Fix the mistake: salt water concentration problems

Salt Water Concentration Problems ① Basics of Concentration

In this lesson, you will learn the basic calculations related to the concentration of salt water. Instead of memorizing formulas, the key is to focus on the “amount of salt.”

Basic Formulas

Let’s learn the three formulas related to the concentration of salt water:

Concentration (%) ＝ Amount of salt ÷ Amount of salt water × 100
Amount of salt ＝ Amount of salt water × Concentration ÷ 100
Amount of salt water ＝ Amount of salt ÷ Concentration × 100

Example 1
There are 16 g of salt dissolved in 200 g of salt water. What is the concentration of this salt water?

Solution:
Concentration ＝ 16 ÷ 200 × 100 ＝ 8%
Example 2
There are 400 g of 5% salt water. How many grams of salt are dissolved in it?

Solution:
Amount of salt ＝ 400 × 5 ÷ 100 ＝ 20 g

Adding Water and Evaporation

When water is added to salt water or water evaporates, the amount of salt does not change, but the concentration does.

Example 3
100 g of water was added to 300 g of 8% salt water. What is the new concentration?

Solution:
Amount of salt: 300 × 8 ÷ 100 ＝ 24 g (unchanged)
New amount of salt water: 300 ＋ 100 ＝ 400 g
New concentration: 24 ÷ 400 × 100 ＝ 6%
Key Points
  • Adding water does not change the amount of salt
  • Evaporation does not change the amount of salt
  • Focusing on the “amount of salt” helps avoid confusion

Practice Problems

  1. There are 9 g of salt dissolved in 150 g of salt water. What is the concentration of this salt water?
  2. If 50 g of water is added to 250 g of 12% salt water, what will the new concentration be?

Answers and Explanations

  1. Answer: 6%
    Explanation: Concentration ＝ salt ÷ salt water × 100 ＝ 9 ÷ 150 × 100 ＝ 6%.
  2. Answer: 10%
    Explanation: Original amount of salt: 250 × 12 ÷ 100 ＝ 30 g (unchanged when water is added). New amount of salt water: 250 ＋ 50 ＝ 300 g. New concentration: 30 ÷ 300 × 100 ＝ 10%.

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