Concentration

Concentration describes how much solute is dissolved in a given amount of solvent or solution. There are several ways to express concentration, each useful in different contexts.

Expressing Concentration

Percentage by Mass (Mass/Mass) - m/m %

This expresses the ratio of the mass of solute to the total mass of the solution.

$$ \text{Percentage by mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100 $$

Where:

  • Mass of solute = mass of dissolved substance
  • Mass of solution = mass of solute + mass of solvent
  • Result is expressed as a percentage (%)
A 5% salt solution contains 5 g of salt dissolved in 95 g of water (total solution = 100 g)

We apply the formula:

$\frac{5 \text{ g}}{100 \text{ g}} \times 100 = 5\%$

Calculate the percentage by mass of 12 g of sugar dissolved in 288 g of water

Calculate the mass of solution:

Mass of solution = 12 g + 288 g = 300 g

Apply the formula:

$\frac{12 \text{ g}}{300 \text{ g}} \times 100 = 4\%$

Advantages:

  • Independent of temperature (mass doesn't change with temperature)
  • Easy to prepare in the laboratory
  • Used in industrial applications where mass is easier to measure

Common applications: Food industry, pharmaceutical preparations, disinfectant solutions

Percentage by Volume (Volume/Volume) - v/v %

This expresses the ratio of the volume of solute to the total volume of the solution.

$$ \text{Percentage by volume} = \frac{\text{volume of solute}}{\text{volume of solution}} \times 100 $$

Where:

  • Volume of solute = volume of dissolved substance
  • Volume of solution ≈ volume of solute + volume of solvent (assuming volumes are additive)
  • Result is expressed as a percentage (%)
A 10% alcohol solution contains 10 mL of alcohol in 100 mL of solution

We apply the formula:

$\frac{10 \text{ mL}}{100 \text{ mL}} \times 100 = 10\%$

Calculate the percentage by volume of 25 mL of ethanol mixed with 75 mL of water

Calculate the volume of solution:

Volume of solution = 25 mL + 75 mL = 100 mL

Apply the formula:

$\frac{25 \text{ mL}}{100 \text{ mL}} \times 100 = 25\%$

Advantages:

  • Used for liquid-liquid solutions
  • Practical for solutions where volumes are easy to measure
  • Important in laboratory work and beverage preparation

Common applications: Alcoholic beverages, disinfectant sprays, vinegar solutions, rubbing alcohol

Mass/Volume (m/v) - Alternative Unit

This expresses the ratio of the mass of solute to the volume of the solution. While less common than percentage by mass or volume, it's sometimes used.

$$ \text{Concentration (m/v)} = \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} $$
A solution containing 10 g of salt dissolved in water to make 500 mL of solution

Calculate the m/v concentration:

$\frac{10 \text{ g}}{500 \text{ mL}} = 0.02 \text{ g/mL}$ or $20 \text{ g/L}$

Advantages:

  • Combines advantages of both mass and volume measurements
  • Useful when solute is solid but measured volume is important

Common applications: Some pharmaceutical solutions, laboratory reagents

Comparison of the Three Methods

MethodFormulaUnitsBest Used For
Mass/Mass (m/m)(mass solute / mass solution) × 100%Solid-liquid solutions, precise preparations
Volume/Volume (v/v)(volume solute / volume solution) × 100%Liquid-liquid solutions, beverages
Mass/Volume (m/v)mass solute / volume solutiong/mL or g/LSome pharmaceuticals, mixed systems

Key Difference:

  • m/m uses mass of both solute and solution
  • v/v uses volume of both solute and solution
  • m/v uses mass of solute but volume of solution

1. What is the formula for percentage by mass? (1 points)

2. Which concentration method is independent of temperature? (1 points)

3. What is the best method to express concentration for liquid-liquid solutions? (1 points)

4. Calculate the percentage by mass of 15 g of salt dissolved in 285 g of water. (1 points)

5. A solution contains 20 mL of alcohol mixed with 80 mL of water. What is the percentage by volume of alcohol? (1 points)

6. You have 100 mL of 10% salt solution. If you add 100 mL of water, what is the new concentration? (1 points)

7. What is the percentage by mass of 8 g of sugar dissolved in 92 g of water? (1 points)

8. A 20% salt solution means: (1 points)

9. How much solute is needed to prepare 250 g of 8% solution? (1 points)

10. If 30 mL of ethanol is mixed with 70 mL of water, what is the percentage by volume? (1 points)

11. Solve these concentration problems: (4 points)

a ) Calculate the percentage by mass of 25 g of NaCl dissolved in 175 g of water.

b ) How many grams of solute are needed to prepare 500 g of a 6% solution?

c ) A solution contains 15 mL of acetone in a total volume of 250 mL. What is the percentage by volume?

d ) How many mL of solute are needed to prepare 1000 mL of a 18% solution by volume?

12. Dilution calculations - solve using the dilution formula C₁V₁ = C₂V₂: (3 points)

a ) You have 200 mL of 25% solution. After adding 800 mL of water, what is the new concentration?

b ) A 15% solution is diluted to 500 mL, resulting in a 3% solution. What was the original volume?

c ) How many mL of water must be added to 50 mL of 40% solution to make a 10% solution?