Concentration

These vessels, which contain a reddish brown dye, show qualitative changes in concentration.

In chemistry, the concentration of a solution is the proportion or relationship between the amount of solute and the amount of solution or, sometimes, solvent; where the solute is the substance that dissolves, the solvent is the substance that dissolves the solute, and the solution is the result of the homogeneous mixture of the two previous ones. The lower the proportion of solute dissolved in the solvent, the less concentrated the solution is, and the higher the proportion, the more concentrated it is.

A solution is a homogeneous mixture at the molecular level of two or more substances.

The term is also used to refer to a concentration process, and to increase the proportion of solute in the solvent, inverse to that of dilution.

Solubility

solubility table at 15 °C

Each substance has a solubility for a given solvent. Solubility is the maximum amount of solute that can remain dissolved in a solution, and depends on conditions such as temperature, pressure, and other dissolved or suspended substances. When the maximum amount of solute in a solution is reached, the solution is said to be saturated, and no more dissolved solute will be admitted into it. If we add a little common salt to a glass of water, for example, and shake it with a teaspoon, the salt will dissolve. If we continue adding salt, there will be more and more concentration of it until the water can no longer dissolve more salt no matter how much we shake it. Then, the solution will be saturated, and the salt that we add to it, instead of dissolving, will precipitate to the bottom of the glass. If we heat the water, it will be able to dissolve more salt (it will increase the solubility of the salt in the water), and if we cool it, the water will have less capacity to retain dissolved salt, and the excess will precipitate.

Ways of expressing concentration

Conceptual map of ways to express the chemical concentration

Quantitative terms are when the concentration is expressed scientifically in a very exact and precise numerical way. Some of these quantitative ways of measuring concentration are solute percentages, molarity, normality, and parts per million, among others. These quantitative forms are used both in the industry for the elaboration of products and also in scientific research.

Examples

Commercial alcohol for domestic use. It usually does not come in a pure form (100% alcohol), but is a solution of alcohol in water in a certain proportion, where alcohol is the solute (the substance that dissolves) and water is the solvent (the substance that dissolves the solute). When the label on the container says that this alcohol is at 70% V/V (of concentration) it means that there is 70% alcohol, and the rest, 30%, is water. Commercial orange juice usually has a concentration of 60% V/V, which indicates that 60% (the solute) is orange juice, and the rest, 40% (the solvent), is water. Iodine tincture, which in a commercial presentation can have a 5% concentration, means that there is 5% iodine, (the solute), dissolved in 95% alcohol, (the solvent).

Concentration in qualitative terms

The concentration of the solutions in qualitative terms, also called empirical, does not take into account quantitatively (numerically) the exact quantity of solute and solvent present, and depending on their proportion the concentration is classified as follows:

Diluted or concentrated

Example of concentrated dissolution: Honey

Often in informal, non-technical language, concentration is described in a qualitative way, using adjectives such as "diluted" or "weak" for solutions of relatively low concentration, and others such as "concentrate" or "strong" for solutions of relatively high concentration. In a mixture, these terms relate the amount of a substance to the observable intensity of the effects or properties, such as color, taste, odor, viscosity, electrical conductivity, etc., caused by that substance. For example, the strength of a coffee can be determined by the intensity of its color and flavor, that of a lemonade by its taste and smell, that of sugar water by its taste. A rule of thumb is that the more concentrated a chromatic solution is, the more intensely colored it is generally.

Example of diluted dissolution: coffee sugar

Depending on the ratio of solute to solvent, a solution can be dilute or concentrated: (taking into account the nature of the components)

• Diluted dissolution: is that where the amount of solute is in a small proportion in a given volume.
• Concentrated dissolution: it is the one that has a considerable amount of solute in a given volume.

Saturated and supersaturated solutions can be diluted or concentrated depending on their solubility, so a saturated solution of NaCl (common salt) will be concentrated, but a saturated solution of CaCO3 (calcite or limestone) will be diluted because it is very slightly soluble.

• Example of diluted dissolution: sugar in coffee.
• Example of concentrated dissolution: honey (sugars of it in water).

