๐Ÿ’ฌ Think about it

Look at a milk powder pack, a glucose bottle, or a vinegar label — each shows how much of something is inside, as a percentage. There are three handy ways to write concentration. Let us learn them with simple sums.

What is mass by mass percentage?
  • It tells how many grams of solute are in 100 grams of solution.
  • It is used for homogeneous mixtures and packaged foods.
  • It is written as % m/m (or % w/w).
Mass by mass %
=
\( \dfrac{\text{Mass of solute}}{\text{Mass of solution}} \times 100 \)
โœŽ Example 5.1

If 10 g of salt is dissolved in 90 g of water, calculate the mass by mass percentage of the solution.

Mass of salt (solute) = 10 g; Mass of water (solvent) = 90 g

Total mass of solution = 10 g + 90 g = 100 g

Mass by mass %
=
\( \dfrac{10}{100} \times 100 = 10\% \ m/m \)
What is mass by volume percentage?
  • It tells how many grams of solute are in 100 mL of solution.
  • It is used where measuring volume is easier than weighing.
  • It is common in medicines and laboratories, written as % m/v.
Mass by volume %
=
\( \dfrac{\text{Mass of solute}}{\text{Volume of solution}} \times 100 \)
โœŽ Example 5.2

If 5 g of glucose is dissolved in water to make 100 mL of solution, calculate its mass by volume percentage.

Mass of glucose (solute) = 5 g; Volume of solution = 100 mL

Mass by volume %
=
\( \dfrac{5}{100} \times 100 = 5\% \ m/v \)
What is volume by volume percentage?
  • It tells how many mL of solute are in 100 mL of solution.
  • It is used when two miscible liquids are mixed.
  • It is common in perfumes, cosmetics and vinegar, written as % v/v.
Volume by volume %
=
\( \dfrac{\text{Volume of solute}}{\text{Volume of solution}} \times 100 \)
โœŽ Example 5.3

If 1 mL of a liquid pesticide is mixed with water to make 100 mL of pesticide spray, calculate its volume by volume percentage.

Volume of pesticide (solute) = 1 mL; Total volume of solution = 100 mL

Volume by volume %
=
\( \dfrac{1}{100} \times 100 = 1\% \ v/v \)
Important Points
  • Mass by mass % = grams of solute per 100 g of solution.
  • Mass by volume % = grams of solute per 100 mL of solution.
  • Volume by volume % = mL of solute per 100 mL of solution.
๐Ÿ“ Note
  • Industries commonly use weight by weight percentage (% w/w).
  • Weight and mass are generally used interchangeably.
  • So % m/m and % w/w are numerically equal.
๐Ÿงฌ Pause and Ponder
  • A talcum powder contains 4% m/m zinc oxide. How much zinc oxide is in 300 g of the powder?
    4% of 300 g = (4/100) × 300 = 12 g of zinc oxide.
  • Two tablespoons (15 mL each) of orange concentrate make 150 mL of juice. What is the % v/v of concentrate?
    Volume of concentrate = 30 mL; % v/v = (30/150) × 100 = 20% v/v.
  • Vinegar is 5% v/v acetic acid. Glacial acetic acid is 100%. How would you make vinegar from it?
    Take 5 mL of glacial acetic acid and add water to make the total volume 100 mL, giving 5% v/v vinegar.
โ“ Test Yourself
  1. What does 10% m/m mean?
    View Answer Hide Answer
    10 g of solute is present in 100 g of solution.
  2. Which method suits a 5% glucose solution in medicine?
    View Answer Hide Answer
    Mass by volume percentage (% m/v).
  3. Which method is used for two miscible liquids like vinegar?
    View Answer Hide Answer
    Volume by volume percentage (% v/v).
Important Definitions
  • Mass by mass percentage — grams of solute per 100 g of solution.
  • Mass by volume percentage — grams of solute per 100 mL of solution.
  • Volume by volume percentage — mL of solute per 100 mL of solution.

๐Ÿ“‹ NCERT Question 4 — Solve the following problems

Express the concentration of cake ingredients, and find copper and zinc in 120 g of brass.
View Answer →

๐Ÿ“‹ NCERT Question 14 — Three students, A, B

Three students make sugar solutions — calculate each % m/m and find whose is most concentrated.
View Answer →
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CA Maninder Singh

CA Maninder Singh is a Chartered Accountant with 16+ years of practical experience and 20+ years of teaching experience. At Teachoo, he simplifies Accounts, Tax and GST with step-by-step examples so students can apply concepts confidently in exams and real life.

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