What is a solution? Types of solutions
A solution is a homogeneous mixture: it looks the same everywhere, even under a microscope. The component present in larger amount is the solvent. The others are solutes. A solution of just two parts is called a binary solution.
The solvent decides the physical state of the solution. With three states for solute and solvent, we get nine types:
| Solvent | Solute | Example |
|---|---|---|
| Gas | Gas | Air (oxygen in nitrogen) |
| Gas | Liquid | Moist air (water vapour in air) |
| Gas | Solid | Camphor vapour in nitrogen |
| Liquid | Gas | Soda water (CO₂ in water) |
| Liquid | Liquid | Ethanol in water |
| Liquid | Solid | Sugar or salt in water |
| Solid | Gas | Hydrogen in palladium |
| Solid | Liquid | Mercury in gold (amalgam) |
| Solid | Solid | Brass (zinc in copper), gold jewellery alloys |
Concentration terms (ways to say how strong a solution is)
Concentration tells how much solute is present in a given amount of solution (or solvent). Class 12 uses these:
- Mass percentage (w/w) = (mass of solute ÷ mass of solution) × 100. A 10% glucose solution has 10 g glucose in 100 g solution.
- Volume percentage (V/V) = (volume of solute ÷ volume of solution) × 100. Used for liquids, like 35% ethanol.
- Mass by volume (w/V) = grams of solute in 100 mL of solution. Common in medicines.
- Parts per million (ppm) = (parts of solute ÷ total parts of solution) × 10⁶. Used for very tiny amounts, like fluoride in water.
- Mole fraction (x) = moles of that component ÷ total moles. For a binary solution x₁ + x₂ = 1. It has no unit.
- Molarity (M) = moles of solute ÷ volume of solution in litres. Unit mol L⁻¹.
- Molality (m) = moles of solute ÷ mass of solvent in kg. Unit mol kg⁻¹.
Which terms change with temperature?
Liquids expand when heated, so volume changes. Terms that use volume (molarity, volume %, w/V) change with temperature. Terms that use only mass or moles (mass %, ppm by mass, mole fraction, molality) do not. That is why molality is used in colligative properties.
Board exam tip
Numericals converting between molarity, molality, mass % and mole fraction are very common (2–3 marks). Always write: moles = mass ÷ molar mass, and convert mL to L and g to kg.
Solubility of solids in liquids
Solubility is the largest amount of a substance that can dissolve in a fixed amount of solvent at a given temperature. When no more can dissolve, the solution is saturated. Less than that is unsaturated.
- Like dissolves like: polar and ionic solids (salt, sugar) dissolve in polar solvents like water. Non-polar solids (naphthalene) dissolve in non-polar solvents like benzene.
- Temperature: in a saturated solution, dissolving and crystallising go on together (a dynamic equilibrium). If dissolving takes in heat (endothermic), heating dissolves more. If it gives out heat (exothermic), heating dissolves less. For most solids, solubility rises with temperature.
- Pressure: has almost no effect on solids and liquids, because they hardly compress.
Solubility of gases and Henry's law
Gas solubility depends strongly on pressure and temperature.
Henry's law (own words): at a fixed temperature, the amount of a gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid. In the most used form:
p = KH · x
Here p is the partial pressure of the gas, x is its mole fraction in the solution, and KH is Henry's law constant (unit: pressure, e.g. kbar). A bigger KH means a less soluble gas, because you need more pressure to push in the same amount.
Why pressure helps
More pressure packs more gas molecules above the liquid. More of them hit the surface and get trapped in the liquid, until a new balance is reached.
Why heat hurts
Dissolving a gas usually gives out heat. So on heating, the balance shifts back and gas leaves. That is why fish need cold water (more oxygen) and why KH rises with temperature.
Applications
- Soft drinks are bottled under high CO₂ pressure.
- Scuba tanks use air diluted with helium to lower nitrogen in blood and avoid the bends.