Unsaturated, saturated and supersaturated

The concentration of a solution can be classified, in terms of solubility. Depending on whether the solute is dissolved in the solvent in the maximum amount possible, or less, or greater than this amount, for a given temperature and pressure:

• Unsaturated dissolution: It is the dissolution in which the solute does not reach its maximum concentration that can dilute.
• Saturated Dissolution: There is a balance between the solute and the solvent.
• Oversaturated dissolution: it has more solute than the maximum allowed in a saturated dissolution. When a saturated dissolution is heated, a greater amount of solute can be dissolved. If this dissolution cools slowly, it can keep this solute in excess if it is not disturbed. However, the oversaturated dissolution is unstable, and with any disturbance, such as a sudden movement, or soft blows in the container that contains it, the excess solute will immediately be precipitated, remaining then as a saturated dissolution.

Concentration in quantitative terms

Quantitative terms of dissolution

For scientific or technical uses, a qualitative appreciation of the concentration is almost never sufficient, therefore quantitative measurements are necessary to describe the concentration.

Unlike concentrations expressed in a qualitative or empirical way, concentrations expressed in quantitative or evaluative terms take into account in a very precise way the proportions between the amounts of solute and solvent that are being used in a solution. This type of concentration classification is widely used in industry, chemical procedures, pharmacy, science, etc., since all of them require very precise measurements of product concentrations.

There are several ways to express concentration quantitatively, based on mass, volume, or both. Depending on how it is expressed, it may not be trivial to convert from one measure to the other, and it may be necessary to know the density. Occasionally this information may not be available, particularly if the temperature varies. Therefore, the concentration of the solution can be expressed as:

• Percentage mass-mass (% m/m)
• Percentage volume-volume (% V/V)
• Percentage mass-volume (% m/V)
• Molarity
• Molality
• Formality
• Normality
• Molar fracture
• In very small concentrations:
  • Parts per million (PPM)
  • Parts per billion (PPB)

• • Parts per trillion (PPT)
• Other:
  • Density
  • Own names

In the International System of Units (SI) the units mol·m^-3 are used.

Mass-to-mass, volume-to-volume and mass-to-volume percentages

Mass-to-mass percentage (% m/m)

It is defined as the mass of solute (substance that dissolves) per 100 mass units of the solution:

${displaystyle$

For example, if 20 g of sugar is dissolved in 80 g of water, the mass percentage will be: ${displaystyle {frac {20}{20+80}}cdot 100=20$ o, to distinguish it from other percentages, 20% p/p (in English, % w/w).

Volume-to-volume percentage (% v/v)

Expresses the volume of solute per hundred units of volume of the solution. It is usually used for liquid or gaseous mixtures, in which the volume is an important parameter to take into account. That is, the percentage that the solute represents in the total volume of the solution. It is usually expressed simply as “% v/v”.

${displaystyle$

For example, if you have a solution of 20% by volume (20% v/v) of alcohol in water, it means that there are 20 ml of alcohol for every 100 ml of solution.

The alcoholic graduation of the drinks is expressed precisely like this: a wine of 12 degrees (12°) has 12% v/v of alcohol.

Mass-volume percentage (% m/v)

The same units can also be used to measure density, although it is not convenient to combine both concepts. The density of the mixture is the mass of the solution divided by the volume of the solution, while the concentration in these units is the mass of solute divided by the volume of the solution times 100. Grams per milliliter (g/mL) is often used.) and is sometimes expressed as “% m/v”.

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Calculations with mass-mass and volume-volume percentages

For calculations with mass-mass and volume-volume percentages we must handle two concepts:

1. The sum of the mass of the solute plus the mass of the solvent is equal to the mass of the dissolution

   Dissolution = solute + solvent

2. The simple three rule is used to calculate proportionality.

Molarity

The molarity (M), or molar concentration, is the amount of substance (n) of solute per liter of solution. For example, if 0.5 moles of solute are dissolved in 1000 mL of solution, you have a concentration of that solute of 0.5 M (0.5 molar). To prepare a solution of this concentration, the solute is usually first dissolved in a smaller volume, for example 300 mL, and this solution is transferred to a volumetric flask, to then make up to volume with more solvent up to 1000 mL.

