisting angle of polarization plane of the light we conduct by using a polarimeter. The twisting angle of polarization plane of the light passing through the solution optically active substance having a concentration c and a thickness l is expressed by the formula :
From the above formula follows that knowing the twisting angle of polarization plane of the light, thickness of the solution and the specific rotation we can determine the concentration of the test substance (eg. concentration of sugar in the urine of people with diabetes).
I. Course of the exercise.
1. Become familiar with the design of the polarimeter, measuring principles and the regulatory system.
2. Turn on the sodium lamp.
3. Pour distilled water into a cuvette, insert the cuvette into the instrument between the polarizer and the analyzer, and then determine the polarimeter's zero position. That position we are looking for turning the knob of analyzer next to the telescope (illumination of both fields of view in the telescope is then equal).
4. Write down the polarimeter's zero position.
5. Fill the cuvette with a solution of an optically active substance of known concentration, and when you insert it into the polarimeter observe the change of illumination.
6. Turning the knob find the position of the analyzer when illumination is uniform. Read the twisting angle of polarization plane of the light.
7. Activities indicated in points 5 and 6 perform successively for all of the prepared solutions of known and increasing concentrations, and for one of the unknown concentration of the substance.
8. Measurements repeat for another substance.
9. The results of the measurements put in the table:
Substance / c [g/cm3] / a [o] /Glucose
Fructose
II. Computational informations.
1. On the basis of the results of measurements plot a graph of the twisting angle of polarization plane of the light versus the concentration : α = f (c) for glucose and fructose.
2. Using the graph determine the unknown concentration of glucose and fructose.
3. Calculate the specific rotation of glucose and fructose, assuming the length of cuvette l = 20 cm. The resulting values expressed in SI units, ie [0 m2/kg].
The substance / c [g/m3] / [a] [0 m2/kg] / [0 m2/kg]Glucose
Fructoze
4. Calculate the absolute and relative error of specific rotation for four known concentrations of glucose.