Mixture concentration

Concentration or the amount of the mixture component is a quantity that quantitatively characterizes the content of the component relative to the entire mixture. IUPAC terminology refers to four values as the concentration of a component: the ratio of the molar or numerical amount of a component, its mass , or volume exclusively to the volume of the solution ^[1] (typical units of measure are mol / l, l ⁻¹ , g / l, respectively, and the dimensionless ). The proportion of the component IUPAC calls the dimensionless ratio of one of the three same-type values - mass, volume or quantity of a substance. ^[2] However, in use, the term “concentration” can also be applied to proportions that are not volumetric fractions, as well as to ratios that are not described by IUPAC. Both terms can be applied to any mixture, including mechanical mixture , but are most often applied to solutions .

Content

Bulk

Mass fraction of the component - the ratio of the mass of the component to the sum of the masses of all components. According to the recommendations of IUPAC, ^{[3] is} indicated by the symbol $w$ ${\ displaystyle w}$ , in the Russian-language literature is more often the designation $\omega$ ${\ displaystyle \ omega}$ . Mass fraction - a dimensionless quantity, usually expressed in fractions of a unit or in percent (to express the mass fraction in percent, the specified expression should be multiplied by 100%):

\omega _{\mathrm {B} }={\frac {m_{\mathrm {B} }}{m}}

{\ displaystyle \ omega _ {\ mathrm {B}} = {\ frac {m _ {\ mathrm {B}}} {m}}}

Where:

ω _B is the mass fraction of component B
m _B is the mass of component B;
$m$ ${\ displaystyle m}$ - the total mass of all components of the mixture.

In binary solutions, there is often an unambiguous ( functional ) relationship between the density of the solution and its concentration (at a given temperature). This makes it possible to determine in practice the concentration of important solutions using a densimeter ( alcohol meter , saccharimeter , lactometer ). Some areometers are not calibrated in terms of density, but directly the concentration of the solution ( alcohol , fat in milk, sugar). It should be borne in mind that for some substances, the density curve of the solution has a maximum; in this case, two measurements are taken: direct, and with a slight dilution of the solution.

Often for the expression of concentration (for example, sulfuric acid in the electrolyte of rechargeable batteries ) they simply use their density. Areometer ( densimeters , densitometers ) are widely distributed , designed to determine the concentration of solutions of substances.

Example: the dependence of the density of H ₂ SO ₄ solutions on its mass fraction in an aqueous solution at 25 ° C
ω,%	five	ten	15	20	thirty	40	50	60	70	80	90	95
ρ H ₂ SO ₄ , g / ml	1,032	1,066	1,102	1,139	1.219	1.303	1,395	1,498	1,611	1,727	1.814	1,834

Bulk Share

The volume fraction of the component is the ratio of the volume of the component to the sum of the volumes of the components before mixing. The volume fraction is measured in fractions of a unit or as a percentage.

\phi _{\mathrm {B} }={\frac {V_{\mathrm {B} }}{\sum V_{i}}}

{\ displaystyle \ phi _ {\ mathrm {B}} = {\ frac {V _ {\ mathrm {B}}} {\ sum V_ {i}}}

,

Where:

$\phi _{\mathrm {B} }$ ${\ displaystyle \ phi _ {\ mathrm {B}}}$ - volume fraction of component B,
V _B is the volume of component B;
$\sum V_{i}$ ${\ displaystyle \ sum V_ {i}}$ - the sum of the volumes of all components before mixing.

When mixing liquids, their total volume may decrease, so you should not replace the sum of the volumes of the components with the volume of the mixture.

As mentioned above, there are areometers designed to determine the concentration of solutions of certain substances. Such areometers are not calibrated in terms of density, but directly the concentration of the solution. For common solutions of ethanol , the concentration of which is usually expressed in volume percent, such hydrometers are called alcohol meters or andrometers .

Molarity ( molar volume concentration )

The molar concentration (molarity, molarity) ^[4] is the amount of a substance (the number of moles) of a component per unit volume of the mixture. Molar concentration in the SI system is measured in mol / m³, but in practice it is much more often expressed in mol / l or mmol / l. The expression “in molarity” is also used. Perhaps another designation of molar concentration, which is usually denoted by M. So, a solution with a concentration of 0.5 mol / l is called 0.5-molar, write "0.5 M".

On the recommendation of IUPAC, indicated by the letter $c$ ${\ displaystyle c}$ or $[B]$ ${\ displaystyle [B]}$ where B is a substance whose concentration is indicated. ^[five]

Note: After the number they write "mol", just as after the number they write "cm", "kg", etc., without inclining cases.

