CHEMICAL CONCENTRATION: EXPRESSION, UNITS, MOLALITY - CHEMISTRY - 2025

The chemical concentration is the numerical measure of the relative amount of solute in a solution. This measurement expresses a ratio of the solute to an amount or volume of the solvent or solution in units of concentration. The term "concentration" is related to the amount of solute present: a solution will be more concentrated the more solute it has.

These units can be physical when the mass and / or volume magnitudes of the solution or chemical components are taken into account, when the concentration of the solute is expressed in terms of its moles or equivalents, taking Avogadro's number as a reference.

By Leiem, from Wikimedia Commons

Thus, by using molecular or atomic weights, and Avogadro's number, it is possible to convert physical units into chemical units when expressing the concentration of a given solute. Therefore, all units can be converted for the same solution.

Diluted and concentrated solutions

How can you tell if a concentration is very dilute or concentrated? At first glance by the manifestation of any of its organoleptic or chemical properties; that is, those that the senses perceive or that can be measured.

The upper image shows a dilution of a concentration of potassium dichromate (K ₂ Cr ₂ O ₇), which exhibits an orange color. From left to right, you can see how the color decreases in intensity as the concentration is diluted, adding more solvent.

This dilution makes it possible to obtain in this way a dilute concentration from a concentrated one. The color (and other "hidden" properties in its orange core) changes in the same way as its concentration does, either with physical or chemical units.

But what are the chemical units of concentration? Among them are the molarity or molar concentration of a solution, which relates the moles of solute by the total volume of the solution in liters.

There is also molality or also called molal concentration, which refers to the moles of solute but which are contained in a standardized amount of the solvent or solvent that is exactly one kilogram.

This solvent can be pure or if the solution contains more than one solvent, the molality will be the moles of solute per kilogram of the solvent mixture.

And the third unit of chemical concentration is the normality or normal concentration of a solution that expresses the number of chemical equivalents of the solute per liter of the solution.

The unit in which normality is expressed is in equivalents per liter (Eq / L) and in medicine the concentration of electrolytes in human serum is expressed in milliequivalents per liter (mEq / L).

Ways of expressing concentration

The concentration of a solution can be denoted in three main ways, even though they have a great variety of terms and units themselves, that can be used to express the measure of this value: qualitative description, quantitative notation, and classification in terms solubility.

Depending on the language and context in which you are working, one of three ways will be chosen to express the concentration of a mixture.

Qualitative description

Used mainly in informal and non-technical language, the qualitative description of the concentration of a mixture is expressed in the form of adjectives, which indicate in a generalized way the level of concentration that a solution has.

Thus, the minimum concentration level according to the qualitative description is that of a "dilute" solution, and the maximum is that of "concentrated".

We speak of dilute solutions when a solution has a very low proportion of solute as a function of the total volume of the solution. If you want to dilute a solution, add more solvent or find a way to reduce the solute.

Now, we speak of concentrated solutions when they have a high proportion of solute as a function of the total volume of solution. To concentrate a solution, add more solute, or reduce the amount of solvent.

In this sense, this classification is called qualitative description, not only because it lacks mathematical measurements but because of its empirical quality (it can be attributed to visual features, smells and tastes, without the need for scientific tests).

Classification by solubility

The solubility of a concentration denotes the maximum solute capacity that a solution possesses, depending on conditions such as temperature, pressure and the substances that are dissolved or in suspension.

Solutions can be classified into three types according to their level of dissolved solute at the time of measurement: unsaturated, saturated, and supersaturated solutions.

- Unsaturated solutions are those that contain a smaller amount of solute than the solution can dissolve. In this case, the solution has not reached its maximum concentration.

- Saturated solutions are those in which the maximum amount of solute possible has been dissolved in the solvent at a specific temperature. In this case there is an equilibrium between both substances and the solution cannot accept more solute (since it will precipitate).

- The supersaturated solutions have more solute than the solution would accept under equilibrium conditions. This is accomplished by heating a saturated solution, adding more solute than normal. Once cold, it will not precipitate the solute automatically, but any disturbance can cause this effect due to its instability.

