Why is molecular refraction needed in work? Molecular refraction and polarizability of molecules. Melting point determination

PART III REFRACTION AND ACCOMMODATION

Refraction

Refraction Refraction is the ability of the eye to refract light rays when the ciliary muscle (ciliary body) is at rest, with the help of which the lens refracts light rays entering the eye more or less strongly. That is, there is a change in the size of the lens: it or

From Maxwell’s electromagnetic theory of light it follows that for wavelengths significantly removed from the region of their absorption by molecules of matter, the equality is true:

where n∞ is the refractive index of light for certain wavelengths.

Taking this into account, the Clausius-Mosotti equation (15) takes the following form:

[ cm3/(g mol)] (19)

From the resulting expression it is clear that the RM index, called molar refraction, has the dimension of the volume of molecules contained in 1 mole of a substance.

Equation (15), which is called the Lorentz-Lorentz equation, was derived in 1880 independently by H. Lorentz and L. Lorentz.

In practice, the specific refraction index r is often used, that is, the refraction of one gram of a substance. Specific and molar refractions are related by the relation: R = r∙M, where M is the molar mass.

Since in equation (19) N is proportional to density, it can be represented in the following form:

[cm3/g] (20)

H. Lorentz and L. Lorentz revealed the physical meaning of the concept of refraction - as a measure of electronic polarizability and laid a solid theoretical foundation for the doctrine of refraction.

The value of specific refraction is practically independent of temperature, pressure and the state of aggregation of a substance.

In research practice, in addition to the molar and specific refraction RM and r, other derivatives of the refractive indices n are used (Table 2).

The refractive index of non-polar substances practically does not depend on the frequency of light waves and therefore equation (19) is valid at all frequencies. For example, for benzene n2 = 2.29 (wavelength 289.3 nm), while ε = 2.27. therefore, if for approximate calculations of refraction it is enough to use the refractive index of the visible spectrum, then for accurate calculations it is necessary to extrapolate using the Cauchy formula:

nλ = n∞ + a/λ2, (21)

where nλ is the refractive index at wavelength λ;

a is an empirical coefficient.

Table 2 Refractometric constants

For polar substances ε > n2. For water, for example, n2 = 1.78 (λ = 589.3 nm), and ε = 78. Moreover, in these cases it is impossible to directly extrapolate nλ using the Cauchy formula due to the fact that the refractive index of polar substances often changes anomalously with frequency . However, there is usually no need to make such an extrapolation, since refraction is an additive quantity and is conserved if the refractive indices of all substances are measured at a certain wavelength. The yellow line in the sodium spectrum (λD = 589.3) was chosen for this standard wavelength. The reference tables provide data specifically for this wavelength. Thus, to calculate molecular refraction (in cm3/mol), a formula is used in which n∞ is replaced by nD.

(R) - relates the electronic polarizability a of a substance (see Polarizability atoms, ions and molecules) with its refraction Within the limits of applicability of expressions for M. r. she, characterizing as P, the ability of a substance to refract light differs from n in that it practically does not depend on the density, temperature and state of aggregation of the substance.

Main faculty of M. r. looks like

Where M- molecular weight of a substance, r is its density, N A - Avogadro's constant. F-la (*) is the equivalent Lorentz - Lorentz formula(with the same restrictions on applicability), but in plural. cases is more convenient for practical purposes. applications. Often M. r. can be represented as the sum of the “refractions” of atoms or groups of atoms that make up a molecule of a complex substance, or their bonds in such a molecule. For example, M. r. saturated hydrocarbon CkH 2 k+2 is equal kR C+ + (2 k + 2)R N ( k= 1, 2,...). This is an important property of M. r. - additivity - allows you to successfully use refractometric. methods for studying the structure of compounds, determining the dipole moments of molecules, studying hydrogen bonds, determining the composition of mixtures, and for other physical-chemical. tasks.

Lit.: Volkenshtein M.V., Molecules and their structure, M.-L., 1955; Ioffe B.V., Refractometric methods of chemistry, 3rd ed., Leningrad, 1983; see also lit. at Art. Lorentz - Lorentz formula.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia.Editor-in-chief A. M. Prokhorov.1988 .

See more words in "

Electronic polarization is also called molar (or molar) refraction and denoted by the letter R.

So, at high enough frequencies for non-polar substances molar refraction can be determined by the formula:

The change in the speed of light when moving from one medium to another is associated with the interaction of light with the electrons of molecules. Therefore, the refractive index n associated with electronic polarization R.

