ARMCQs DIGITAL STUDY NOTES
Chapter 6: Solutions
Solutions: The Essential Idea
What is a solution?
A solution is a homogeneous mixture of two or more substances. Its composition is the same throughout. A phase is a part of matter with uniform properties.
Understand it simply
In a true solution, the dissolved substance is spread evenly. A small sample from one part has the same composition as a sample from another part.
A solution can be a solid, a liquid or a gas.
Its substances are mixed physically. They are not chemically joined in a fixed ratio.
Solution | Solute | Solvent |
|---|---|---|
Salt water | NaCl | Water |
Sugar water | Sugar | Water |
Air | Oxygen and other gases | Mainly nitrogen |
Brass | Zinc | Copper |
Formation Of A Solution
Change the model · explore the parts
Keep the solute amount fixed and double final solution volume. What happens to concentration?
Choose what you expect, then test it below. You can explore without answering first.
Start: 12 solute particles, 1 volume unit, relative concentration 12.0.
Keep Model solute particles at 12. Move Final solution volume from 1 to 2 units.Each dot represents a solute particle; colours only help distinguish the dots. Model quantities are illustrative. Increasing final volume with the same solute lowers concentration. Particles are not drawn to scale.
Change the controls to see the result. Choose Explore diagram parts for a guided explanation.
View complete static diagram
Milk is a colloid. Muddy water is a suspension. Neither is a true solution.
Solute, Solvent and Aqueous Solutions
Solute
The substance dissolved in a solution is the solute. In simple examples, it is usually present in a smaller amount.
Solvent
The substance doing the dissolving is the solvent. It is often present in a larger amount and generally determines the solution's state.
Aqueous solution
If water is the solvent, the solution is aqueous, shown by (aq); e.g. NaCl(aq).
Term | Meaning | Example |
|---|---|---|
Solute | Dissolved substance | Sugar |
Solvent | Dissolving medium | Water |
Solution | Homogeneous mixture | Sugar water |
Water dissolves many substances, so it is often called a universal solvent. It does not dissolve everything. Most oils do not dissolve in water.
A solution is a mixture. Its substances keep their identities, and their amounts can vary.
Unsaturated, Saturated and Supersaturated
Unsaturated solution
An unsaturated solution can dissolve more solute at the given temperature.
Saturated solution
A saturated solution contains the maximum amount of dissolved solute at the given temperature. Any extra solute remains undissolved.
Supersaturated solution
A supersaturated solution contains more dissolved solute than a saturated solution at the same temperature. It is not fully stable. Disturbing it or adding a small crystal may cause the extra solute to form crystals.
Saturation At A Fixed Temperature
Change the model · explore the parts
The model dissolves at most 20 particles at fixed conditions. What happens if you add 24?
Choose what you expect, then test it below. You can explore without answering first.
Fixed temperature and solvent amount. The model solubility limit is 20 particles.
Move Model solute particles to 24. Compare Dissolved and Undissolved.Illustrative limit: 20 model particles at a fixed temperature and solvent amount. Extra solute settles as solid. Adding excess solute does not make a supersaturated solution. Choose Explore diagram to compare the supersaturated state.
Change the controls to see the result. Choose Explore diagram parts for a guided explanation.
View complete static diagram
Solution | Dissolved amount | Added solute |
|---|---|---|
Unsaturated | Below limit | Can dissolve |
Saturated | At limit | Usually remains undissolved |
Supersaturated | Above limit | Excess can crystallize |
How supersaturation is prepared
Dissolve a suitable solute in hot solvent until the solution is saturated.
Let it cool slowly. Avoid shaking it or adding seed crystals.
If more solute stays dissolved than normally allowed at the lower temperature, the solution is supersaturated.
Heating alone does not prove supersaturation. Neither do crystals at the bottom. Supersaturation means extra solute is still dissolved at the stated temperature.
Dilution and the Dilution Formula
Dilute vs concentrated
A dilute solution has relatively little dissolved solute; a concentrated one has relatively more. Either can be unsaturated or saturated depending on the solute.
Dilution
When only solvent is added, concentration decreases while the amount of dissolved solute stays unchanged.
