Concentration and Solubility: How Much Is Dissolved?
Hello, young scientist! Every time you stir sugar into a cup of tea, you are making a solution. But how sweet is your drink? And how much sugar can the water really hold? In this chapter you will see why no mass is lost when something dissolves, calculate concentration in g/mL, and read solubility curves like a real chemist. These skills help you in the lab, in the kitchen and in exams!
1. Quick Recap: Solute, Solvent and Solution
A solution is a mixture formed when a solute dissolves in a solvent.
Solute – the substance present in the lesser amount (by mass or by volume).
Solvent – the substance present in the greater amount (by mass or by volume).
Examples: In salt water, salt is the solute and water is the solvent. In a mixture of 70 mL of alcohol and 30 mL of water, alcohol is the solvent, because there is more of it!
Memory aid: soluTe = Tiny amount; solVent = Vast amount.
The rate of dissolving (temperature, stirring, surface area) is covered in the chapter Dissolving. Here we focus on how much is dissolved.
Key takeaway: \(\text{solute} + \text{solvent} \rightarrow \text{solution}\)
2. Mass Is Conserved During Dissolving
When you stir sugar into water, the sugar seems to disappear. But it is still there – it has just broken up into particles too small to see. You can still taste it! Nothing is lost and nothing is added, so mass is conserved during dissolving:
\(\text{mass of solution} = \text{mass of solvent} + \text{mass of solute}\)
Checking it with an experiment
1. Put a beaker of water and a small dish of salt together on an electronic balance. Record the total mass.
2. Tip all the salt into the water and stir until it has all dissolved.
3. Put the empty dish back on the balance next to the beaker. Record the total mass again.
Result: The two readings are the same. Mass is conserved!
Why? A particle view
Dissolving is a physical change. The solute particles simply spread out between the solvent particles. No particles are destroyed or made, so the total mass does not change.
Worked example
Q: 20 g of sugar is dissolved in 150 g of water. What is the mass of the solution?
A: \(150\ \text{g} + 20\ \text{g} = 170\ \text{g}\)
Q: A salt solution has a mass of 260 g and contains 60 g of salt. What mass of water does it contain?
A: \(260\ \text{g} - 60\ \text{g} = 200\ \text{g}\)
Did you know? Mass always adds up, but volume does not always! Mix 50 mL of water with 50 mL of alcohol and you get slightly less than 100 mL, because some particles fit into the gaps between the others. So always measure the volume of a solution instead of guessing it.
Key takeaway: Dissolving never changes the total mass – the solute is still there, just spread out.
3. Concentration: How Strong Is a Solution?
Two cups of lemon tea can contain different amounts of sugar. To compare them fairly, we use concentration: the mass of solute in each millilitre of solution.
\(\text{concentration (g/mL)} = \dfrac{\text{mass of solute (g)}}{\text{volume of solution (mL)}}\)
The unit g/mL means 'grams per millilitre'. A concentration of 0.05 g/mL means every 1 mL of the solution contains 0.05 g of solute.
Dilute or concentrated?
A dilute solution has a small mass of solute in a certain volume. A concentrated solution has a large mass of solute in the same volume. These words are comparisons: a 0.2 g/mL sugar solution is concentrated compared with a 0.02 g/mL one.
More dilute: add more solvent (e.g. water).
More concentrated: dissolve more solute, or evaporate some solvent.
Example: 100 mL of syrup contains 20 g of sugar (0.2 g/mL). Water is added to make 200 mL of solution. The sugar is still 20 g, so the concentration is now \(\dfrac{20\ \text{g}}{200\ \text{mL}} = 0.1\ \text{g/mL}\). Doubling the volume halves the concentration.
Worked examples
Example 1: A simple calculation
10 g of sugar is dissolved in water to make 200 mL of solution. Find the concentration.
\(\text{concentration} = \dfrac{10\ \text{g}}{200\ \text{mL}} = 0.05\ \text{g/mL}\)
Example 2: Which drink is sweeter?
Cup A has 6 g of sugar in 300 mL of tea. Cup B has 4 g of sugar in 100 mL of tea.
Cup A: \(\dfrac{6\ \text{g}}{300\ \text{mL}} = 0.02\ \text{g/mL}\); Cup B: \(\dfrac{4\ \text{g}}{100\ \text{mL}} = 0.04\ \text{g/mL}\)
Cup B is sweeter, even though it contains less sugar in total!
Example 3: Watch the units!
5 g of salt is dissolved to make 0.25 L of solution. Find the concentration in g/mL.
Step 1: \(0.25\ \text{L} = 0.25 \times 1000\ \text{mL} = 250\ \text{mL}\)
Step 2: \(\dfrac{5\ \text{g}}{250\ \text{mL}} = 0.02\ \text{g/mL}\)
Example 4: Finding the mass of solute
How much salt is needed to make 50 mL of a 0.1 g/mL salt solution?
\(\text{mass of solute} = \text{concentration} \times \text{volume of solution} = 0.1 \times 50 = 5\ \text{g}\)
Unit care: Mass must be in grams (\(1\ \text{kg} = 1000\ \text{g}\)). Volume must be in millilitres (\(1\ \text{L} = 1000\ \text{mL}\), \(1\ \text{cm}^3 = 1\ \text{mL}\)). Always write g/mL in your answer.