Based on the electromagnetic theory of light, Maxwell proved that for transparent non-polar substances there is a relationship:

where n ¥ is the refractive index of a substance at an infinite wavelength, l ® ¥.

Let's substitute Maxwell's relation into formula (4.21). We get the following equation

R= (4.23)

Since R = P el = ,

That (4.24)

Relationship (4.24) is called the Lorentz–Lorentz formula. It relates the refractive index of a substance n with electronic polarizability a its constituent particles. Formula (4.24) was obtained in 1880 by the Dutch physicist H.A. Lorentz and, independently of him, the Danish physicist L. Lorentz. Formula (4.23) is convenient to use for pure substances.

Refractive index n depends on the wavelength according to the Cauchy formula:

n l = n ¥ + a/l 2 ,

where a is some empirical constant.

Consequently, refraction is also a function of wavelength, i.e. R = f(l).

Usually, to determine refraction, it is enough to use the refractive index corresponding to the visible region of the spectrum. The yellow line in the sodium spectrum was chosen as the standard (for a more accurate determination of the refractive index, a sodium lamp is used as a light source). The wavelength corresponding to the yellow line Na, l D = 5893 A 0 = 589.3 nm. Refractive index accordingly nD.

For nonpolar substances, n weakly depends on frequency (or wavelength).

For example, for benzene A

For polar substances, Maxwell's relation does not hold. Yes, for water A .

If the molecule is approximately considered as a sphere of radius r, then a » r 3,

and R = , (4.25)

those. molar refraction R is equal to the volume of all molecules, contained in one mole of a substance, and characterizes the polarizability of all electrons contained in 1 mole of a substance. This is physical meaning of refraction.

Dimension [R] = m 3 (in the SI system), [R] = cm 3 (in the GHS system).

Molar refraction R has a number of properties, thanks to which it is widely used in solving issues related to the structure of matter.

Let's consider the properties of refraction.

1. Refraction practically does not depend on the state of aggregation, temperature, pressure. Therefore, it can be considered as some constant characteristic of a given substance.

2. Molar refraction is the quantity additive . This property is manifested in the fact that the refraction of a molecule will consist of the refractions of ions, atoms, atomic groups, and individual bonds.

Thus, the molar refraction of a substance can be calculated using the formula:

R= , (4.26)

where R i (at) – atomic refraction;

R i (inc) – refraction of increments, i.e. additional terms for double, triple bonds, cycles, etc.;

n i – number of atoms, bonds, cycles.

The latter method is physically more justified, because the polarizable electron cloud belongs to the bond, not to individual atoms. However, both methods usually lead to almost the same results.

The refraction values ​​of individual atoms and bonds were obtained by comparing the experimental values ​​of molar refractions determined from the refractive indices for different molecules containing these atoms and bonds.

3. Refraction is a quantity constitutive , i.e. the value of R can be used to judge the structure of molecules.

Application of refraction. Using refraction values, you can solve many problems:

1. Calculation of electronic polarizability a el and effective radius of the particle (atom, molecule). Using the Lorentz–Lorentz formula (4.24) and the relation a el » r 3 we can write:

,

(4.27)

However, the value for r, calculated using formula (4.28) is correct only to a first approximation.

2. Refraction can be used for an approximate estimate of the dipole moment of polar molecules .

It is known that P = P el + P at + P or

Because P at<< П эл, то П » П эл + П ор или П = R + П ор,

hence P or = P – R

On the other hand P or =

From the last two expressions we get:

(4.29)

This method of determination m makes sense only for weakly polar substances, because polar molecules interact with each other. It is much more effective to use the method of dilute solutions of polar substances in non-polar solvents to determine polarization.

3. The equation R 1.2 = x 1 R 1 + x 2 R 2 can be used to determine the composition of the mixture And refractive components . Based on the value of refraction, the concentration of solutions can be determined with a very high degree of accuracy.

x 2 = , (4.30)

where R 1 is the refraction of the solvent;

R 2 - refraction of the dissolved substance;

R 1.2 - refraction of the mixture.

4. Constitutivity of refraction used as a simple a way to check the correctness of the expected structure of molecules .

When determining the structural formula of a substance, proceed as follows:

A) determine r, n at one temperature;

b) according to the Lorentz–Lorentz formula, they calculate R– experimental value;

V) Having written several structural formulas that correspond to the empirical formula of the substance, calculate the refraction value for each structure, using tabular data for this R at And R St;

G) compare the experimental value of refraction R op and calculated R calc. The correct structural formula is the one with R op closest to R calc .

