Calculating concentrations
The concentrationThe concentration of a solution tells us how much of a substance is dissolved in water. The higher the concentration, the more particles of the substance are present. of a solutionMixture formed by a solute and a solvent. can be shown in g/dm3 or mol/dm3. It is often more useful to know the concentration of a reactantsSubstances present at the start of a chemical reaction. in mol/dm3 so that the amountIn chemistry, a measure of the number of particles in a substance. of reactant in a given volume can be calculated.
Concentration using moles
The concentration of a solution can be calculated using:
- the amount of dissolvedA substance is said to be dissolved when it breaks up and mixes completely with a solvent to produce a solution.soluteThe dissolved substance in a solution. in moleThe amount of substance that contains the same number of particles as there are atoms in 12 g of carbon-12 (contains the Avogadro's constant 6.0 脳10虏鲁 number of particles)., mol
- the volume of solution (or solventThe liquid in which the solute dissolves to form a solution.) in cubic decimetres, dm3
Example
0.5 mol of sodium hydroxide is dissolved in 2 dm3 of water. Calculate the concentration of the sodium hydroxide solution formed.
\(Concentration~in~mol/dm^{3} = \frac{amount~of~solute~in~mol}{volume~in~dm^{3}}\)
Concentration = \(\frac{\textup{0.5~mol}}{\textup{2~dm}^3}\)
Concentration = 0.25 mol/dm3
Volume units
Volumes used in concentration calculations must be in dm3, not in cm3. It is useful to know that 1 dm3 = 1000 cm3. This means:
- divide by 1000 to convert from cm3 to dm3
- multiply by 1000 to convert from dm3 to cm3
For example, 250 cm3 is 0.25 dm3 (250 梅 1000). It is often easiest to convert from cm3 to dm3 before continuing with a concentration calculation.
Question
100 cm3 of dilute hydrochloric acid contains 0.02 mol of dissolved hydrogen chloride. Calculate the concentration of the acid in mol/dm3.
Volume of acid = 100 梅 1000 = 0.1 dm3
Concentration of acid = 0.02 mol 梅 0.1 dm3
= 0.2 mol/dm3
Converting between units
The relative formula massThe sum of the relative atomic masses of the atoms in a chemical formula. of the solute is used to convert between mol/dm3 and g/dm3:
- to convert from mol/dm3 to g/dm3, multiply by the relative formula mass
- to convert from g/dm3 to mol/dm3, divide by the relative formula mass
Remember: the molar mass is the Ar or Mr in grams per mol.
Example
Calculate the concentration of 0.1 mol/dm3 sodium hydroxide solution in g/dm3. (Mr of NaOH = 40)
Concentration = 0.1 脳 40
= 4 g/dm3
Question
Calculate the concentration of 7.3 g/dm3 hydrochloric acid in mol/dm3. (Mr of HCl = 36.5)
Concentration = 7.3 梅 36.5
= 0.2 mol/dm3