Quantitative notation

When studying a solution to be used in the technical or scientific field, a precision measured and expressed in units is required, which describe the concentration according to its exact values ​​of mass and / or volume.

This is why there is a series of units used to express the concentration of a solution in its quantitative notation, which are divided into physical and chemical, and which in turn have their own subdivisions.

The units of physical concentrations are those of "relative concentration", which are expressed in terms of percentages. There are three ways to express percent concentrations: mass percentages, volume percentages, and mass-volume percentages.

Instead, units of chemical concentrations are based on molar amounts, gram equivalents, parts per million, and other characteristics of the solute relative to solution.

These units are the most common due to their high precision when measuring concentrations, and for this reason they are usually the ones that you want to know when working with chemical solutions.

Concentration units

As described in the previous sections, when quantitatively characterizing the concentration of a solution, the calculations should be governed by the existing units for this purpose.

Likewise, the concentration units are divided into those of relative concentration, those of dilute concentrations, those based on moles, and additional ones.

Relative concentration units

Relative concentrations are those expressed in percentages, as named in the previous section. These units are divided into mass-mass percent, volume-volume percent, and mass-volume percent, and are calculated as follows:

-% mass = mass of solute (g) / mass of total solution (g) x 100

-% volume = volume of solute (ml) / volume of total solution (ml) x 100

-% mass / volume = mass of solute (g) / volume of total solution (ml) x 100

In this case, to calculate the mass or volume of the total solution, the mass or volume of the solute must be added with that of the solvent.

Units of dilute concentration

The units of dilute concentration are those that are used to express those very small concentrations that are in the form of traces within a dilute solution; the most common use for these units is to find traces of one gas dissolved in another, such as agents that pollute the air.

These units are listed in the form of parts per million (ppm), parts per billion (ppb), and parts per trillion (ppt), and are expressed as follows:

- ppm = 1 mg solute / 1 L solution

- ppb = 1 μg solute / 1 L solution

- ppt = 1 ng solute / 1 L solution

In these expressions mg is equal to milligrams (0.001 g), μg is equal to micrograms (0.000001 g), and ng is equal to nanograms (0.000000001 g). These units can also be expressed in terms of volume / volume.

Concentration units as a function of moles

The concentration units based on moles are those of the mole fraction, mole percentage, molarity and molality (the latter two are better described at the end of the article).

The mole fraction of a substance is the fraction of all its constituent molecules (or atoms) as a function of the total molecules or atoms. It is calculated as follows:

X _A = number of moles of substance A / total number of moles in solution

This procedure is repeated for the other substances in solution, taking into account that the sum of X _A + X _B + X _C … must be equal to one.

The mole percentage is worked in a similar way to X _A, only in terms of percentage:

Molar percent of A = X _A x 100%

The final section will discuss molarity and molality in detail.

Formality and normality

Finally, there are two units of concentration that are currently in disuse: formality and normality.

The formality of a solution represents the number of weight-formula-gram per liter of total solution. It is expressed as:

F = No. PFG / L solution

In this expression PFG is equal to the weight of each atom of the substance, expressed in grams.

Instead, normality represents the number of solute equivalents divided by liters of solution, as expressed below:

N = equivalent grams of solute / L solution

In said expression, the equivalent grams of solute can be calculated by the number of moles H ⁺, OH ^- or other methods, depending on the type of molecule.

Molarity

The molarity or molar concentration of a solute is the unit of chemical concentration that expresses or relates the moles of the solute (n) that are contained in one (1) liter (L) of the solution.

Molarity is designated by the capital letter M and to determine the moles of the solute (n), the grams of the solute (g) are divided by the molecular weight (MW) of the solute.

Likewise, the molecular weight MW of the solute is obtained from the sum of the atomic weights (PA) or atomic mass of the chemical elements, considering the proportion in which they combine to form the solute. Thus, different solutes have their own PM (although this is not always the case).

These definitions are summarized in the following formulas used to perform the corresponding calculations:

Molarity: M = n (moles of solute) / V (liter of solution)

Number of moles: n = g of solute / MW of solute

Exercise 1

Calculate the Molarity of a solution that is prepared with 45 g of Ca (OH) ₂ dissolved in 250 mL of water.