DETERMINATION OF MELTING TEMPERATURE

Goal of the work: determine the melting point of naphthalene and, based on its temperature range, evaluate the degree of its purity.

2.1.1. Materials, reagents, equipment:

Glass capillary (diameter 1 mm, length 40-50 mm) sealed at one end, glass tube (diameter 10 mm, length 40-50 mm), a device for determining the melting point, naphthalene, electric stove.

General provisions.

Melting point determination

Melting point of the substance is the temperature at which its solid phase is in equilibrium with its own melt.

Melting point is the most important characteristic of a compound. By the value of the melting temperature, it is possible to identify a compound, since this constant is always given in reference books on the properties of compounds, for example, /2, 4/.

To identify substances, the so-called is also often used. "mixed melting sample". To do this, carefully mix equal quantities of the substance being identified and the known substance. If the melting point of the mixture remains unchanged, then a conclusion is made about the identity of both substances. If the melting point of the sample is lower than the melting point of the starting substances, then, consequently, these substances are different. This method is based on the established fact that pure substances have a clearly defined (“sharp”) melting point (with an accuracy of 0.01 C). The presence of impurities tends to lower the melting point. In addition, substances containing any impurities melt in temperature range, i.e., they do not have a clearly defined melting point. Thus, determining the melting point can provide qualitative information about the purity of a substance.

Determining the melting point also allows one to draw indirect conclusions about the possible molecular structure of the substance. For example, it has been established that isomers with symmetrical molecules melt at a higher temperature than substances with a less symmetrical structure. The melting point also increases with increasing degree of association of molecules (for example, due to intermolecular hydrogen bonds).

Approximately estimate The melting point of a substance can be determined using a regular laboratory thermometer. Several crystals of the compound being tested are carefully placed directly onto the mercury bulb of the thermometer. Next, the thermometer with crystals is carefully placed over the surface of a preheated hotplate with a closed spiral. By adjusting the height of the thermometer above the heated surface, the rate of temperature rise is roughly set. Carefully observing alternately the state of the crystals and the temperature value, note Start melting of the substance (appearance of the first droplets of the liquid phase). This process can be repeated several times, achieving the most accurate determination of the beginning of the melting process. Of course, this method gives only an approximate idea of ​​the melting temperature, but it makes it possible to significantly simplify further experiments to accurately determine this constant.

General process methodology

To accurately determine the melting point, there are several structurally different devices of varying degrees of complexity and ease of use, but the principle of their operation is the same. The compound to be tested is placed in a glass capillary (diameter 1 mm, length 40–50 mm), sealed at one end. First, the substance is ground in a mortar into a fine powder. To fill the capillary, its open end is immersed in powder, with some of the substance entering the upper part of the capillary. Next (to move the substance to the lower part of the capillary and compact the layer), the capillary is thrown, sealed end down, into a long, narrow, vertically placed glass tube (diameter 10 mm, length 40 - 50 cm). By repeating this technique several times, one achieves a dense layer of the substance in a capillary 3-5 mm high.

Direct determination of the melting point is carried out in a special glass device (Figure 5), consisting of a round-bottomed flask (1) with a high-boiling coolant, a test tube (2) and a thermometer (3). The capillary (4) with the test substance is attached to the thermometer with a ring of rubber tube (5) so that the column of the substance is at the level of the middle of the mercury ball. The device is heated in an air bath (heating mantle, electric stove) quickly at first, and the last 15-20 below the expected melting temperature, the temperature is increased at a rate of no more than 2 degrees min –1. The melting point is the temperature at the moment of complete melting of a substance.

Typically, a substance melts within a temperature range, and the purer the substance, the smaller the range. The beginning of melting is considered to be the moment the first drop appears in the capillary, and the end is the disappearance of the last crystals of the substance.

Processing the results

In the course of the work done, the melting point of naphthalene was determined, it was found that the temperature range exceeds the permissible values, so we can say that technical naphthalene is not pure enough. It can also be added that mixtures of different substances, as a rule, melt at a lower temperature than the individual substances themselves. To establish whether substances with similar melting points are the same or different, determine the melting point of a mixture of these substances (mixed sample); if the melting point of the sample is lower than the melting point of the substances taken for preparation, then, therefore, we are dealing with different substances. On the contrary, the absence of a depression in the melting point of a mixed sample is considered evidence of the identity of the substances taken.

Lab 2.2

DETERMINATION OF MOLECULAR REFRACTION

ORGANIC COMPOUNDS

Goal of the work: determine the refractive index and identify an unknown organic compound.