- At high altitude, low oxygen pressure means less oxygen in blood (anoxia): climbers feel weak.
Limits
Henry's law works best at low pressure, for gases that do not react with the solvent (NH₃ and CO₂ react with water, so they deviate).
Try it (at home)
Take two unopened bottles of the same soda. Keep one in the fridge and one in the sun for an hour. Open both over a sink. Predict first: which fizzes more? The warm one does, because hot water holds less gas. Also notice: the closed bottle hardly fizzes, the open one does, because opening drops the pressure. In the 3D, move the pressure slider to see the same idea.
Key formulas and definitions
- Mass % = (mass of solute ÷ mass of solution) × 100
- ppm = (parts of solute ÷ total parts) × 10⁶
- Mole fraction xA = nA ÷ (nA + nB); xA + xB = 1
- Molarity M = moles of solute ÷ volume of solution (L)
- Molality m = moles of solute ÷ mass of solvent (kg)
- Henry's law: p = KH · x
- Dilution: M₁V₁ = M₂V₂
Worked examples
1. 5 g of salt is dissolved in 45 g of water. Find the mass percentage of salt.
Mass of solution = 5 + 45 = 50 g. Mass % = (5 ÷ 50) × 100 = 10%.
2. Find the molarity of a solution made by dissolving 4 g of NaOH (M = 40 g/mol) to make 250 mL of solution.
Moles = 4 ÷ 40 = 0.1 mol. Volume = 250 mL = 0.25 L. M = 0.1 ÷ 0.25 = 0.4 mol L⁻¹.
3. 18 g of glucose (C₆H₁₂O₆, M = 180 g/mol) is dissolved in 500 g of water. Find the molality.
Moles = 18 ÷ 180 = 0.1 mol. Solvent mass = 500 g = 0.5 kg. m = 0.1 ÷ 0.5 = 0.2 mol kg⁻¹.
4. A solution has 1 mol of ethanol and 9 mol of water. Find the mole fraction of each.
Total moles = 10. x(ethanol) = 1 ÷ 10 = 0.1. x(water) = 9 ÷ 10 = 0.9. Check: 0.1 + 0.9 = 1.
5. A 1 L water sample contains 2 mg of fluoride. Take 1 L water = 1000 g. Express this in ppm.
Mass of fluoride = 0.002 g. ppm = (0.002 ÷ 1000) × 10⁶ = 2 ppm.
6. KH for a gas in water at 298 K is 50 kbar. Find the mole fraction of the gas in water when its partial pressure is 0.5 bar.
Use x = p ÷ KH. KH = 50 kbar = 50 000 bar. x = 0.5 ÷ 50 000 = 1 × 10⁻⁵.
7. A solution of H₂SO₄ is 20% by mass and has density 1.2 g/mL. Find its molarity (M of H₂SO₄ = 98 g/mol).
Take 100 g solution: 20 g acid. Moles = 20 ÷ 98 = 0.204 mol. Volume = 100 ÷ 1.2 = 83.3 mL = 0.0833 L. M = 0.204 ÷ 0.0833 ≈ 2.45 mol L⁻¹.
8. Find the molality of a 2 M NaCl solution whose density is 1.1 g/mL (M of NaCl = 58.5 g/mol).
Take 1 L = 1000 mL solution. Mass of solution = 1000 × 1.1 = 1100 g. NaCl = 2 mol = 2 × 58.5 = 117 g. Water = 1100 − 117 = 983 g = 0.983 kg. m = 2 ÷ 0.983 ≈ 2.03 mol kg⁻¹.
Common mistakes
- Using the mass of the solution instead of the mass of the solvent in molality. Molality divides by solvent mass only, in kg.
- Forgetting to change mL to L (molarity) or g to kg (molality). 250 mL is 0.25 L, 500 g is 0.5 kg.
- Thinking a bigger KH means a more soluble gas. It is the opposite: bigger KH, less soluble.
- Saying heating always increases solubility. It helps most solids, but gases always dissolve less when hot.