{c_{\mathrm {B} }}={\frac {n_{\mathrm {B} }}{V}}

{\ displaystyle {c _ {\ mathrm {B}}} = {\ frac {n _ {\ mathrm {B}}} {V}}}

,

Where:

$n_{\mathrm {B} }$ ${\ displaystyle n _ {\ mathrm {B}}}$ - the amount of the substance component, mol;
V is the total volume of the mixture, l.

Normal concentration ( molar concentration equivalent , " normality ")

Normal concentration - the number of equivalents of the substance in 1 liter of the mixture. The normal concentration is expressed in mol eq / l or g-eq / l (meaning mole equivalents). To record the concentration of such solutions use the abbreviation " n " or " N ". For example, a solution containing 0.1 mol eq / l is called decinormal and is recorded as 0.1 n .

c(f_{eq}~\mathrm {B} )=c{\big (}(1/z)~\mathrm {B} {\big )}=z\cdot c_{\mathrm {B} }=z\cdot {\frac {n_{\mathrm {B} }}{V}}={\frac {1}{f_{eq}}}\cdot {\frac {n_{\mathrm {B} }}{V}}

{\ displaystyle c (f_ {eq} ~ \ mathrm {B}) = c {\ big (} (1 / z) ~ \ mathrm {B} {\ big)} = z \ cdot c _ {\ mathrm {B} } = z \ cdot {\ frac {n _ {\ mathrm {B}}} {V}} = {\ frac {1} {f_ {eq}}} \ cdot {\ frac {n _ {\ mathrm {B}} } {V}}}

,

Where:

$n_{\mathrm {B} }$ ${\ displaystyle n _ {\ mathrm {B}}}$ - the amount of the substance component, mol;
$V$ ${\ displaystyle V}$ - total volume of the mixture, liters;
$z$ ${\ displaystyle z}$ - equivalence number ( equivalence factor $f_{eq}=1/z$ ${\ displaystyle f_ {eq} = 1 / z}$ ).

The normal concentration may vary depending on the reaction in which the substance is involved. For example, a single molar solution of H ₂ SO ₄ will be one-normal if it is intended to react with alkali to form potassium hydrosulfate KHSO ₄ , and two-normal in reaction to form K ₂ SO ₄ .

Molar ( molar ) fraction

The mole fraction is the ratio of the number of moles of a given component to the total number of moles of all components. The mole fraction is expressed in fractions of a unit. IUPAC recommends denoting the mole fraction $x$ ${\ displaystyle x}$ (and for gases - $y$ ${\ displaystyle y}$ ) ^[6] , also in the literature there are notations $\chi$ ${\ displaystyle \ chi}$ , $X$ ${\ displaystyle X}$ .

x_{\mathrm {B} }={\frac {n_{\mathrm {B} }}{\sum n_{i}}}

{\ displaystyle x _ {\ mathrm {B}} = {\ frac {n _ {\ mathrm {B}}} {\ sum n_ {i}}}}

,

Where:

$x_{\mathrm {B} }$ ${\ displaystyle x _ {\ mathrm {B}}}$ - the mole fraction of component B;
$n_{\mathrm {B} }$ ${\ displaystyle n _ {\ mathrm {B}}}$ - the number of component B, mol;
$\sum n_{i}$ ${\ displaystyle \ sum n_ {i}}$ - the sum of the quantities of all components.

The mole fraction can be used, for example, to quantify the level of pollution in the air, while it is often expressed in parts per million (ppm). However, as is the case with other dimensionless quantities, in order to avoid confusion, the value to which the indicated value refers should be indicated.

Molarity ( molar weight concentration , mol concentration )

Molar concentration (molality, ^[4] molar weight concentration) is the amount of dissolved substance (mol) in 1000 g of solvent. It is measured in moles per kg, and the expression in “molality” is also common. Thus, a solution with a concentration of 0.5 mol / kg is called 0.5 molar .

{m_{\mathrm {B} }}={\frac {n_{\mathrm {B} }}{m_{\mathrm {A} }}}

{\ displaystyle {m _ {\ mathrm {B}}} = {\ frac {n _ {\ mathrm {B}}} {m _ {\ mathrm {A}}}}}

,

Where:

$n_{\mathrm {B} }$ ${\ displaystyle n _ {\ mathrm {B}}}$ - amount of solute , mol ;
$m_{\mathrm {A} }$ ${\ displaystyle m _ {\ mathrm {A}}}$ - mass of solvent, kg.