2.2.1. Materials, reagents, equipment:

Abbe refractometer, conical flask with an unknown compound, pipette, cotton wool (moistened with ether).

General provisions

The refractive index relative to vacuum is called the absolute refractive index. When measuring refractive indices liquids and solids are usually determined by the relative refractive indices relative to the air in the laboratory room.

The refractive index of a substance is determined by its nature, but also depends on external conditions - temperature and wavelength of light. For organic liquids, with an increase in temperature by 1, it drops by 4·10 –4 -5 · 10 –4.

The refractive index characterizes the polarizability of a molecule, which is understood as its ability to polarize, that is, to change the state of the electron cloud under the influence of an external electric field. As the polarizability of the molecule increases, n increases, and this value is related to the molecular refraction MR according to the Lorentz-Lorentz equation:

,

where n is the refractive index of the substance or solution;

M is the molecular weight of the substance;

d is the specific gravity of the substance (density).

Unlike the refractive index, molecular refraction does not depend on temperature.

In the electromagnetic field of visible light, the polarizability of molecules is almost entirely due to the displacement of electrons and is equal to the sum of the effects of the displacements of individual electrons. The latter circumstance gives the MR of chemical compounds the character of an additive constant. It can be defined theoretically as the sum of the refractions of individual atoms that make up the molecule, taking into account additives (incrementals) that take into account the presence and number of multiple bonds:

MR theor. = Σ AR at. + Σ ink. ,

where AR at. – atomic refraction of one atom;

ink– increment of one connection.

The AR values ​​for individual atoms and the increments of multiple bonds are known and are given in most relevant manuals and reference books
/5, p. 17/ (Table 1). Knowing the hypothetical structural formula of a compound, one can calculate its MR theorem. as the sum of AR at.

For example, for isopropylbenzene (cumene) MR theor. is equal to:

MR theor. = AR C 9 + AR H 12 + ink dv. St. · 3

Substituting the corresponding values ​​of AR and ink (Table 1), we obtain:

MR theor. = 2.418 ∙ 9 + 1.100 ∙ 12 + 1.733 ∙ 3 = 40.161

Table 1 – Atomic refractions of individual atoms and increments

To determine the value of the refractive index, a special device is used - a refractometer. The standard instrument for organic chemistry laboratories is the Abbe refractometer. It is designed in such a way that, when using polychromatic (solar or artificial) light, it gives the refractive index value for the sodium D-line. The measurement requires only a few drops of liquid, and the measurement accuracy is 0.0001 refractive index units. To achieve such accuracy, a constant temperature must be maintained during measurement with an accuracy of 0.2 C (which is achieved using a thermostat). It is advisable to measure the refractive index at 20C, and for low-melting solids - slightly above the melting point.

Since each substance is characterized by its own refractive index value, refractometry, together with other methods, can be used to identify (recognize) substances. Identification is carried out on the basis of the coincidence of the measured and reference values ​​of the refractive index of pure substances found under the same conditions. Due to the fact that different substances may have similar refractive index values, refractometry is usually complemented by other methods of identifying substances (spectral measurements, determination of melting or boiling points, etc.). The refractive index can also be used to judge the purity of a substance. The discrepancy in the measured and reference (for a pure substance) values ​​of the refractive indices of substances found under the same conditions indicates the presence of impurities in it. In cases where there is no information in the literature about the physical constants of a substance (including the refractive index), it can be considered pure only when the physical constants do not change during repeated purification processes. Refractometric structural analysis provides the greatest accuracy for liquid substances. In this case, it is necessary to have data on the composition and molecular weight (gross formula) or grounds for assuming the structural formula of the substance. A conclusion about the structure of a substance is made based on a comparison of MR exp, found using the Lorentz-Lorentz formula, and MR theor. The coincidence of the values ​​of MR exp and MR theor with an accuracy of 0.3-0.4 confirms the probability of the proposed gross formula and structure. Discrepancy Mr theor Mr exp. more than 0.3-0.4 units indicates that the MR theory made when calculating was incorrect. assumptions about the structure and composition of matter. In this case, it is necessary to consider other possible molecular structures of the substance for a given gross formula.

Since the refractive index depends on the concentration of solutions, refractometry is also used to determine their concentration, to check the purity of substances and to monitor separation processes, for example, distillation can be monitored (for analytical purposes). The refractive index of a binary mixture depends linearly on the concentration of the components (in percent by volume), unless there is a change in volume during mixing. If deviations from the linear relationship occur, it is necessary to construct a calibration curve.