The first thing to calculate is the molecular weight of Ca (OH) ₂ (calcium hydroxide). According to its chemical formula, the compound is made up of a calcium cation and two hydroxyl anions. Here the weight of an electron less or additional to the species is negligible, so the atomic weights are taken:

Source: Gabriel Bolívar

The number of moles of the solute will then be:

n = 45 g / (74 g / mol)

n = 0.61 moles of Ca (OH) ₂

0.61 moles of the solute are obtained but it is important to remember that these moles lie dissolved in 250 mL of solution. As the definition of Molarity is moles in a liter or 1000 mL, a simple rule of three must then be made to calculate the moles that are in 1000 mL of said solution

If in 250 mL of solution there are => 0.61 moles of solute

In 1000 mL of solution => x How many moles are there?

x = (0.61 mol) (1000 mL) / 250 mL

X = 2.44 M (mol / L)

Another way

The other way to obtain the moles to apply the formula requires that the 250 mL be taken to liters, also applying a rule of three:

If 1000 ml => are 1 liter

250 ml => x How many liters are they?

x = (250 mL) (1 L) / 1000 mL

x = 0.25 L

Substituting then in the Molarity formula:

M = (0.61 mol of solute) / (0.25 L of solution)

M = 2.44 mol / L

Exercise 2

What does it mean for an HCl solution to be 2.5 M?

The HCl solution is 2.5 molar, that is, one liter of it has dissolved 2.5 moles of hydrochloric acid.

Normal

The normality or equivalent concentration is the unit of chemical concentration of the solutions that is designated with the capital letter N. This unit of concentration indicates the reactivity of the solute and is equal to the number of equivalents of solute (Eq) divided by the volume of the solution expressed in liters.

N = Eq / L

The number of equivalents (Eq) is equal to the grams of solute divided by the equivalent weight (PEq).

Eq = g solute / PEq

The equivalent weight, or also known as gram equivalent, is calculated by obtaining the molecular weight of the solute and dividing it by an equivalent factor that for the purposes of summarizing in the equation is called delta zeta (ΔZ).

PEq = PM / ΔZ

Calculation

The calculation of normality will have a very specific variation in the equivalent factor or ΔZ, which also depends on the type of chemical reaction in which the solute or reactive species participates. Some cases of this variation can be mentioned below:

-When it is an acid or base, ΔZ or the equivalent factor, will be equal to the number of hydrogen ions (H ⁺) or hydroxyl OH ^- that the solute has. For example, sulfuric acid (H ₂ SO ₄) has two equivalents because it has two acidic protons.

-When it comes to oxidation-reduction reactions, ΔZ will correspond to the number of electrons involved in the oxidation or reduction process, depending on the specific case. Here the balancing of chemical equations and the specification of the reaction come into play.

-Also, this equivalent factor or ΔZ will correspond to the number of ions that precipitate in reactions classified as precipitation.

Exercise 1

Determine the Normality of 185 g of Na ₂ SO ₄ found in 1.3 L of solution.

The molecular weight of the solute in this solution will first be calculated:

Source: Gabriel Bolívar

The second step is to calculate the equivalent factor or ΔZ. In this case, as sodium sulfate is a salt, the valence or charge of the cation or metal Na ^{+ will be considered}, which will be multiplied by 2, which is the subscript of the chemical formula of the salt or solute:

Na ₂ SO ₄ => ∆Z = Valencia Cation x Subscript

∆Z = 1 x 2

To obtain the equivalent weight, it is substituted in its respective equation:

PEq = (142.039 g / mol) / (2 Eq / mol)

PEq = 71.02 g / Eq

And then you can proceed to calculate the number of equivalents, again resorting to another simple calculation:

Eq = (185 g) / (71.02 g / Eq)

Number of equivalents = 2.605 Eq

Finally, with all the necessary data, normality is now calculated by substituting according to its definition:

N = 2.605 Eq / 1.3 L

N = 2.0 N

Molality

Molality is designated by the lowercase letter m and is equal to the moles of solute that are present in one (1) kilogram of the solvent. It is also known as molal concentration and is calculated using the following formula:

m = moles of solute / Kg of solvent

While Molarity establishes the ratio of the moles of solute contained in one (1) liter of the solution, the molality relates the moles of solute that exist in one (1) kilogram of solvent.