It should be noted that, despite the similarity of the names, the mole concentration and the mole are different. First of all, unlike the molar concentration, when expressing the concentration in molality, the calculation is carried out on the mass of the solvent , and not on the volume of the solution. Molarity, unlike molar concentration, does not depend on temperature.

Mass Concentration (Titer)

Mass concentration - the ratio of the mass of the solute to the volume of the solution. By IUPAC recommendation, indicated by $\gamma$ ${\ displaystyle \ gamma}$ or $\rho$ ${\ displaystyle \ rho}$ ^[7] .

\rho _{\mathrm {B} }={\frac {m_{\mathrm {B} }}{V}}

{\ displaystyle \ rho _ {\ mathrm {B}} = {\ frac {m _ {\ mathrm {B}}} {V}}}

.

Where:

$m_{\mathrm {B} }$ ${\ displaystyle m _ {\ mathrm {B}}}$ - mass of solute;
$V$ ${\ displaystyle V}$ - total volume of the solution;

Analytical chemistry uses the notion of a titer for a dissolved or determined substance (denoted by the letter $T$ ${\ displaystyle T}$ ).

Particle Concentration

According to IUPAC recommendations, the concentration of particles is indicated by the letter $C$ ${\ displaystyle C}$ ^[8] , however, the designation $n$ ${\ displaystyle n}$ (not to be confused with the amount of substance).

C_{\mathrm {B} }={\frac {N_{\mathrm {B} }}{V}}={\frac {n_{\mathrm {B} }\cdot N_{\mathrm {A} }}{V}}=c_{\mathrm {B} }\cdot N_{\mathrm {A} }

{\ displaystyle C _ {\ mathrm {B}} = {\ frac {N _ {\ mathrm {B}}} {V}} = {\ frac {n _ {\ mathrm {B}} \ cdot N _ {\ mathrm {A }}} {V}} = c _ {\ mathrm {B}} \ cdot N _ {\ mathrm {A}}}

,

Where:

$N_{\mathrm {B} }$ ${\ displaystyle N _ {\ mathrm {B}}}$ - the number of particles
$V$ ${\ displaystyle V}$ - volume,
${\ce {n_{\mathrm {B} }}}$ ${\ displaystyle {\ ce {n _ {\ mathrm {B}}}}}$ - the amount of substance B,
$N_{\mathrm {A} }$ ${\ displaystyle N _ {\ mathrm {A}}}$ - Avogadro's constant ,
$c_{\mathrm {B} }$ ${\ displaystyle c _ {\ mathrm {B}}}$ - molar concentration of B.

Weight per cent (mass-volume) percentages

Sometimes there is the use of the so-called "weight percent" ^[9] , which correspond to the mass concentration of the substance, where the unit of measure g / (100 ml) is replaced by the percentage. This method of expression is used, for example, in spectrophotometry , if the molar mass of the substance is unknown or if the composition of the mixture is unknown, as well as traditionally in pharmacopoeial analysis. ^[10] It is worth noting that since the mass and volume have different dimensions, the use of percentages for their ratio is formally incorrect. Also, the International Bureau of Weights and Measures ^[11] and IUPAC ^[12] do not recommend adding additional labels (for example, “% (m / m)” for mass fraction) to the units of measurement.

Other ways of expressing concentration

There are other methods of expressing concentration that are common in certain areas of knowledge or technology. For example, when preparing solutions of acids in laboratory practice, it is often indicated how many parts by volume of water fall on one volume part of the concentrated acid (for example, 1: 3). Sometimes the ratio of the masses (the ratio of the mass of the dissolved substance to the mass of the solvent) and the ratio of the volumes (similarly, the ratio of the volume of the dissolved substance to the volume of the solvent) are also used.

Applicability of methods for expressing the concentration of solutions, their properties

Due to the fact that the molality, mass fraction, molar fraction does not include the volume values, the concentration of such solutions remains unchanged with a change in temperature. Molarity, volume fraction, titer, normality change with temperature, as this changes the density of the solutions. It is the molality that is used in the formulas for raising the boiling point and lowering the freezing temperature of solutions.

Different types of expression of the concentration of solutions are used in different fields of activity, in accordance with the ease of use and preparation of solutions of specified concentrations. Thus, the solution titer is convenient in analytical chemistry for volumetry ( titrimetric analysis ), etc.

