Molar concentration tells us how many moles of a dissolved substance there are per unit volume of solution. It is a fundamental quantity in solution chemistry, essential for stoichiometric calculations and for preparing solutions of a given concentration. In this article we explain the formula, the units, and we show the calculations using an example.
The molar concentration formula
Molar concentration, denoted by the letter c, is calculated by dividing the number of moles of a substance by the volume of solution:
- c = n / V — concentration equals the number of moles divided by volume
- n = c × V — the number of moles equals concentration times volume
- V = n / c — volume equals the number of moles divided by concentration
The symbol n stands for the number of moles, and V for the volume of the solution, not of the solvent alone.
Units
Molar concentration is expressed in moles per cubic decimetre (mol/dm³), which is the same as moles per litre. The shorthand 1 M denotes a one-molar solution, that is 1 mol/dm³.
- Number of moles n — mole
- Volume V — cubic decimetre (dm³), that is a litre
- Concentration c — mol/dm³ (mol/l)
Remember that 1 dm³ = 1000 cm³, so 250 cm³ is 0.25 dm³.
How to calculate the number of moles?
We work out the number of moles from the mass of the substance and its molar mass M:
- n = m / M — the number of moles equals mass divided by molar mass
We read the molar mass off the periodic table, adding up the atomic masses of the elements in the molecule. For example, the molar mass of sodium chloride NaCl is 23 + 35.5 = 58.5 g/mol.
Worked example
We dissolve 11.7 g of table salt NaCl in water so as to obtain 500 cm³ of solution. We calculate the molar concentration.
- Molar mass of NaCl: M = 58.5 g/mol.
- Number of moles: n = m / M = 11.7 / 58.5 = 0.2 mol.
- Volume in dm³: V = 500 cm³ = 0.5 dm³.
- Molar concentration: c = n / V = 0.2 / 0.5 = 0.4 mol/dm³.
We have obtained a solution with a concentration of 0.4 mol/dm³, that is 0.4 M.
Diluting solutions
When diluting, the number of moles of the substance does not change, so the following relationship holds:
- c₁ × V₁ = c₂ × V₂
It lets you calculate how much water to add in order to turn a concentrated solution into one with a lower concentration.
Second example: how much substance to weigh out?
We want to prepare 2 dm³ of a glucose solution with a concentration of 0.5 mol/dm³. The molar mass of glucose is M = 180 g/mol. How many grams of glucose should we weigh out?
- Number of moles: n = c × V = 0.5 × 2 = 1 mol.
- Mass: m = n × M = 1 × 180 = 180 g.
We should weigh out 180 g of glucose and top it up with water to 2 litres of solution.
Why do we calculate molar concentration?
Molar concentration is the basis of calculations in analytical and laboratory chemistry. It lets us precisely measure out the amount of substance needed in a reaction, because chemical reactions take place in fixed molar ratios, not mass ratios. Knowing the concentration, we can also calculate how much reagent will be used up during a titration and predict the yield of a reaction. In the pharmaceutical and food industries, precise concentrations determine the quality and safety of a product, which is why being able to calculate them is essential.
Percentage concentration versus molar concentration
Molar concentration is not the same as percentage concentration. Percentage concentration tells us how many grams of substance there are per 100 g of solution, while molar concentration refers to the number of moles per litre. In problems you have to read carefully which concentration is meant, because the formulas are different.
Most common mistakes
- Volume in cm³ instead of dm³ — this is the most common mistake, understating or overstating the result.
- Wrong molar mass — check the sum of the atomic masses in the periodic table.
- Confusing the volume of the solution with the volume of water — what counts is the volume of the finished solution.
- Confusing molar concentration with percentage concentration — these are two different quantities with different formulas.
Frequently asked questions
- What is a 1 M solution? It is a solution with a concentration of 1 mol/dm³, that is one containing one mole of substance in one litre.
- Is the volume measured before or after dissolving? What counts is the volume of the finished solution, which is why the substance is dissolved and then topped up with solvent to the required volume.
- How can I quickly find the molar mass? You add up the atomic masses of all the elements in the molecule, read off the periodic table.
Summary
Molar concentration c = n / V expresses the number of moles of a substance in a litre of solution. We find the number of moles from the formula n = m / M. By keeping an eye on the units (volume in dm³) you can quickly calculate the concentration of any solution.
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