Exploring Mixtures and their Separation · Lesson 3 of 13
How Do We Express Concentration?
“Three percentage methods walk into a solution, and the denominator decides who is who.”
• Choose an appropriate percentage form for a mixture. • Calculate mass by mass percentage. • Calculate mass by volume percentage. • Calculate volume by volume percentage. • Work backwards from a percentage to find an unknown quantity.
A label that says “five per cent” is incomplete unless we know what has been measured. Were grams compared with grams, grams with millilitres, or millilitres with millilitres? Percentage concentration becomes meaningful only when both the numerator and denominator are identified.
The percentage forms used here all compare the amount of a component with the total amount of the mixture or solution, then multiply the ratio by 100. The word total is crucial: the denominator is not automatically the amount of solvent.
Mass by Mass Percentage
Mass by mass percentage tells how many grams of a component are present in 100 grams of the total mixture or solution.
Problem
Ten grams of salt is dissolved in 90 g of water. Find the mass by mass percentage.
- 1.Mass of solute = 10 g.
- 2.Mass of solvent = 90 g.
- 3.Mass of solution = 10 g + 90 g = 100 g.
- 4.Percentage = (10 g ÷ 100 g) × 100.
- 5.The concentration is 10% m/m.
Problem
A mixture contains 75 g sugar, 420 g flour and 5 g sodium hydrogencarbonate. Find the percentage by mass of every component.
- 1.Total mass = 75 g + 420 g + 5 g = 500 g.
- 2.Sugar percentage = (75 ÷ 500) × 100 = 15% m/m.
- 3.Flour percentage = (420 ÷ 500) × 100 = 84% m/m.
- 4.Sodium hydrogencarbonate percentage = (5 ÷ 500) × 100 = 1% m/m.
- 5.Check: 15% + 84% + 1% = 100%.
Mass by Volume Percentage
Mass by volume percentage tells how many grams of solute are present in 100 millilitres of solution.
Problem
Five grams of glucose is used to prepare 100 mL of solution. Find the mass by volume percentage.
- 1.Mass of solute = 5 g.
- 2.Final volume of solution = 100 mL.
- 3.Percentage = (5 g ÷ 100 mL) × 100.
- 4.The concentration is 5% m/v.
Threads of Curiosity
A saline solution commonly used in hospitals is 0.9% m/v sodium chloride in water. This means that every 100 mL of the final solution contains 0.9 g sodium chloride. It does not mean 0.9 g salt added to 100 mL water, because the formula refers to the final solution volume.
Volume by Volume Percentage
Volume by volume percentage tells how many millilitres of a liquid solute are present in 100 millilitres of the final solution.
Problem
One millilitre of liquid pesticide is used to prepare 100 mL of spray. Find the volume by volume percentage.
- 1.Volume of liquid solute = 1 mL.
- 2.Final volume of solution = 100 mL.
- 3.Percentage = (1 mL ÷ 100 mL) × 100.
- 4.The concentration is 1% v/v.
Pause and Ponder
Problem
Talcum powder contains 4% m/m zinc oxide. How much zinc oxide is present in 300 g powder?
- 1.Write 4% as 4 per 100.
- 2.Required mass = (4 ÷ 100) × 300 g.
- 3.Required mass = 12 g.
- 4.Therefore, 300 g talcum powder contains 12 g zinc oxide.
Problem
Two tablespoons of concentrate, each 15 mL, are used to prepare 150 mL juice. Find the volume percentage.
- 1.Volume of concentrate = 2 × 15 mL = 30 mL.
- 2.Final volume of juice = 150 mL.
- 3.Percentage = (30 ÷ 150) × 100.
- 4.The concentration is 20% v/v.
Problem
How much pure liquid acetic acid is needed to prepare 500 mL vinegar containing 5% v/v acetic acid?
- 1.Required solute volume = (percentage ÷ 100) × final solution volume.
- 2.Acetic acid volume = (5 ÷ 100) × 500 mL = 25 mL.
- 3.Measure 25 mL acetic acid carefully.
- 4.Add water until the final solution volume reaches 500 mL.
- 5.This description uses final volume, not 500 mL water.
Note
The expression weight by weight percentage is commonly used on industrial labels. For the situations considered here, its numerical value is treated as equal to mass by mass percentage.
For mass by mass percentage use total mass of solution; for mass by volume and volume by volume percentages use final volume of solution. Do not divide by the solvent amount unless the question specifically defines a different ratio.
Quiz
Which description best matches Mass by Mass Percentage?
Which description best matches Mass by Volume Percentage?
Which term matches this description: Mass by mass percentage tells how many grams of a component are present in 100 grams of the total mixture or solution.
Which term matches this description: Mass by volume percentage tells how many grams of solute are present in 100 millilitres of solution.
Which statement is a key takeaway from this lesson?
Practice Problems
- A solution contains 18 g sugar and 132 g water. Find its mass by mass percentage.
- How many grams of glucose are present in 250 mL of a 5% m/v solution?
- How much liquid solute is present in 400 mL of a 2% v/v mixture?
- A brass sample contains 70% copper by mass. Find the masses of copper and zinc in 120 g brass.
Key Takeaways
• Percentage concentration requires a clearly identified numerator and denominator. • Mass by mass compares mass with total mass. • Mass by volume compares solute mass with final solution volume. • Volume by volume compares solute volume with final solution volume. • Reverse percentage problems multiply the stated fraction by the total quantity.