In those cases that the solution is prepared with more than one solvent, the molality will express the same mole of solute per kilogram of the solvent mixture.

Exercise 1

Determine the molality of a solution that was prepared by mixing 150 g of sucrose (C ₁₂ H ₂₂ 0 ₁₁) with 300 g of water.

The molecular weight of sucrose is first determined to proceed to calculate the moles of solute in this solution:

Source: Gabriel Bolívar

The number of moles of sucrose is calculated:

n = (150g sucrose) / (342.109 g / mol)

n = 0.438 moles of sucrose

The grams of solvent are then converted to kilograms in order to apply the final formula.

Substituting then:

m = 0.438 moles of sucrose / 0.3 kilograms of water

m = 1.46 mol C ₁₂ H ₂₂ 0 ₁₁ / Kg H ₂ O

Although there is currently a debate about the final expression of molality, this result can also be expressed as:

1.26 m C ₁₂ H ₂₂ 0 ₁₁ or 1.26 molal

It is sometimes considered advantageous to express the concentration of the solution in terms of molality, since the masses of the solute and the solvent do not suffer slight fluctuations or inapparent changes due to the effects of temperature or pressure; as it happens in solutions with gaseous solute.

Furthermore, it is pointed out that this concentration unit referred to a specific solute is unchanged by the existence of other solutes in the solution.

Recommendations and Important Notes on Chemical Concentration

The volume of the solution is always greater than that of the solvent

As the solution exercises are solved, the error of interpreting the volume of a solution as if it were that of the solvent arises. For example, if one gram of powdered chocolate is dissolved in one liter of water, the volume of the solution is not equal to that of one liter of water.

Why not? Because the solute will always occupy space between the solvent molecules. When the solvent has a high affinity for the solute, the change in volume after dissolution can be negligible or negligible.

But, if not, and even more so if the amount of solute is large, the change in volume must be taken into account. Being this way: Vsolvent + Vsolute = Vsolution. Only in dilute solutions or where the amounts of solute are small is valid Vsolvent = Vsolution.

This error should be kept in mind especially when working with liquid solutes. For example, if instead of dissolving powdered chocolate, honey is dissolved in alcohol, then the volume of honey added will have a noticeable effect on the total volume of the solution.

Therefore, in these cases the volume of the solute must be added to that of the solvent.

Utility of Molarity

-Knowing the Molarity of a concentrated solution allows dilution calculations to be made using the simple formula M1V1 = M2V2, where M1 corresponds to the initial Molarity of the solution and M2 the Molarity of the solution to be prepared from the solution with M1.

-Knowing the Molarity of a solution, its Normality can be easily calculated using the following formula: Normality = number of equivalent x M

The formulas are not memorized but the units or definitions are

However, sometimes memory fails when trying to remember all the equations pertinent to concentration calculations. For this, it is very useful to have a very clear definition of each concept.

Starting from the definition, the units are written using the conversion factors to express those that correspond to what is to be determined.

For example, if you have molality and you want to convert it to normal, proceed as follows:

(mol / Kg solvent) x (kg / 1000g) (g solvent / mL) (mL solvent / mL solution) (1000mL / L) (Eq / mol)

Note that (g solvent / mL) is the density of the solvent. The term (mL solvent / mL solution) refers to how much volume of the solution actually corresponds to the solvent. In many exercises this last term is equal to 1, for practical reasons, although it is never completely true.

References

1. Introductory Chemistry- 1 ^st Canadian Edition. Quantitative Units of Concentration. Chapter 11 Solutions. Taken from: opentextbc.ca
2. Wikipedia. (2018). Equivalent Concentration. Taken from: en.wikipedia.org
3. PharmaFactz. (2018). What is molarity? Taken from: pharmafactz.com
4. Whitten, Davis, Peck & Stanley. Chemistry. (8th ed.). CENGAGE Learning, p 101-103, 512, 513.
5. Aqueous Solutions-Molarity. Taken from: chem.ucla.edu
6. Quimicas.net (2018). Examples of Normality. Recovered from: quimicas.net.