What is called refraction of matter. Refractometric method of analysis in chemistry

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:

(21)

Dimension of molar refraction: [ cm 3 / (g mol)]

From the resulting expression it is clear that the indicator R M, 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 relationship: R = r∙M, where M is the molar mass.

Since R = r∙M, the specific refraction is equal to:

(22)

Specific refraction dimension: [cm 3 /g]

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 R M and r, other derivatives of the refractive index are used n.

The refractive index of nonpolar substances is practically independent of the frequency of light waves, and therefore equation (19) is valid at all frequencies. For example, for benzene n 2 = 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.

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 .

MOLECULAR REFRACTION

(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.

Basic f-la 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.

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From the book Qigong for the eyes by Zhong Bin

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Almost all methods for studying polarizability are based on changes in the characteristics of light during its interaction with matter. The limiting case is a constant electric field.

The internal local field F acting on the molecule is not identical to the external field E imposed on the dielectric. To calculate it, the Lorentz model is usually used. According to this model

F = (e + 2) ∙ E / 3,

where e is the dielectric constant (permeability).

The sum of the dipole moments induced in each of the N 1 molecules contained in a unit volume is the polarization of the substance

P = N 1 ∙a∙F = N 1 ∙a∙E∙(e+2)/3,

where a is polarizability.

Molar polarization (cm 3 /mol) is described by the Clausius-Mossotti equation

P = (e-1) / (e+2)∙M/r = 2.52∙10 24 ∙a,

in the SI system (F∙m 2 ∙mol -1)

P = N∙a / 3∙e 0 = 2.52∙10 37 ∙a

In the case of an alternating electric field, including the field of a light wave, various polarization components appear due to the shift of electrons and atomic nuclei, depending on the frequency.

For non-polar dielectrics, according to Maxwell’s theory, e = n 2, therefore, with appropriate replacement, the Lorentz-Lorentz equation of molecular refraction is obtained

R = (n 2 –1) / (n 2 +2)∙M / r = 4/3∙p∙N∙a,

where n is the refractive index; r - density; N is Avogadro's number.

A similar equation can describe the specific refraction

(n 2 –1) / (n+2)∙1/r = 4/3∙p∙N 1 ∙a.

Molecular refraction is the polarization of one mole of a substance in the electric field of a light wave of a certain length. This is the physical meaning of molecular refraction.

When extrapolated to an infinite wavelength, the electronic polarization P e is obtained:

P e = P ¥ = (n 2 ¥ -1)/(n 2 ¥ +2)∙M/r = 4/3∙N∙a e

Calculation from molecular refraction is the only practically used method for finding the average polarizability a, cm 3. Substituting the numerical values ​​of the constants gives

a = 0.3964∙10 24 ∙R ¥ .

The experimental determination of molecular refraction involves measurements of refractive index and density.

The most important property of molecular refraction is its additivity. The possibility of a priori calculation of the value of refraction from the increments of the corresponding atoms and bonds allows, in some cases, to accurately identify a chemical compound, as well as to study the resulting intra- and intermolecular interactions based on the deviations of the experiment from the calculation.

The refraction of the mixture is additive - specific refraction by mass fractions of components w, molecular - by mole fractions x, which makes it possible to calculate the refraction of substances from data for solutions. If we denote the parameters of the solvent by index 1, the dissolved substance by 2, and the solution by 1.2, we get

R 2 =1/f 2 ×[(n 1.2 2 – 1)/(n 1.2 2 + 2) × (M 2 f 2 + M 1 (1 – f 2))/r 1.2 – R 1 × (1 – f 2)] .

When expressing the concentration in moles per 1 liter (C), we have

R 2 =(n 1 2 –1)/(n 1 2 +2)(M 2 /r 1 –1000/C(r 1.2 –r 1)/r 1)+1000/C((n 1, 2 2 –1)/(n 1,2 2 +2)–(n 1 2 –1)(n 1 2 +2)).

The best results are obtained by graphical or analytical extrapolation of the refraction or refractive indices and densities of solutions to infinite dilution. If the concentration dependences of the latter are expressed by the equations

r 1,2 = r 1 ×(1 + b×w 1),

n 1,2 = n 1 × (1 + g×w 2),

then the specific refraction

¥ R 2 = R 1 (1-b) + 3n 1 2 g/r 1 (n 1 2 + 2) 2 .

When carrying out measurements in solutions, it is necessary to fulfill certain experimental conditions, in particular, the use of the maximum possible concentrations of the analyte.

4.1.1. Calculation of polarizability values ​​of atoms and molecules from refractometric data. Boettcher, based on the Onsager model, obtained the equation of molecular refraction in the form

R=4/3pNa9n 2 /((n 2 +2)[(2n 2 +1)–a/r 3 (2n 2 –2)]),

where r is the radius of the molecule.

This equation allows one to simultaneously determine polarizability and molecular sizes.

An approximate calculation of atomic polarizability as a certain fraction of electronic polarizability or molecular refraction has become widespread: P a = kP e, where the coefficient k is 0.1 or 0.05.