M₁V₁ = M₂V₂.
1 means the starting solution. 2 means the diluted solution. V₂ is the final volume after dilution.
Dilution Of A Stock Solution
Change the model · explore the parts
Keep the solute amount fixed and double final solution volume. What happens to concentration?
Choose what you expect, then test it below. You can explore without answering first.
Start: 12 solute particles, 1 volume unit, relative concentration 12.0.
Keep Model solute particles at 12. Move Final solution volume from 1 to 2 units.Each dot represents a solute particle; colours only help distinguish the dots. Model quantities are illustrative. Increasing final volume with the same solute lowers concentration. Particles are not drawn to scale.
Change the controls to see the result. Choose Explore diagram parts for a guided explanation.
View complete static diagram
Example 6.1: 100 mL of 0.40 M MgSO₄ from a 2.0 M stock
V₁ = (M₂V₂)/M₁ = (0.40 × 100)/2.0 = 20 mL.
Take 20 mL of stock and add water to make 100 mL of FINAL solution.
Example 6.2: 500 mL of 0.20 M NaOH from 1.5 M stock
V₁ = (0.20 × 500)/1.5 = 66.7 mL.
Measure 66.7 mL of stock and dilute to a final volume of 500 mL.
Concentrated acids can burn skin and eyes. Dilution needs trained supervision and protective equipment. Add acid to water, never water to concentrated acid.
Types of Solutions by Physical State
Understand it simply
The solvent usually determines whether a solution is solid, liquid or gas.
Solute | Solvent | State of solution | Example |
|---|---|---|---|
Gas | Gas | Gas | O₂ mixed with N₂ (air) |
Gas | Liquid | Liquid | CO₂ in carbonated water |
Gas | Solid | Solid | Hydrogen in palladium |
Liquid | Liquid | Liquid | Ethanol in water |
Solid | Liquid | Liquid | Salt in water |
Solid | Solid | Solid | Brass (Zn in Cu) |
Remember
Fog and smoke contain tiny droplets or particles in air. They are not true solutions. Butter and cheese are also complex mixtures, not simple solid solutions.
Concentration and Common Units
Definition
Concentration means the amount of solute in a given amount of solution (or solvent for certain units).
Understand it simply
Ask: How much solute is present in this amount of solution? More solute in the same volume means a higher concentration.
Mass concentration
Concentration in g/dm³ = mass of solute in grams ÷ volume of FINAL solution in dm³.
Unit | Equivalent |
|---|---|
1 dm³ | 1 L = 1000 cm³ = 1000 mL |
1 cm³ | 1 mL |
100 cm³ | 0.100 dm³ |
500 cm³ | 0.500 dm³ |
Concentration
Change the model · explore the parts
Keep the solute amount fixed and double final solution volume. What happens to concentration?
Choose what you expect, then test it below. You can explore without answering first.
Start: 12 solute particles, 1 volume unit, relative concentration 12.0.
Keep Model solute particles at 12. Move Final solution volume from 1 to 2 units.Each dot represents a solute particle; colours only help distinguish the dots. Model quantities are illustrative. Increasing final volume with the same solute lowers concentration. Particles are not drawn to scale.
Change the controls to see the result. Choose Explore diagram parts for a guided explanation.
View complete static diagram
Use the final volume of the whole solution. Do not simply use the volume of water added. Dissolving and mixing can change the volume.
Concentration tells us how much is dissolved now. Solubility tells us how much can dissolve at the stated temperature and pressure.
Four Forms of Percentage Concentration
Mass by mass % (m/m)
% (m/m) = (mass of solute / mass of solution) × 100. Example: 5 g sugar in 100 g solution = 5% m/m.
Mass by volume % (m/v)
% (m/v) = mass of solute (g) / FINAL solution volume (mL) × 100. Example: 5 g solute per 100 mL solution = 5% m/v.
Volume by volume % (v/v)
% (v/v) = volume of solute / FINAL volume of solution × 100. Example: 5 mL ethanol in 100 mL solution = 5% v/v.