Formulas for the transition from one concentration expression to another

Depending on the formula chosen, the conversion error ranges from zero to some decimal place.

From mass fraction to molarity

c_{\mathrm {B} }={\frac {\rho \cdot \omega _{\mathrm {B} }}{M(\mathrm {B} )}}

{\ displaystyle c _ {\ mathrm {B}} = {\ frac {\ rho \ cdot \ omega _ {\ mathrm {B}}} {M (\ mathrm {B})}}}

,

Where:

$c_{\mathrm {B} }$ ${\ displaystyle c _ {\ mathrm {B}}}$ - molar concentration of substance B
$\rho$ ${\ displaystyle \ rho}$ - solution density ;
$\omega _{\mathrm {B} }$ ${\ displaystyle \ omega _ {\ mathrm {B}}}$ - mass fraction of substance B;
$M(\mathrm {B} )$ ${\ displaystyle M (\ mathrm {B})}$ - the molar mass of substance B.

If the density of the solution is expressed in g / ml and the molar mass in g / mol, then the expression should be multiplied by 1000 ml / l to express the response in mol / l. If the mass fraction is expressed as a percentage, then the expression should also be divided by 100%.

From molar concentration to normal

{c((1/z)~\mathrm {B} )}={c_{\mathrm {B} }}\cdot {z}

{\ displaystyle {c ((1 / z) ~ \ mathrm {B})} = {c _ {\ mathrm {B}}} \ cdot {z}}

,

Where:

${c_{\mathrm {B} }}$ ${\ displaystyle {c _ {\ mathrm {B}}}}$ - molar concentration, mol / l;
$z$ ${\ displaystyle z}$ - equivalence number .

From mass fraction to caption

{T}={\rho }\cdot {\omega }

{\ displaystyle {T} = {\ rho} \ cdot {\ omega}}

,

Where:

$\rho$ ${\ displaystyle \ rho}$ - solution density , g / ml;
$\omega$ ${\ displaystyle \ omega}$ - mass fraction of the dissolved substance, in fractions from 1;

From molarity to caption

{T}={c_{\mathrm {B} }}\cdot {M}

{\ displaystyle {T} = {c _ {\ mathrm {B}}} \ cdot {M}}

,

Where:

${c_{\mathrm {B} }}$ ${\ displaystyle {c _ {\ mathrm {B}}}}$ - molar concentration;
$M$ ${\ displaystyle M}$ - the molar mass of the solute.

If the molar concentration is expressed in mol / l and the molar mass is in g / mol, then to express the response in g / ml, it should be divided into 1000 ml / l.

From molarity to molality

m_{\mathrm {B} }={\frac {c_{\mathrm {B} }}{\rho }}

{\ displaystyle m _ {\ mathrm {B}} = {\ frac {c _ {\ mathrm {B}}} {\ rho}}}

,

Where:

${c_{\mathrm {B} }}$ ${\ displaystyle {c _ {\ mathrm {B}}}}$ - molar concentration, mol / l;
$\rho$ ${\ displaystyle \ rho}$ - solution density, g / ml;

From molality to mole fraction

x_{\mathrm {B} }={\frac {m_{\mathrm {B} }}{m_{\mathrm {B} }+{\frac {1}{M(\mathrm {A} )}}}}

{\ displaystyle x _ {\ mathrm {B}} = {\ frac {m _ {\ mathrm {B}}} {m _ {\ mathrm {B}} + {\ frac {1} {M (\ mathrm {A}) }}}}}

,

Where:

$m_{\mathrm {B} }$ ${\ displaystyle m _ {\ mathrm {B}}}$ - molality
$M(\mathrm {A} )$ ${\ displaystyle M (\ mathrm {A})}$ - the molar mass of the solvent.

If the molality is expressed in mol / kg and the molar mass of the solvent is in g / mol, then the unit in the formula should be represented as 1000 g / kg so that the terms in the denominator have the same units of measurement.

