Mixing Salt Solutions
When two salt solutions with different concentrations are mixed, a new salt solution is made.
The key is to think in terms of the “total amount of salt.”
What You Will Learn
When two salt solutions (A and B) are mixed:
Weight of the mixed salt solution = weight of A ＋ weight of B
Weight of the salt in the mixed solution = salt in A ＋ salt in B
Concentration of the mixed solution ＝（salt in A ＋ salt in B）÷（weight of A ＋ weight of B）× 100
Example
We mixed 200g of 5% salt solution with 300g of 15% salt solution. What is the concentration of the mixed solution?
Solution:
① Weight of the salt in A: 200 × 0.05 ＝ 10g
② Weight of the salt in B: 300 × 0.15 ＝ 45g
③ Total weight of the salt: 10 ＋ 45 ＝ 55g
④ Total weight of the salt solution: 200 ＋ 300 ＝ 500g
⑤ Calculate the concentration: 55 ÷ 500 × 100 ＝ 11%
We mixed 200g of 5% salt solution with 300g of 15% salt solution. What is the concentration of the mixed solution?
Solution:
① Weight of the salt in A: 200 × 0.05 ＝ 10g
② Weight of the salt in B: 300 × 0.15 ＝ 45g
③ Total weight of the salt: 10 ＋ 45 ＝ 55g
④ Total weight of the salt solution: 200 ＋ 300 ＝ 500g
⑤ Calculate the concentration: 55 ÷ 500 × 100 ＝ 11%
Key Points
Remember
- In mixing problems, the basic step is to first add together the “amounts of salt.”
- The concentration after mixing will be a value between the original two concentrations.
- Remember that the resulting concentration will be closer to the concentration of the solution with the greater amount.
Practice Problems
- We mixed 150g of 8% salt solution with 100g of 2% salt solution. What is the concentration?
- When 100g of water was added to a 10% salt solution, its concentration became 8%. How many grams of salt solution were there at first?
- 24g of salt was added to 400g of 6% salt solution. What is the concentration?
Answers and Explanations
- Answer: Concentration = 5.6%
Explanation: Salt in the 8% salt solution = 150 × 0.08 = 12g. Salt in the 2% salt solution = 100 × 0.02 = 2g. Total salt = 14g, and total weight = 250g. Concentration = 14 ÷ 250 × 100 = 5.6%. - Answer: Initial weight of the salt solution = 400g
Explanation: Let the initial weight of the salt solution be x g. Amount of salt = x × 0.10 = 0.1x g (unchanged). When 100g of water is added, the weight of the salt solution becomes (x+100) g. The new concentration = 0.1x ÷ (x+100) × 100 = 8, so 0.1x = 0.08(x+100) → 0.1x = 0.08x + 8 → 0.02x = 8 → x = 400g. - Answer: Concentration = Approximately 11.3%
Explanation: Salt in the original salt solution = 400 × 0.06 = 24g. When 24g of salt is added, the amount of salt becomes 24+24=48g, and the weight of the salt solution becomes 400+24=424g. Concentration = 48 ÷ 424 × 100 ≈ 11.3%.