Volume by mass (v/m)
Volume by mass expresses the volume of solute in mL per 100 g of solution. Write these units clearly because volume and mass are different quantities.
Concentration Formulas
Explore each part · follow the explanation
Mass / mass. Divide solute mass by total solution mass, then multiply by 100.
Choose a part for its explanation. Use Focus to enlarge it, or view the whole diagram to see every connection.
View complete static diagram
Example 6.3
15 g salt and 110 g water: total mass = 125 g; % m/m = 15/125 × 100 = 12%.
Example 6.4
25 cm³ ethanol in a FINAL 150 cm³ solution: % v/v = 25/150 × 100 = 16.7%.
Water and ethanol volumes do not add exactly. Measure the final solution volume instead of adding the starting volumes.
Molarity and Worked Molarity Problems
Definition
Molarity, M = moles of solute / volume of FINAL solution (L). Units: mol/L or mol/dm³.
Understand it simply
Molarity counts moles in each litre of the final solution. A 1 M solution contains 1 mole of solute per litre.
Moles = mass (g) / molar mass (g/mol). So M = mass / (molar mass × volume in L).
When volume is in cm³: M = [mass / molar mass] × [1000 / volume in cm³].
Preparation of 1.0 M NaCl
Measure about 58.5 g NaCl: approximately 1 mole. Dissolve it in some water. Transfer it to a volumetric flask. Add water until the final solution volume is 1.000 L.
Preparing A Molar Solution
Explore each part · follow the explanation
One mole. Using the rounded molar mass, 58.5 g NaCl is approximately 1 mole.
Choose a part for its explanation. Use Focus to enlarge it, or view the whole diagram to see every connection.
View complete static diagram
Example 6.5: 20 g NaCl in 500 cm³ solution
n = 20/58.5 ≈ 0.3419 mol, V = 0.500 L; M = 0.3419/0.500 ≈ 0.684 M.
Example 6.6: oxalic acid C₂H₂O₄
For 100 cm³ of 2 M: moles = 2 × 0.100 = 0.20 mol. Anhydrous C₂H₂O₄ has molar mass 90 g/mol; mass = 0.20 × 90 = 18 g.
Anhydrous means without water of crystallization. Oxalic acid dihydrate contains water in its crystals. It has a higher molar mass, so more mass is needed. The 18 g answer is for anhydrous oxalic acid.
Example 6.7: H₂SO₄ dilution
For 500 cm³ of 0.5 M from 20 M stock: V₁ = 0.5 × 500/20 = 12.5 cm³. This is a mathematical illustration; such concentrated acid needs specialist handling.
Solubility: How Much Can Dissolve?
Definition
Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a stated temperature and pressure. At equilibrium, dissolving and crystal formation balance each other, so the dissolved amount stays constant.
Understand it simply
Solubility is a limit. It tells us how much can dissolve, not just how much is already there.
A common unit is grams of solute per 100 g of solvent. Always state the temperature.
A saturated solution contains the equilibrium maximum amount.
A concentrated solution may still be able to dissolve more solute.
A substance with low solubility can make a saturated solution even when very little has dissolved.
NaCl dissolves readily in water while AgCl dissolves only slightly.
Concentration versus solubility
Concentration is the amount dissolved now. Solubility is the maximum amount that can stay dissolved at equilibrium.
Why Does a Solute Dissolve?
Like dissolves like
As a useful guide, polar and ionic solutes tend to dissolve in polar solvents, while nonpolar solutes tend to dissolve in nonpolar solvents.
Three interactions
Some attractions between solute particles must be overcome so they can separate.
Some solvent particles must move apart too.
New attractions form between solute and solvent particles.
Dissolving depends on energy changes and how particles spread out. Attractions matter, but comparing attractions alone does not always tell us whether a substance will dissolve.
NaCl in water
Water has slightly charged ends. Its oxygen end, δ−, attracts Na⁺. Its hydrogen ends, δ+, attract Cl⁻. Water surrounds the separated ions and helps keep them in solution.
Hydration Of Ions
Change the model · explore the parts
Which end of water faces a positive Na⁺ ion?
Choose what you expect, then test it below. You can explore without answering first.