Common mistake: Dividing by the volume of water instead of the volume of the solution, or putting the numbers upside down. Remember: solute on top, solution at the bottom.
Key takeaway: Concentration tells you how 'crowded' the solute is: mass of solute (g) divided by volume of solution (mL).
4. Colour and Concentration
When the solute is coloured, you can often see the concentration. The more concentrated the solution, the deeper (more intense) its colour. Add water to a glass of fruit cordial and the colour becomes paler, because the drink becomes more dilute.
Activity: Food dye and colour intensity
Put 10 mL, 8 mL, 6 mL, 4 mL and 2 mL of a food dye solution into five identical test tubes. Add water so that every tube holds 10 mL. Compare the colours in front of white paper.
Independent variable – concentration of the dye
Dependent variable – colour intensity
Control variables – same dye, same total volume, same size of test tube, same lighting
Result: The higher the concentration, the deeper the colour. A colorimeter can measure colour intensity with numbers, which is more objective than judging by eye.
Key takeaway: For a coloured solute, a deeper colour means a higher concentration.
5. Solubility: How Much Can Dissolve?
Keep stirring sugar into a glass of water. Sooner or later, the extra sugar just sits at the bottom – the water cannot hold any more!
Solubility is the maximum mass of solute that can dissolve in a fixed amount of solvent at a specific temperature. It is often given in grams per 100 g of water (about the same as per 100 mL, since 1 mL of water has a mass of about 1 g).
Example: The solubility of table salt (sodium chloride) at 20 °C is about 36 g per 100 g of water. At 20 °C, 100 g of water can dissolve up to about 36 g of salt, and no more.
Saturated and unsaturated solutions
A saturated solution cannot dissolve any more solute at that temperature; extra solute stays at the bottom. An unsaturated solution can still dissolve more.
How to test: Add a little more solute and stir. If it dissolves, the solution was unsaturated. If it stays as a solid, the solution is saturated.
Finding solubility with a fair test
Heat a fixed volume of water (e.g. 10 mL) in a water bath to a set temperature. Add the solute a little at a time, stirring, until no more dissolves. Weigh the solute before and after to find the mass dissolved. Repeat at other temperatures. Temperature is the independent variable; the maximum mass dissolved is the dependent variable; the type of solute and the volume of water are control variables.
Common mistake: 'Stirring makes more sugar dissolve.' Not quite! Stirring and crushing only make a solute dissolve faster. They do not change how much can dissolve. Temperature changes both the rate and the solubility.
Key takeaway: Solubility is a maximum, and it depends on temperature. A saturated solution holds that maximum amount.
6. Reading a Solubility Curve
A solubility curve shows the solubility of a solute (y-axis, g per 100 g of water) at different temperatures (x-axis, °C). Here are simple data for two example salts:
Temperature (°C): 0 | 20 | 40 | 60 | 80
Salt A: 15 | 30 | 60 | 100 | 150
Salt B: 35 | 36 | 37 | 37 | 38
Plotted as smooth curves, Salt A gives a steep curve and Salt B an almost flat one. Potassium nitrate behaves like Salt A; table salt behaves like Salt B.
Skill 1: Read the solubility at a temperature
Find the temperature on the x-axis, go up to the curve, then across to the y-axis.
Example: At 40 °C, the solubility of Salt A is 60 g per 100 g of water.
You can also work backwards: read across from 100 g to the Salt A curve, then down. So 100 g of Salt A just dissolves in 100 g of water at 60 °C.
Skill 2: Describe how solubility changes with temperature
For most solids, solubility increases as temperature increases. A steep curve means solubility changes a lot with temperature; a flat curve means temperature has little effect.
Did you know? Gases are the other way round: they are less soluble in warm water. That is why a warm can of soft drink goes flat faster than a cold one.
Skill 3: Find the mass that crystallises on cooling
When a hot saturated solution cools, its solubility falls. The solute that can no longer stay dissolved comes out as solid crystals.
Example: A saturated solution of Salt A in 100 g of water at 60 °C is cooled to 20 °C. What mass of crystals forms?
Dissolved at 60 °C: 100 g. Can stay dissolved at 20 °C: 30 g.
\(\text{mass of crystals} = 100\ \text{g} - 30\ \text{g} = 70\ \text{g}\)
Careful: The curve is for 100 g of water. With 50 g of water, halve the answer: 35 g of crystals.
Key takeaway: Read up, then across. Most solids dissolve more when hot. Cooling a saturated solution forms crystals.
Quick Review
1. A solution forms when a solute (the lesser amount) dissolves in a solvent (the greater amount).
2. Mass is conserved: the mass of the solution equals the mass of the solvent plus the mass of the solute.
3. Concentration in g/mL is the mass of solute (g) divided by the volume of solution (mL). Check the units first!
4. Adding water makes a solution more dilute; for coloured solutions, deeper colour means more concentrated.
5. Solubility is the maximum mass of solute that dissolves in a fixed amount of solvent at a specific temperature. A saturated solution cannot dissolve any more.
6. On a solubility curve, read up then across. Most solids are more soluble when hot, and cooling a saturated solution forms crystals.
Great work! Next time you stir a drink, think like a chemist. Keep it up!