Ways of Expressing Concentration

 Dilute versus Concentrated Solutions:

• Some liquid cleaning solutions are sold in "concentrated" form, and the instructions require you to "dilute" them prior to use
• A concentrated solution is one where the solute is present in high concentration
• A dilute solution is one where the solute is present in low concentration

• We need a formal description of the concentration of a solute in a solution

• A formal description of concentration that refers to the ratio of the mass of the component of interest (e.g. solute) with the entire mass of the sample:

For example, a 100g aqueous solution containing NaCl is evaporated to dryness, leaving only the NaCl. The NaCl is weighed and contains 5g. What was the mass percentage of NaCl in the original solution?

For very dilute solutions (again, a relative term) the concentrations are often expressed as "parts per million" (abreviated as ppm)

• For a pure sample, the concentration would be 100% or 1 million parts per million

For example:

ppm of component is therefore given as:

• A mass percentage of 1% would be equal to 10,000 ppm
• 1 ppm would be equal to .0001%

For really, really dilute solutions, the concentrations of solute are sometimes expressed as parts per billion (abbreviated as ppb)

ppb of component is given as:

A key point when doing mass percentage calculations on dilute aqueous solutions:

• Therefore, 1.0L of dilute aqueous solution has a mass of 1000g

A 100ml sample of tapwater is evaporated to dryness and the dry residue is found to contain 75mg of Pb²⁺ ion. How many ppm of lead ion are in the original sample?

• It is quite common to refer to concentration of a solute in terms of the number of moles of solute

• The symbol X is used to refer to the mole fraction of a component in a sample
• A subscript is sometimes added to indicate the component being referred to. For example, the mole fraction of lead ion in a sample might be indicated by

• The symbol M is used to refer to the molarity of a solute in a solution
• Molarity defines the concentration of a solute in terms of the number of moles of solute and the total volume of solution

Molality:

• The symbol m is used to refer to the molality of a solute in solution
• Molality defines the concentration of a solute in terms of the number of moles of solute and the mass of the solvent component

A certain malt liquor contains 7% ethanol (C₂H₅OH) by mass. Calculate the mole fraction, the molarity and the molality

Mole fraction:

• 7% by mass would mean that we have 7g ethanol in a 100g sample (and, therefore, 93g H₂O)
• Molar mass of ethanol is (2 x 12.0) + (6 x 1.01) + (1 x 16.0) = 46.1g/mole
• Molar mass of H₂O is (2 x 1.01) + (1 x 16.0) = 18.0g/mole

• Total moles in sample is (0.152 + 5.17) = 5.32

Molarity:

• In the same 100g sample assume that the volume is 100ml

Molality:

• In the same 100g sample, the ethanol comprises 7g and the H₂O comprises 93g, therefore: