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๐ฌ 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?
Mass by Mass Percentage (%
m/m
)
Step 1 — Weigh the solute
e.g. salt = 10 g
↓
Step 2 — Weigh the solution
solute + solvent = 10 g + 90 g = 100 g
↓
Step 3 — Divide, then × 100
(10 ÷ 100) × 100
↓
%
m/m
=
10 %
— grams of solute in 100 g of solution (5.1)
- 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 %
=
Mass of solute
Mass of solution
× 100
โ Example 5.1 — If 10 g of salt
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 %
=
10
100
× 100 = 10% m/m
What is mass by volume percentage?
Mass by Volume Percentage (%
m/v
)
Step 1 — Weigh the solute
e.g. glucose = 5 g
↓
Step 2 — Measure the volume of the solution
= 100 mL
↓
Step 3 — Divide, then × 100
(5 ÷ 100) × 100
↓
%
m/v
=
5 %
— grams of solute in 100 mL of solution (5.2)
- 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 %
=
Mass of solute
Volume of solution
× 100
โ Example 5.2 — If 5 g of glucose
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 %
=
5
100
× 100 = 5% m/v
What is volume by volume percentage?
Volume by Volume Percentage (%
v/v
)
Step 1 — Measure the volume of the solute
e.g. pesticide = 1 mL
↓
Step 2 — Measure the volume of the solution
= 100 mL
↓
Step 3 — Divide, then × 100
(1 ÷ 100) × 100
↓
%
v/v
=
1 %
— mL of solute in 100 mL of solution (5.3)
| % m/m | % m/v | % v/v | |
|---|---|---|---|
| Solute measured as | mass (g) | mass (g) | volume (mL) |
| Solution measured as | mass (g) | volume (mL) | volume (mL) |
| Used when | the mixture is weighed — milk powder, spice mixes, packaged food labels | a liquid volume is easier to measure — medicines, laboratories | two miscible liquids are mixed — perfumes, cosmetics, vinegar |
| Example | 10 % m/m salt solution | 5 % m/v glucose solution | 5 % v/v acetic acid in vinegar |
- 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 %
=
Volume of solute
Volume of solution
× 100
โ Example 5.3 — If 1 mL of a
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 %
=
1
100
× 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.
๐ 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.
๐งฌ 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
-
What does 10% m/m mean?
View Answer
10 g of solute is present in 100 g of solution. -
Which method suits a 5% glucose solution in medicine?
View Answer
Mass by volume percentage (% m/v). -
Which method is used for two miscible liquids like vinegar?
View 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.
๐ NCERT Question 4 — Solve the following problems
Solve the following problems:
(i) A cake recipe uses dry ingredients, namely 75 g of sugar for 420 g of all-purpose flour and 5 g of sodium hydrogencarbonate. Express the concentration of each component in the mixture using an appropriate method.
(ii) A brass alloy contains 70% copper by mass. Calculate the quantities of copper and zinc present in 120 g of brass.
View Answer →
(i) A cake recipe uses dry ingredients, namely 75 g of sugar for 420 g of all-purpose flour and 5 g of sodium hydrogencarbonate. Express the concentration of each component in the mixture using an appropriate method.
(ii) A brass alloy contains 70% copper by mass. Calculate the quantities of copper and zinc present in 120 g of brass.
๐ NCERT Question 14 — Three students, A, B and
Three students, A, B and C, are preparing sugar solutions for an experiment:
• Student A dissolves 20 g of sugar in 80 g of water.
• Student B dissolves 20 g of sugar in 100 g of water.
• Student C dissolves 30 g of sugar in 80 g of water.
(i) Calculate the mass percentage (% m/m ) concentration of sugar in each student's solution.
(ii) Whose solution is the most concentrated? Explain why.
View Answer →
• Student A dissolves 20 g of sugar in 80 g of water.
• Student B dissolves 20 g of sugar in 100 g of water.
• Student C dissolves 30 g of sugar in 80 g of water.
(i) Calculate the mass percentage (% m/m ) concentration of sugar in each student's solution.
(ii) Whose solution is the most concentrated? Explain why.
๐งฉ Threads of Curiosity
- A saline drip in hospitals is usually 0.9 % m/v sodium chloride.
- Sodium chloride is common salt, dissolved in water.
- That means 0.9 g of salt in 100 mL of solution (Fig. 5.5).
- 0.9 % saline solution is safe for blood.
- It replaces the fluids lost from the body.
