How strong is it?
The hydrogen peroxide you buy at a drugstore is labeled 3%, and the saline used in IVs is 0.9% sodium chloride. Farmers in some countries sort seeds in 16% salt water: plump seeds sink and empty ones float, but if the solution is too weak nothing floats, and if it’s too strong even good seeds float. To say exactly how strong a solution is, you need a number.
Mass percent of solute
The mass percent溶质的质量分数 of a solute (written ω) is the mass of solute divided by the mass of the whole solution:
Rearranged: .
Only solute that has actually dissolved counts. Undissolved solid is neither solute nor part of the solution.
🔧 Math tool card · Ratios & PercentagesSkip it if you already know this
A percentage is part ÷ whole × 100%. Know any two of the three, and you can find the third:
- part = whole × percentage, for example 50 g × 6% = 3 g;
- whole = part ÷ percentage, for example 49 g ÷ 20% = 245 g.
To divide by a percentage, turn it into a decimal first: 49 g ÷ 0.20 = 245 g.
200 g of solution contains 30 g of solute. What is the mass percent of solute?
30 g ÷ 200 g × 100% = 15%. 17.6% comes from dividing by the 170 g of solvent instead of the whole solution.
Choose a calculation and change the numbers to see how each step is set up:
Mass percent of a saturated solution
At a given temperature, a saturated solution has the highest mass percent possible. If the solubility is S (in grams per 100 g of water):
At 20 °C the solubility of sodium chloride is 36.0 g, so its saturated solution has . You simply can’t make a 30% sodium chloride solution at 20 °C.
Dilution
Adding water to a solution increases its mass, but the mass of solute stays the same:
Preparing a solution
Here’s how to make 50 g of a 6% sodium chloride solution. Put the steps in order:
Steps to place (click to add)
Your order (click a step to send it back)
- Calculate: you need 50 g × 6% = 3 g of sodium chloride and 47 g (about 47 mL) of waterWork out the solute and solvent first. Water's density is about 1 g/mL, so 47 g of water is about 47 mL.
- Weigh: weigh out 3 g of sodium chloride on a balance and put it in a beakerWeigh the solid on a piece of weighing paper (or in a weighing boat).
- Measure: measure 47 mL of water in a 50 mL graduated cylinder and pour it into the beakerChoose a cylinder a bit larger than 47 mL and read it at eye level with the bottom of the meniscus.
- Dissolve: stir with a glass rod until all the sodium chloride dissolvesStirring speeds up dissolving.
- Store: pour the solution into a reagent bottle and label it with the name and mass percentThe label must show what the solution is and its mass percent.
Example 1: Salt water for sorting seeds
How many kilograms of sodium chloride and of water are needed to make 150 kg of 16% sodium chloride solution?
- Find the solute. .
- Find the solvent. .
- Answer. 24 kg of sodium chloride and 126 kg of water.
Example 2: Diluting concentrated sulfuric acid
How much water must be added to 50 g of 98% sulfuric acid to dilute it to 20%?
- The solute doesn’t change. Mass of solute = 50 g × 98% = 49 g, before and after.
- Find the mass of the dilute solution. .
- Find the water added. 245 g − 50 g = 195 g.
- Safety. Always pour the concentrated acid slowly into the water while stirring, never water into the acid (lesson 1.8.4).
- Reading the graduated cylinder from below (looking up) when measuring the water
Looking up makes the reading too low, so you actually measure out too much water, and the solution is too dilute.
- Reading the graduated cylinder from above (looking down) when measuring the water
Looking down makes the reading too high, so you measure out too little water.
- The sodium chloride contains some insoluble impurity
Less sodium chloride actually dissolves.
- The beaker already had a little water in it
There's extra solvent, so the solution is more dilute.
- Some of the measured water spills while pouring it into the beaker
Less water ends up in the beaker, so the solution is more concentrated.
- Some of the finished solution spills while it's being bottled
A solution is uniform, so losing some doesn't change the mass percent of the rest.
- Adding more sodium chloride than calculated
More solute in the same water gives a higher mass percent.
Common mistakes
Mistake 1: Treating solubility as mass percent. The solubility of sodium chloride at 20 °C is 36.0 g, but its saturated solution is 36.0 ÷ 136.0 ≈ 26.5%, not 36%.
Mistake 2: Counting undissolved solid. Stir 40 g of sodium chloride into 100 g of water at 20 °C and only 36.0 g dissolves, so the mass percent is 26.5%, not 40 ÷ 140.
Mistake 3: “Diluting reduces the mass of solute.” Adding water only adds solvent. The mass of solute stays the same; it’s the mass percent that drops.
Quick check
10 g of sodium chloride is completely dissolved in 90 g of water. What is the mass percent of solute?
10 g ÷ (10 g + 90 g) × 100% = 10%. 11.1% comes from dividing by the 90 g of water.
The solubility of sodium chloride at 20 °C is 36.0 g. What is the mass percent of a saturated sodium chloride solution at 20 °C?
ω = 36.0 g ÷ (100 g + 36.0 g) × 100% ≈ 26.5%.
Summary
- Mass percent of solute ω = mass of solute ÷ mass of solution × 100%, where mass of solution = mass of solute + mass of solvent. Count only dissolved solute.
- A saturated solution’s mass percent = S ÷ (100 g + S) × 100%, the maximum possible at that temperature.
- In dilution the solute’s mass doesn’t change: .
- Preparing a solution: calculate, weigh, measure, dissolve, bottle and label. Reading the water volume looking up makes the result too low; looking down makes it too high.
On to AP (for later)
AP topic 3.7 usually describes concentration as molarity (mol/L), and the dilution equation becomes , built on exactly the same idea: the amount of solute doesn’t change. Topic 1.4 also uses mass percent to describe the composition of mixtures.