Chemistry

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Molar concentration

• Definition of molar concentration
• The molar concentration influence on a solution
• Determine a molar concentration
• Molar concentration and mass concentration
• Use the molar concentration to calculate a quantity of solute
• Use the molar concentration to calculate the volume of the solution
• Molar concentration and dilution
• Molar concentration and vaporization
• Molar concentration and saturation
• Preparation of a solution with a known molar concentration

Definition of molar concentration

The molar concentration is a quantity characterizing any solution, it reflects the proportion of a dissolved chemical species (solute) in a solvent. The molar concentration (C) of a chemical species is the ratio of the quantity (n) of this chemical species by the volume (V) of the solution, which results in the following formula:

C =   n  
        V

• C is usually expressed in moles per liter (mol / L), other units are possible (mmol / L, mol / mL etc.) but the mol / L is the most common unit (most relations intervening molar concentration require this unit).
• n is mole (mol)
• V is in liter (L)

NB:
• The notation C is often accompanied by an indication of the concerned chemical species whose name or formula may be mentioned in parentheses or in subscript.
• The volume V used to calculate a molar concentration is the volume of the solution and not the volume of the solvent but when the quantity of matter is low, it is often possible to make an approximation that the volume of the solution is the same as that of the solvent.
• When the term "concentration" is used without precision it usually refers to the molar concentration and not to the mass concentration. Similarly, if the notation "C" is used without precision then it refers to the molar concentration and not to the mass concentration.

Example
If a 100 mL solution was obtained by dissolving 0.050 mol of glucose in water, then:
C(glucose) = 0,05
                    0,100

                  = 0.5 mol / L

The molar concentration influence on a solution

The molar concentration can influence the appearance of the solution:

• if the solute is a colored chemical species then the color is more intense as the concentration of this species is high.
• If the dissolved chemical species has a taste then this taste will be "strong" as the well as concentration is high.
• If the dissolved chemical species is acidic then the acidity of the solution will be stronger (low pH) as well as the concentration is higher.
• Conversely, if a chemical species is basic then the basicity of a solution will be stronger (high pH) as well as the molar concentration is high.
• If the dissolved chemical species is a reagent then the reaction will be faster as the concentration is high.

Determine a molar concentration

By calculation
If we know the volume of the solution and the quantity of matter, then the molar concentration can be calculated using the relation which defines it as the ratio of these two quantities:
C =   n  
        V

Framing by a hue scale
If the dissolved chemical species is colored, then it is possible to provide a framing of its concentration by performing a color scale: the solution of unknown concentration is compared to a series of solutions having a decreasing known concentrations. If its hue is intermediate between two solutions (lighter than one but darker than the others) then the concentrations of these two solutions provide a framing of the desired concentration.

By a dosage
The dosage is an experimental technique that exploits chemical or physical properties of a chemical species in order to determine its concentration, it is possible to perform pH-metric dosage, redox, conductimetric and spectrophotometric dosage.

Molar concentration and mass concentration

Each of these concentrations reflects the proportion of solute dissolved in a solution, the first refers to the quantity of matter and the second to the mass. It is possible to establish a relation between the two and to express one according to the other.

• C the molar concentration of a chemical species in a solution (in mol / L)
• Cm the mass concentration of this chemical species in the same solution (in g / L)
• n the matter quantity of this chemical species (in mol)
• m mass of the chemical species in this solution (in g)
• V the volume of the solution (in L)
• M the molar mass of the chemical species (in g / mol)

The molar concentration is defined by the following relation
C =   n
        V
and n =   m
              M
C = m . 1
      M   V
C = 1 . m
      M  V
With C_m =  m  
                   V
Thus
C = 1 . C_m
      M

C=

Cm   M

The molar concentration of a chemical species can be obtained by the ratio of the mass concentration divided by the molar mass of the chemical species.

We can also deduce the mass concentration from the molar concentration thanks to the following relation:
C_m = C.M

This formula indicates that the mass concentration is the product of the molar concentration by the molar mass of the chemical species.

Use the molar concentration to calculate a quantity of solute

When we have a solution with a known concentration, it is possible to express the quantity of matter contained in the totality of the solution or in a sample of volume V from a relation.
We know that:
C =   n
        V

We obtain the following formula: n = C.V

This means that the quantity of solute corresponds to the product of its concentration by the volume of solution.

Use the molar concentration to calculate the volume of the solution

To determine the volume to be taken from a solution in order to obtain a given quantity of matter, we can adapt the previous relations to obtain the following formulas:

V =   n
        C

Molar concentration and dilution

By definition, the dilution of an aqueous solution consists in adding solvent to it without modifying the quantity matter that it contains. Since the concentration of this solution is given by the relation C = n / V , the increase of the term "V" without variation of "n" indicates that the concentration decreases:

Dilution of a solution induces a decrease in the concentration

For example, if a solution is diluted by doubling the volume of solvent then the concentration C₂ of this diluted solution is:

C₂ =   n  
         2V
C₂ = 1 . n
        2   V
C₂ = 1 . C
        2

Doubling the solvent volume is dividing the concentration by two, but it could also be shown that multiplying the volume by 3 leads to dividing the concentration by 3, multiplying the volume by 4 divides the concentration by 4, etc.

Since a dilution induces a decrease in concentration there can also be:

• a lightening of the hue (for a colored solution)
• a taste (salty, sweet or other) less pronounced (if the solute has a taste)
• a decrease in acidity (for an acidic solution)
• a decrease in basicity (for a basic solution)
etc.

Molar concentration and vaporization

Vaporization leads to a loss of solvent and is accompanied by a decrease in the volume of the solution while the amount of material does not vary (in general the solute is not vaporized). A vaporization has the inverses consequences of a dilution:

• the concentration increases
• the shade darkens
• the taste increases
etc.

Molar concentration and saturation

The molar concentration of a chemical species in a given solvent is always limited, when this limit is reached it is said that the solution is saturated and the concentration takes on a particular value: it corresponds to the solubility of the chemical species in the solvent.

Preparation of a solution with a known molar concentration

The preparation of a solution is generally carried out following this protocol:

• Look for a volumetric flask whose V capacity corresponds to the volume of solution that you want to prepare.
• Determine the quantity of material "n" needed to obtain a given concentration "C" in a volume solution "V": n = C.V
• Determine the mass "m" of solute to dissolve: m = M.n (M is the molar mass of the solute)
• If the solute is solid, it is removed with a spatula and placed in a cup or directly in a beaker. The beaker placed on a scale and after a tare (reset) a mass "m" of solute is added.
• Dissolution begins in the beaker by adding a much smaller volume of solvent than the solution. Stirring is preferably done using a magnetic stirrer.
After complete dissolution, the homogeneous mixture is transferred to the volumetric flask of volume V. The beaker is rinsed with the solvent and then poured into the flask.
• The solvent completes the solution; it is added until the lower part of the meniscus (on the surface) coincides with the mark.
• The vial is then shaken (with a stopper) to homogenize the solution
• The solution is ready.

Note
If the solvent is liquid, it is necessary to determine the volume V 'to be taken from the mass "m" (already calculated) and the density:
V =   m
        ρ

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