This method is commonly used for
homogeneous mixtures
.
It tells us how many
grams of solute
are present in
100 grams of solution
.
Mass by mass percentage
=
Mass of solute
Mass of solution
× 100 (5.1)
Example
It is also used for heterogeneous mixtures such as
milk powder
and spice mixtures, and for labelling packaged food to show how much salt, sugar or protein it contains.
What is mass by volume percentage (% m/v)?
This is used where measuring the
volume
of a liquid is easier than weighing it — for example in medicines and laboratories.
It tells us how many
grams of solute
are present in
100 mL of solution
.
Mass by volume percentage
=
Mass of solute
Volume of solution
× 100 (5.2)
Example
A common example is a
5 % glucose solution
used in hospitals.
Example 5.2 — 5 g of glucose is dissolved in water to make 100 mL of solution. Find its concentration.
What is given
Solute is
glucose
, mass = 5 g
Solution volume =
100 mL
The solvent is water, but its amount is not given separately.
⚠️ One thing to be careful about
5 g is a
mass
and 100 mL is a
volume
, so we cannot subtract one from the other to find the solvent.
The 100 mL is the volume of the
whole solution
— solute and solvent together.
Calculation
Mass by volume percentage
=
Mass of solute
Volume of solution
× 100
=
5 g
100 mL
× 100 =
5 % m/v
We wrote
m/v
because a mass (5 g) was divided by a volume (100 mL).
What is volume by volume percentage (% v/v)?
This is used when
two miscible liquids
are mixed — for example in perfumes, cosmetics and vinegar.
It tells us how many
millilitres of solute
are present in
100 mL of solution
.
Volume by volume percentage
=
Volume of solute
Volume of solution
× 100 (5.3)
Example 5.3 — 1 mL of liquid pesticide is mixed with water to make 100 mL of spray. Find its concentration.
What is given
Solute is
liquid pesticide
, volume = 1 mL
Solution volume =
100 mL
So the solvent, water, is about
99 mL
. This time we could subtract, because both are volumes.
Calculation
Volume by volume percentage
=
Volume of solute
Volume of solution
× 100
=
1 mL
100 mL
× 100 =
1 % v/v
We wrote
v/v
because a volume (1 mL) was divided by a volume (100 mL).
Let us put all three formulas together
Way
Formula
Units
Mass by mass (% m/m)
Mass of solute ÷ Mass of solution × 100 (5.1)
gram ÷ gram
Mass by volume (% m/v)
Mass of solute ÷ Volume of solution × 100 (5.2)
gram ÷ mL
Volume by volume (% v/v)
Volume of solute ÷ Volume of solution × 100 (5.3)
mL ÷ mL
In all three, the denominator is always the
solution
— never the solvent alone.
Where is concentration used in real life?
Why the right concentration matters
Concentration
The right proportion
ORS
Fixed salt and sugar in fixed water
If changed:
It is a solution
but not ORS
Pesticide spray
Right pesticide in fixed water
If changed:
Too little — no protection
Too much — damage
Saline drip
0.9 % m/v salt in water
Means:
0.9 g salt
in 100 mL solution
ORS
— a fixed amount of salt and sugar goes into a fixed amount of water. Change the amounts and you still get a solution, but it is no longer ORS, because its concentration has changed.
Pesticide spray
— farmers must mix the right amount of pesticide with a fixed amount of water. Too little will not protect the crop; too much damages the crop, the soil and the environment.
Saline drip
— hospital saline is usually
0.9 % m/v
, that is 0.9 g of salt in 100 mL of solution. It is safe for blood and replaces the water the body has lost.
📌 Note
Industries commonly use
weight by weight percentage (% w/w)
, because weight and mass are generally used interchangeably.
Numerically,
% m/m and % w/w are equal
.
👨🔬 Meet a Scientist — Dilip Mahalanabis
An Indian paediatrician who first developed and implemented the treatment for dehydration caused by diseases such as diarrhoea and cholera.
He formulated the
ORS
that revolutionised rehydration therapy.
It has saved millions of lives after the World Health Organization (WHO) popularised it worldwide.
Pause and Ponder
🤔 Pause and Ponder — Questions 1 to 3
1. A common talcum powder contains 4 % m/m zinc oxide, which acts as an antiseptic. How much zinc oxide is present in 300 g of the talcum powder?
View answer
Hide answer
Answer
12 g
of zinc oxide is present in 300 g of the talcum powder.
Explanation
Given:
concentration = 4 % m/m, mass of powder = 300 g.
To find:
mass of zinc oxide.
An antiseptic is something that kills germs. 4 % m/m means 4 g of zinc oxide in every 100 g of powder.
Mass of zinc oxide
=
4
100
× 300 g
=
12 g
In a full 300 g pack, only 12 g is actually zinc oxide.
2. Your mother gives you a bottle of orange juice concentrate to mix with water and serve it to your visiting friends. She asks you to mix two tablespoons of the concentrate with water in a glass tumbler. If each tablespoon measures 15 mL and you make 150 mL of juice per person, what is the % v/v of orange juice concentrate in the mixture you prepared?
View answer
Hide answer
Answer
The concentration is
20 % v/v
.
Explanation
Given:
2 tablespoons, each 15 mL; total solution = 150 mL.
To find:
% v/v. "Concentrate" means thick juice from which water has been removed.
Volume of concentrate
=
2 × 15 mL = 30 mL
Volume by volume percentage
=
30 mL
150 mL
× 100 =
20 % v/v
One-fifth of the glass is real concentrate; the rest is water.
3. Vinegar, used as a food preservative and additive, contains 5 % v/v acetic acid. Glacial acetic acid is a liquid, i.e., 100 % acetic acid. If you want to make vinegar from glacial acetic acid, how would you proceed?
View answer
Hide answer
Answer
Take
5 mL of glacial acetic acid
and add water to it until the total volume becomes
100 mL
.
Explanation
Given:
vinegar needed at 5 % v/v; source is 100 % acetic acid.
To find:
the method.
5 % v/v means 5 mL of acid in every 100 mL of vinegar. So measure out 5 mL of glacial acetic acid and keep adding water until the total volume reaches 100 mL.
Safety first
— acid is always added
to water
, never water to acid, and this should be done under adult supervision.
For 200 mL of vinegar you would need 10 mL of acid, and for 500 mL you would need 25 mL.
📝 Summary - What we have learnt
A
solute
dissolves, a
solvent
dissolves it, and together they make a
solution
.
Every solution is a
homogeneous mixture
.
Concentration
is how much solute is present in a given amount of solvent or solution.
It is expressed three ways —
% m/m
,
% m/v
and
% v/v
, and the denominator is always the solution.
ORS, pesticide sprays and saline drips all depend on getting the concentration right.
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.
For an uninterrupted learning experience, students can use Teachoo Black to remove ads and focus better.
You are here
