Lesson 30 – Concentration of Solutions
Concentration of a solution is defined as the amount of solute per unit volume of a solvent.
In chemistry, it is commonly expressed in 𝑔/𝑑𝑚3 or 𝑚𝑜𝑙/𝑑𝑚3 . However, in Mathematics,
we are concerned with the percentage concentration instead.
Example 1
The concentration of 500 ml of a saline solution is 8%. How much water, in ml, must be
added to dilute the solution such that its concentration drops to 5%?
Practice
1. The concentration of 100 ml of a saline solution is 10%. How much water, in ml, must
be added to dilute the solution such that its concentration drops to 8%?
2. The concentration of 60 ml of a saline solution is 25%. How much water, in ml, must be
added to dilute the solution such that its concentration drops to 6%?
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Example 2
The concentration of 350 ml of a sugar solution is 20%. How much sugar, in grams, must be
added to the solution such that its concentration increases to 30%?
Practice
3. 40 kg of pancake mix contains 16% of salt. How much salt must be added, in kg, to the
mixture to increase the salt concentration to 20%?
4. Crystallization is the process of heating a salt solution such that water evaporates,
leaving behind salt crystals. A 50 ml salt solution that contained 20% of salt was heated
during the crystallization process. How much water, in ml, must be evaporated such
that the solution has a 25% concentration of salt?
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Example 3
200 ml of Liquor A with a 60% concentration of alcohol is mixed with 300 ml of Liquor B
with a 30% concentration of alcohol to make Liquor C. What is the percentage
concentration of alcohol in Liquor C?
Example 4
The concentration of active ingredients in drugs A and B are 60% and 35%, respectively. A
pharmacist wants to prepare 5000 ml of a new drug C with a 50% concentration of active
ingredients. In what the ratio must drugs A and B be mixed to create the new drug C?
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Practice
5. Acid A and B has 𝐻+ ion concentrations of 60% and 90%, respectively. In what ratio
must they be mixed to prepare 300 ml of Acid C with a 𝐻+ ion concentration of 70%?
6. The concentrations of two solutions are 20% and 5%, respectively. In what ratio must
they be mixed to prepare a 600 ml solution with a 15% concentration?
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7. 300 ml of salt water sample A has a salt concentration of 8%. 120 ml of salt water
sample B has a salt concentration of 12.5%. After the same amount of water was poured
into each sample, their salt concentrations became the same. How much water was
poured into each salt water sample A and B, respectively?
8. In the morning, 1000 kg of watermelons contained 97% water. After some evaporation
occurred in the afternoon, the water content dropped to 95%. What is the total mass
of water lost, in kg?
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Challenging
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1. Lincoln has a glass of goat’s milk filled to the brim. He drank of it then filled it to the
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brim with soy milk. He went through this process a total of 5 times. What fraction of
the total amount of milk he drank was goat’s milk?
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2. When 𝑥 litres of water is added into a salt solution, its salt concentration becomes 15%.
When another 𝑥 litres of water is added again, its salt concentration becomes 12%.
What is the concentration of salt in the solution if 𝑥 litres of water is added a third time?
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