Red is oxygen; blue is hydrogen. δ− and δ+ are partial charges.
Compare Na⁺ with Cl⁻. Switch Partial charges off and on to follow the water orientation.Red = oxygen; blue = hydrogen. Opposite charges attract. This 2D arrangement shows orientation, not a fixed hydration number or a rigid shell of water molecules.
Change the controls to see the result. Choose Explore diagram parts for a guided explanation.
View complete static diagram
Why do water and gasoline not mix?
Gasoline is mostly nonpolar. Water is polar and forms strong attractions with other water molecules. The two liquids mostly stay in separate layers.
Ethanol’s –OH group forms hydrogen bonds with water. This helps ethanol mix with water.
Effects of Temperature and Pressure on Solubility
Solid solutes in liquids
Heating lets many solid solutes dissolve in larger amounts. But some do not follow this trend. Dissolving faster and dissolving more are different ideas.
Gases in liquids
At fixed gas pressure, most gases become less soluble in water as temperature rises.
Pressure
At fixed temperature, higher pressure of a gas above a liquid usually makes more of that gas dissolve. This is Henry’s law. The pressure due to that gas alone is its partial pressure.
Temperature Vs Solubility
Explore each part · follow the explanation
Many solid solutes. Many solids become more soluble as temperature rises, but there are exceptions. Dissolving faster is not the same as dissolving more.
Choose a part for its explanation. Use Focus to enlarge it, or view the whole diagram to see every connection.
View complete static diagram
A sealed fizzy drink holds CO₂ under pressure. Opening it lowers the pressure. Some CO₂ then escapes as bubbles.
True Solutions, Colloids and Suspensions
True solution
A homogeneous mixture of molecules or ions, with solute particle size generally below about 1 nm. It is normally transparent without visible Tyndall scattering.
Understand it simply
Compare particle size and behaviour. True solutions have the smallest dissolved particles. Colloids and suspensions have larger particles.
Colloid
A colloid has particles roughly 1–1000 nm in size spread through another substance. Its particles are not mixed at the molecular level, so it is heterogeneous, though it may look uniform. It can remain stable for a long time and often scatters light.
Suspension
A heterogeneous dispersion with larger particles, frequently above 1000 nm. Particles may settle on standing and are often trapped by ordinary filter paper.
Feature | True solution | Colloid | Suspension |
|---|---|---|---|
Approx. particle size | <1 nm | 1–1000 nm | >1000 nm |
Nature | Homogeneous | Heterogeneous on small scale | Heterogeneous |
Settles easily? | No | Usually no | Often yes |
Ordinary filter | Passes | Usually passes | Often retained |
Tyndall light scattering | Usually not visible | Often visible | May scatter |
Example | Salt in water | Milk, fog | Mud in water |
True Solution • Colloid • Suspension
Explore each part · follow the explanation
True solution. Particles are molecules or ions, usually below about 1 nm. They do not settle under ordinary conditions.
Choose a part for its explanation. Use Focus to enlarge it, or view the whole diagram to see every connection.
View complete static diagram
Particle sizes are useful guides, not exact limits for every mixture. Some colloids look transparent. Filter behaviour can also vary.
Tyndall Effect and Colloids in Daily Life
Definition
The Tyndall effect is the visible scattering of light by particles in a colloid or similar fine dispersion.
Understand it simply
We see a beam inside a colloid because particles send some light sideways towards our eyes.
Why is the beam visible?
Colloid particles scatter light sideways. Some light reaches our eyes, so we see the beam’s path. Salt and sugar solutions usually scatter too little light to show a bright path.
The Tyndall Effect
Explore each part · follow the explanation
True solution. A salt or sugar solution normally does not scatter enough light to reveal a bright beam path.
Choose a part for its explanation. Use Focus to enlarge it, or view the whole diagram to see every connection.
View complete static diagram
Milk has tiny fat droplets spread through water. This type of colloid is an emulsion.
Fog has tiny water droplets spread through air. This is an aerosol.
Smoke often has tiny solid particles or liquid droplets spread through air.
Paint particles may settle while the paint is stored.
