Molar concentration

Definition and physical meaning

Molar concentration (denoted as $c$) is numerically equal to the amount of solute contained in exactly one liter of the prepared solution. The primary unit of measurement is mol/L. In medical and laboratory practice, millimoles per liter (mmol/L) are often used to express small amounts of a substance. The conversion between these units is direct: one mole per liter equals one thousand millimoles per liter.

This quantity makes it extremely simple to calculate the amount of substance ($n$) in any given volume: simply multiply the concentration by the volume ($n = c \cdot V$). If the molar mass of the substance ($M$) is also known, one can immediately calculate the mass of the dry component required for the work: $m = n \cdot M$. This is precisely why in professional slang this parameter is often simply called "concentration" — the dimensionality is obvious from the context.

Relationship with mass fraction

Often in the laboratory, a stock solution is available whose composition is given by mass fraction (in percentage) and density (in g/mL). To convert mass fraction into molar concentration, the universal formula is used:

$c = \frac{10 \cdot \omega\% \cdot \rho}{M}$

This formula can be derived using a logical "from the result" algorithm. To simplify calculations, a conventional solution volume equal to one liter ($1000$ mL) is taken. Knowing the density, the total mass of the solution is calculated ($m_{sol} = V \cdot \rho$). Then, using the given mass fraction, the mass of the pure dry substance is found. At the final stage, the found mass is divided by the molar mass, yielding the amount of substance in moles. Since the calculation was initially based on one liter, the obtained amount of substance is the desired molar concentration.

Solution preparation technique

Laboratory preparation of solutions is strictly regulated and depends on the state of aggregation of the initial reagent.

If the solution is prepared from a solid powder:

1. Measure the calculated mass of the substance (the sample) on an analytical balance.
2. Carefully transfer the solid substance into a volumetric flask of the required volume.
3. Add a portion of the solvent (e.g., distilled water) and mix thoroughly until the crystals are completely dissolved.
4. Add solvent strictly up to the mark on the narrow neck of the flask.

If it is required to prepare a dilute solution from a concentrated liquid:

1. Assess the concentration of the initial solution (recalculate from mass fraction if necessary).
2. Calculate the mass or amount of pure substance required for the target solution.
3. Calculate the required volume of the initial concentrated solution and measure it with a graduated cylinder.
4. Transfer the liquid into a volumetric flask and dilute with water up to the mark.

Basics of volumetric analysis (titration)

Molar concentration forms the basis of quantitative chemical analysis, specifically titration. The goal of volumetric analysis is to determine the unknown concentration of a substance by measuring exact volumes of reacting solutions.

A titrant — a reagent solution of maximally precisely known concentration — is added dropwise to the sample of the analyte. The exact moment of completion of the chemical reaction is recorded visually, most often by a color change of a special indicator (e.g., transition from blue to violet). Knowing the volumes of both solutions and the concentration of the titrant, one can calculate the initial molar concentration of the test sample with high precision.

Briefly: answers to topical questions

Class and exam questions

What else to study on this topic

• Stoichiometric calculations taking into account excess and limiting reagents.
• Features of back titration for the analysis of contaminated solid samples.
• Calculation of the molar concentration of gases under standard and normal conditions.
• Changes in substance concentration upon dilution and addition of solvent.
• Calculation of the mass of a substance in a given volume based on the results of volumetric analysis.

Other topics in "Chapter 4. Solutions"

Prepared by WhiteCoat Pro faculty in accordance with the medical school curriculum. For educational purposes only.