4.1.2. Additive nature of molecular refraction and polarizability. The basis on which the use of polarizability to establish the chemical structure, distribution of electrons and the nature of intramolecular interactions, configuration and conformation of molecules is built is the idea of ​​additivity of molecular quantities. According to the principle of additivity, each structural fragment - a chemical bond, an atom, a group of atoms, or even individual electron pairs - is assigned a certain value of the parameter in question. The molecular value is represented as a sum over these structural fragments. Any molecule is a system of atoms or bonds interacting with each other. Strict additivity assumes that the parameters of each structural fragment remain unchanged during the transition from one molecule containing it to another. Any interactions lead to changes in the properties of atoms and bonds or to the appearance of additional contributions to molecular quantities. In other words, the additive value of a property assigned to each atom depends not only on its nature, but also on its environment in the molecule. Therefore, no physical property can be strictly additive. In such a situation, the way in which the principle of additivity is used must be adjusted to certain specified conditions.

To date, two main trends have emerged in the development and application of additive polarizability schemes. On the one hand, the dependence of the polarizability parameters of atoms or bonds on their environment forces us to specify the additive scheme, introducing, for example, increments for atoms of any element in different valence states or different types of bonds; then the nature of the substitution at the neighboring atom is taken into account, etc. In the limit, this approach leads to a set of polarizabilities of each fragment or to the calculation of average polarizabilities and anisotropies of large structural units, a kind of “submolecules” that automatically take into account the interactions within them.

The second tendency is to use some additive scheme and consider all deviations from it as manifestations of interactions.

The first approach is considered more acceptable when studying the spatial structure of molecules, when identifying the effects of mutual influence is unimportant.

The second approach is used mainly in analyzing the electronic structure of rigid molecules.

In 1856, Berthelot pointed out that there is a simple relationship between the molecular refractions of neighboring members of a homologous series:

R n–1 – R n = const = R CH 2

In accordance with this equation, the molecular refraction of the nth member of the homologous series can be considered as the sum of the molecular refractions of the first member and n–1 CH 2 groups:

R n = R 1 + (n–1)∙R CH2 ,

where n is the serial number of the member of the homologous series.

In chemistry, two schemes are used for calculating molecular refraction - by atoms and by bonds that make up the compound under study.

According to the first scheme, molecular refraction for some groups of compounds depends only on the nature and number of atoms in the molecule, and can be calculated by summing the atomic refractions characteristic of a given element:

R(C n H m O p X g)=n×R C +m×R H +p×R O +g×R X ,

where R(C n H m O p X g) is the molecular refraction of the compound with the composition C n H m O p X g ; R C, R H, etc. – atomic refractions of carbon, hydrogen and other elements.

In the second case, molecular refraction is calculated from bonds. The use of this calculation scheme was facilitated by the establishment of the influence of the nature of bonds on molecular refraction, which was of great importance, because opened up the possibility of using molecular refraction to determine the structure of organic substances. It was shown that the value of molecular refraction also reflects the nature of the bonds of other elements. In addition to the nature of the atoms forming the bond and the multiplicity of the bond, the influence of strained cycles on molecular refraction was proven and special increments were derived for three-membered and then four-membered carbon rings.

In complex functional groups with multivalent elements (–NO 2 , –NO 3 , –SO 3 , etc.) it is impossible to strictly determine atomic refractions without conditional assumptions, so group refractions of radicals began to be used.

Subsequently, it was found that the values ​​of molecular refraction are determined mainly by the number and properties of higher (valence) electrons involved in the formation of chemical bonds, in addition, the nature of the chemical bonds plays a decisive role. In this regard, Steiger (1920), and then Fajans and Klorr proposed to consider molecular refraction as the sum of bond refractions. For example, for CH 4:

R CH4 = R C + 4R H = 4R C-H

R C-H = R H + 1/4×R C

R CH2 = R C + 2×R H = R C-C + 2×R C-H

R C - C = 1/2×R C

The method of calculating bonds using refractions is more consistent, simpler and more accurate. In chemistry, both bond refractions and atomic refractions are used.

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Molecular refraction

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Description

Molecular refraction connects the molecular polarizability a of a substance with its refractive index n. Within the limits of applicability of expression (1), it characterizes, like n, the ability of a substance to refract light. At the same time, molecular refraction differs from n in that it practically does not depend on the density, temperature and state of aggregation of the substance. The basic formula for molecular refraction is:

, (1)

where M is the molecular weight of the substance;

r is the density of the substance;

N A - Avogadro's constant.

Formula (1) is equivalent to the Lorentz-Lorentz formula (with the same restrictions on applicability), but in many cases it is more convenient for practical applications. Often, molecular refraction can be represented as the sum of the “refractions” of atoms or groups of atoms that make up the molecule of a complex substance, or their bonds in such a molecule. For example, the molecular refraction of a saturated hydrocarbon C k H 2k+2 is equal to kR c +(2k+2)R h.

Timing characteristics

Initiation time (log to -9 to -6);

Lifetime (log tc from -6 to 9);

Degradation time (log td from -9 to -6);

Time of optimal development (log tk from -6 to 6).

Diagram:

Technical implementations of the effect

Technical implementation of the effect

The technical implementation diagram is presented in Fig. 1. Radiation from a helium-neon laser passes through a prismatic vessel filled with propane at atmospheric pressure. Next, the pressure of the propane increases until it liquefies. As the pressure increases, the angle of deflection of the transmitted beam monotonically increases.

Observation of molecular refraction

Rice. 1

Applying an effect

Molecular refraction allows you to successfully study the structures of compounds, determine the dipole moments of molecules, study hydrogen bonds, determine the composition of mixtures and solve other physicochemical problems.