${displaystyle M={frac {mbox{moles de soluto (n)}}{mbox{volumen de disolucion (L)}}}}$

It is the most common method of expressing concentration in chemistry, especially when working with chemical reactions and stoichiometric relationships. However, this process has the drawback that the volume changes with temperature.

It is also represented as: M = n / V, where "n" is the amount of substance (n= mol solute/molar mass) and "V" is the volume of the solution expressed in liters.

Molality

The molality (m) is the number of moles of solute contained in one kilogram of solvent. To prepare solutions of a certain molality, a volumetric flask is not used as in the case of molarity, but can be done in a beaker and weighed with an analytical balance, after weighing the empty glass to be able to subtract the corresponding value..

${displaystyle m={frac {mbox{moles de soluto (n)}{mbox{masa de solvent (kg)}}}}$

The main advantage of this method of measurement with respect to molarity is that since the volume of a solution depends on temperature and pressure, when these change, the volume changes with them. Because molality is not a function of volume, it is independent of temperature and pressure, and can be measured with greater precision.

It is less used than molarity but just as important.

The SI unit for molality is the mol/kg.

Formality

The formality (F) is the number of weight-formula-gram or Relative Molecular Mass per liter of solution, or number of moles of solute.

${displaystyle F={frac {mbox{no PFG}}{mbox{volumen (liter dissolution)}}}}$

The number of weight-formula-gram has unit of g / PFG.

Normal

The normality (N) is the number of equivalents (eq-g) of solute (sto) between the volume of the solution in liters (L)

${displaystyle N={frac {eqg_{sto}}{V_{L}}}}$

Acid-base normality

It is the normality of a solution when it is used for a reaction as an acid or as a base. For this reason they are usually titrated using pH indicators.

In this case, the equivalents can be expressed as follows:

${displaystyle n={moles}cdot {H^{+}}}}$ for an acid, or ${displaystyle n={moles}cdot {OH^{-}}}}$ for a base.

Where:

• moles It's the amount of moles.
• OH^- is the amount of hydroxyl yielded by a base molecule.

For this, we can say the following:

${displaystyle N={M}cdot {H^{+}}}}}$ for an acid, or ${displaystyle N={M}cdot {OH^{-}}}}$ for a base.

Where:

• M is the molarity of dissolution.
• H⁺ is the amount of protons yielded by an acid molecule.
• OH^- is the amount of hydroxyl yielded by a base molecule.

Examples:

• A dissolution 1 M of HCl yields 1 H+, therefore, is a dissolution 1 N.
• A 1 M dissolution of Ca (OH)2 yields 2 OH–, therefore, is a dissolution 2 N.

Redox normality

It is the normality of a solution when it is used for a reaction as an oxidizing agent or as a reducing agent. As the same compound can act as an oxidant or as a reducer, it is usually indicated whether it is normal as an oxidant (N_ox) or as a reducer (N_rd). For this reason, they are usually titled using redox indicators.

In this case, the equivalents can be expressed as follows:

${displaystyle n={moles}cdot {e^{-}}}}$.

Where:

• n is the amount of equivalents.
• moles It's the amount of moles.
• e^- is the amount of electrons exchanged in oxidation semirreaction or reduction.

For this, we can say the following:

${displaystyle N={M}cdot {e^{}}}}$.

Where:

• N is the normality of dissolution.
• M is the molarity of dissolution.
• e^-: It is the amount of electrons exchanged in oxidation semirreaction or reduction by substance mol.

Examples:

• In the following case we see that nitrate anion in acid (e.g. nitric acid) can act as oxidant, and then a dissolution 1 M is 3 N_ox.

4 H+ + NO3– + 3 e– 7.00 NO + 2 H2O

• In the following case we see that iodide anion can act as a reducer, and then a dissolution 1 M is 1 N_rd.

2 I- ↔ I2 + 2 e-

• In the following case we see that the argentic catheion can act as oxidant, where a dissolution 1 M is 1 N_ox.

