Structure 1.4.5—The molar concentration is determined by the amount of solute and the volume of solution.

**What You’ll Learn:**

- Solve problems involving the molar concentration, amount of solute and volume of solution.
- The use of square brackets to represent molar concentration is required.
- Units of concentration should include g dm
^{–3 }and mol dm^{–3 }and conversion between these. - The relationship n = CV is given in the data booklet.

**Keywords**

IBDP chemistry, mole, mol, amount of substance, elementary entities, atoms, molecules, ions, electrons, carbon-12, Avogadro’s constant, N_{A}, 6.022 x 10^23 mol^{-1}, amount of substance, n, number of entities, formula, oxygen atoms, water molecules, data booklet, units

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**Syllabus Links**

Tool 1—What are the considerations in the choice of glassware used in preparing a standard solution and a serial dilution?

Tool 1, Inquiry 2—How can a calibration curve be used to determine the concentration of a solution?

## Molar concentrations

## mol dm^{–}³

Molar concentration, also known as molarity, is a measure of the amount of a solute dissolved in a solution. It is good practice to use the standard unit of volume for molar concentration, which is cubic decimeters (dm³), also known as liters (L). This is because molarity is defined as the number of moles of solute per dm^{3} or liter of solution. To calculate the molar concentration of a solution, follow these steps:

- Determine the amount of solute in moles. This can be done by dividing the mass of the solute by its molar mass. For example, if you have 5 grams of sodium chloride (NaCl), which has a molar mass of 58.44 g/mol, you can calculate the number of moles as follows: Moles of NaCl = 5 g / 58.44 g/mol = 0.0854 mol
- Determine the volume of the solution in dm
^{3}. This is typically measured in a volumetric flask or pipette. For example, if you have 250 milliliters (mL) of solution, you can convert this to dm^{3}by dividing by 1000: Volume of solution = 250 mL / 1000 = 0.250 dm^{3} - Divide the amount of solute in moles by the volume of the solution in liters. This gives you the molar concentration of the solution in units of moles per liter (mol/L), also known as Molarity. Molarity = Moles of solute / Volume of solution Molarity = 0.0854 mol / 0.250 dm
^{3}= 0.3416 mol/dm^{3}

So, the molar concentration of the solution is 0.3416 mol/dm^{3}, or mol dm^{-3}, or 0.3416 M.

Worksheet: Concentration Calculations

## Square Brackets denote concentration

In chemistry, square brackets are often used to denote the concentration of a substance in a solution. The concentration of a solution is the amount of solute per unit volume of solution, typically expressed in moles per liter (M).

For example, if the concentration of a solution of hydrochloric acid (HCl) is 0.1 M, we can write this as [HCl] = 0.1 M, where the square brackets indicate that we are referring to the concentration of HCl in the solution.

The use of square brackets to denote concentration is a convention that helps to clearly indicate which quantity we are referring to in a chemical equation or reaction.

## g/dm³

To find the grams per cubic decimeter (g/dm³) of a substance in a solution, you need to know the mass of the substance and the volume of the solution in cubic decimeters (dm³). Here are the steps to follow:

- Measure the mass of the substance in grams (g).
- Measure the volume of the solution in cubic centimeters (cm³) or milliliters (mL), and convert it to cubic decimeters (dm³) by dividing by 1000. Alternatively, you can directly measure the volume of the solution in cubic decimeters if you have a suitable measuring device.
- Divide the mass of the substance in grams by the volume of the solution in cubic decimeters to obtain the grams per cubic decimeter of the substance in the solution. The resulting unit will be g/dm³.

For example, let’s say you have a solution that contains 10 grams of salt (NaCl) in 0.5 dm³ of water. To find the grams per cubic decimeter of NaCl in the solution, follow these steps:

- Measure the mass of NaCl in grams: 10 g.
- Measure the volume of the solution in cubic decimeters: 0.5 dm³.
- Divide the mass of NaCl in grams by the volume of the solution in cubic decimeters:Grams per cubic decimeter = 10 g / 0.5 dm³ = 20 g/dm³

So, the grams per cubic decimeter of NaCl in the solution is 20 g/dm³.

This calculation can be useful in many applications, such as determining the concentration of a solute in a solution or calculating the density of a solution.

Questions

- What is the standard unit of volume for molar concentration?
- What is molarity?
- How do you calculate the number of moles of solute in a solution?
- What is the formula for calculating molarity?
- What is the molarity of a solution that contains 3 moles of solute in 2 liters of solution?
- What is the volume of a solution that contains 0.5 moles of solute and has a molarity of 0.25 M?
- What is the concentration of a solution that contains 25 grams of solute in 500 milliliters of solution?
- How do you convert milliliters to cubic decimeters?
- What is the difference between mol/dm³ and M?
- How do you calculate the grams per cubic decimeter of a substance in a solution?