Notes

↑ International Union of Pure and Applied Chemistry. concentration (Eng.) // IUPAC Compendium of Chemical Terminology. - Research Triagle Park, NC: IUPAC. - ISBN 0967855098 . - DOI : 10.1351 / goldbook.C01222 .
↑ International Union of Pure and Applied Chemistry. fraction (English) // IUPAC Compendium of Chemical Terminology. - Research Triagle Park, NC: IUPAC. - ISBN 0967855098 . - DOI : 10.1351 / goldbook.F02494 .
↑ International Union of Pure and Applied Chemistry. IUPAC Gold Book - mass fraction, w (English) . goldbook.iupac.org. The appeal date is December 11, 2018.
↑ ¹ ² Z. Sobecka, W. Choiński, P. Majorek. Dictionary of Chemical Technology: In Six Languages: English / German / Spanish / French / Polish / Russian . - Elsevier, 2013-09-24. - p. 641. - 1334 p. - ISBN 9781483284439 .
↑ International Union of Pure and Applied Chemistry. IUPAC Gold Book - amount concentration, c (English) . goldbook.iupac.org. The appeal date is December 11, 2018.
↑ International Union of Pure and Applied Chemistry. IUPAC Gold Book - amount fraction, x (y for gaseous mixtures) (English) . goldbook.iupac.org. The appeal date is December 11, 2018.
↑ International Union of Pure and Applied Chemistry. IUPAC Gold Book - mass concentration, γ, ρ (English) . goldbook.iupac.org. The appeal date is December 16, 2018.
↑ International Union of Pure and Applied Chemistry. IUPAC Gold Book - number concentration, C, n (English) . goldbook.iupac.org. The appeal date is December 11, 2018.
↑ Methods of preparation of solutions for Medkurs. Ru
↑ Bernstein I. Ya. , Kaminsky Yu. L. Spectrophotometric analysis in organic chemistry. - 2nd ed. - Leningrad: Chemistry, 1986. - p. five
↑ The International System of Units (SI) (Unidentified) . www.bipm.org. The appeal date is December 23, 2018.
↑ Quantities, Units and Symbols in Physical Chemistry (Neopr.) . www.iupac.org. The appeal date is December 23, 2018.

[1] International Union of Pure and Applied Chemistry. concentration (Eng.) // IUPAC Compendium of Chemical Terminology. - Research Triagle Park, NC: IUPAC. - ISBN 0967855098 . - DOI : 10.1351 / goldbook.C01222 .

[2] International Union of Pure and Applied Chemistry. fraction (English) // IUPAC Compendium of Chemical Terminology. - Research Triagle Park, NC: IUPAC. - ISBN 0967855098 . - DOI : 10.1351 / goldbook.F02494 .

[3] International Union of Pure and Applied Chemistry. IUPAC Gold Book - mass fraction, w (English) . goldbook.iupac.org. The appeal date is December 11, 2018.

[:0-4] ¹ ² Z. Sobecka, W. Choiński, P. Majorek. Dictionary of Chemical Technology: In Six Languages: English / German / Spanish / French / Polish / Russian . - Elsevier, 2013-09-24. - p. 641. - 1334 p. - ISBN 9781483284439 .

[5] International Union of Pure and Applied Chemistry. IUPAC Gold Book - amount concentration, c (English) . goldbook.iupac.org. The appeal date is December 11, 2018.

[6] International Union of Pure and Applied Chemistry. IUPAC Gold Book - amount fraction, x (y for gaseous mixtures) (English) . goldbook.iupac.org. The appeal date is December 11, 2018.

[7] International Union of Pure and Applied Chemistry. IUPAC Gold Book - mass concentration, γ, ρ (English) . goldbook.iupac.org. The appeal date is December 16, 2018.

[8] International Union of Pure and Applied Chemistry. IUPAC Gold Book - number concentration, C, n (English) . goldbook.iupac.org. The appeal date is December 11, 2018.

[9] Methods of preparation of solutions for Medkurs. Ru

[10] Bernstein I. Ya. , Kaminsky Yu. L. Spectrophotometric analysis in organic chemistry. - 2nd ed. - Leningrad: Chemistry, 1986. - p. five

[11] The International System of Units (SI) (Unidentified) . www.bipm.org. The appeal date is December 23, 2018.

[12] Quantities, Units and Symbols in Physical Chemistry (Neopr.) . www.iupac.org. The appeal date is December 23, 2018.

Mixture concentration

Content

Bulk

Bulk Share

Molarity ( molar volume concentration )

Normal concentration ( molar concentration equivalent , " normality ")

Molar ( molar ) fraction

Molarity ( molar weight concentration , mol concentration )

Mass Concentration (Titer)

Particle Concentration

Weight per cent (mass-volume) percentages

Other ways of expressing concentration

Applicability of methods for expressing the concentration of solutions, their properties

Formulas for the transition from one concentration expression to another

From mass fraction to molarity

From molar concentration to normal

From mass fraction to caption

From molarity to caption

From molarity to molality

From molality to mole fraction

Notes

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