1 Ag+ + 1 e– ↔

Small concentrations

To express very small concentrations, traces of a highly diluted substance in another, it is common to use the relationships parts per million (ppm), parts per & #34;billion" (ppb) and parts per "trillion" (ppt). The million equals 10⁶, the US trillion or billion equals 10⁹, and the US trillion equals 10¹².

It is used relatively frequently in measuring the composition of the Earth's atmosphere. Thus, the increase in carbon dioxide in the air, one of the causes of global warming, usually occurs in these units.

The most frequently used units are:

However, other units are sometimes used.

For example, 1 ppm of CO₂ in air could be, in some contexts, one molecule of CO₂ in a million molecules of air components.

Another example: speaking of traces in aqueous solutions, 1 ppm corresponds to 1 mg solute/ kg solution or, what is the same, 1 mg solute/ L solution -since in these cases, the volume of the solute is negligible, and the density of water is 1 kg/L.

Smaller relationships are also sometimes referred to, for example "quadrillion". However, they are excessively small concentrations and are not usually used.

The IUPAC discourages the use of these relationships (especially in the case of mass between volume) and recommends using the corresponding units.

The use of ppb and ppt is particularly tricky, given the different meanings of billion and trillion in the US and European environments.

Useful conversions

${displaystyle X_{st}={frac {m}{{{frac {1000}{P_{sv}}}}}}}$

• Molar friction to grind (X)st→m), and recalling that Xst + Xsv = 1

${displaystyle X={frac {1000cdot X_{st}}{P_{sv}cdot X{sv}}}}}}$

• Molality to molarity (m→M)

${displaystyle M={frac {1000cdot dcdot m}{1000+(mcdot P_{st}}}}}}}$

• Molarity to molarity (M→m)

${displaystyle m={frac {1000cdot M}{1000cdot d-Mcdot P_{st}}}}}$

• Percentage in weight to percentage in volume

${displaystyle$

• Volume weight to molarity

${displaystyle M={frac {$

Where:

• P_sv = Molar weight of the solvent (g/mol)
• P_st = Ground weight of the solute (g/mol)
• d = density (g/mL)
• %P/P = Concentration in g soluto/100 g dissolution
• %P/V = Concentration in g soluto/100 mL dissolution
• m = Soluto milling/kg solvent

Other ways of indicating concentration

For certain frequently used solutions (for example sulfuric acid, sodium hydroxide, etc.) the concentration is indicated in other ways:

Density

Although density is not a way of expressing concentration, it is proportional to concentration (under the same conditions of temperature and pressure). For this reason, sometimes the density of the solution is expressed under normal conditions instead of indicating the concentration; but it is used more practically and with very widely used solutions. There are also density-to-concentration conversion tables for these solutions, although the use of density to indicate concentration is a practice that is falling out of favor.

Baume Scale

The Baumé scale is a scale used to measure the concentrations of certain solutions (syrups, acids). It was created by the French chemist and pharmacist Antoine Baumé (1728 – 1804) in 1768 when he built his hydrometer. Each element of the Baumé scale division is called Baumé degree and is symbolized by ºB or ºBé.

Brix Scale

The Brix degrees (symbol °Bx) are used to determine the total ratio of sucrose dissolved in a liquid. A 25 °Bx solution contains 25 g of sugar (sucrose) per 100 g of liquid. In other words, in 100 g of solution there are 25 g of sucrose and 75 g of water.

Brix degrees are quantified with a saccharimeter -which measures the density (or specific gravity) of liquids- or, more easily, with a refractometer or a polarimeter.

The Brix scale is a refinement of the Balling scale tables, developed by the German chemist Karl Balling. The Plato scale, which measures Plato degrees, is also part of the Balling scale. All three are used, often interchangeably. Their differences are of minor importance. The Brix scale is used, above all, in the manufacture of juices (juices), fruit wines and cane-based sugar. The Plato scale is used primarily in brewing. The Balling scale is obsolete, but still appears on older saccharimeters.

Proper nouns

Some solutions are used in a certain concentration for some specific techniques. And in these cases a proper name is usually used.