Why should paints be stirred before use?
Stirring spreads the separated particles through the paint again.
Glucose in water is a true solution. Starch paste often behaves as a colloid.
Quick Concept Checks and Common Mistakes
Basic questions
A solution is homogeneous because its components mix uniformly at the molecular or ionic scale.
Nitrogen is considered the solvent component of air because it is the most abundant gas (~78% of dry air).
An aqueous solution has water as solvent.
2 M solution is more dilute than 3 M solution of the same solute.
Saturation and percentages
Unsaturated: can dissolve more at current temperature. Saturated: equilibrium limit reached. Supersaturated: more dissolved than equilibrium limit at same temperature.
10 g sugar + 140 g water gives 10/150 × 100 = 6.67% by mass.
A 10% m/m solution can be made from 10 g sugar + 90 g water (100 g final mixture).
1.2 M NaOH contains 1.2 × 40 = 48 g NaOH per dm³.
Remember
Milk and fog are colloids, not true homogeneous solutions.
Solubility depends on temperature and solvent; do not assume every solid solute increases in solubility with heating.
A saturated solution may contain undissolved solid, but this is not the definition of a supersaturated solution.
Adding more salt does not by itself prove that a solution is saturated. Check the temperature, solubility and whether extra solid remains after enough time for dissolving.
Solved Textbook Short Questions — Section B
1. Explain NaCl dissolving in water.
Water molecules attract Na⁺ and Cl⁻ ions and surround them. The oxygen side of water faces Na⁺, while the hydrogen side faces Cl⁻. Attraction between an ion and a polar molecule is called an ion–dipole attraction.
2. Saturated vs unsaturated
Saturated reaches the equilibrium solubility limit at specified temperature; unsaturated has room to dissolve more.
3. What is a solution? Name components.
A solution is a homogeneous mixture made from solute (dissolved material) and solvent (dissolving medium).
4. What is mass/volume percent?
Grams of solute per 100 mL of FINAL solution: % m/v = (mass g / solution mL) × 100.
5. One-molar solution with example
1 M means 1 mol dissolved solute in 1 L of FINAL solution. Example: 58.5 g NaCl made up to 1 L.
6. Why do colloids show Tyndall effect?
Colloidal particles scatter visible light.
7. Define dilution, concentration, solubility, molarity
Dilution: lower concentration by adding solvent. Concentration: amount of solute per defined amount. Solubility: maximum equilibrium dissolvable amount. Molarity: moles per litre of solution.
8. Why do ionic and polar solutes often dissolve in polar solvents?
Because polar solvents can stabilize solute ions or molecules through ion–dipole attractions, dipole interactions and hydrogen bonding.
9. Why might polar solute not dissolve in nonpolar solvent?
The nonpolar solvent may not provide enough favourable interactions to compensate for disrupting those in the original solute.
10. Importance of solutions
Solutions are used in medicines, intravenous fluids, drinks, cleaning, plant nutrients and industry.
11. Why does salt dissolve in water?
Polar water molecules surround Na⁺ and Cl⁻ ions and help separate them from the crystal. Surrounding dissolved particles with water molecules is called hydration.
12. Why is N₂ the solvent in air?
N₂ is the major component of dry air (about 78% by volume).
13. Why does gasoline not dissolve in water?
Gasoline is mainly nonpolar and water polar; their interactions do not favour mixing.
Solved Textbook Detailed Questions — Section C
1. How to prepare dilute solution from concentrated stock
Calculate stock volume using M₁V₁ = M₂V₂, measure carefully, transfer to a volumetric flask and add water until the FINAL target volume is reached. Mix well. For corrosive acids, follow proper laboratory precautions under trained supervision.
2. Define solubility and explain solute–solvent interactions
Solubility is the maximum equilibrium amount dissolved at a given temperature and pressure. Dissolving requires disrupting solute–solute and solvent–solvent forces and creating new solute–solvent interactions. Both energy changes and the spreading of particles help determine whether mixing occurs.
3. Why does solubility of some salts increase with temperature?
For many salts, heating favours greater equilibrium dissolution; the effect depends on the energy changes involved, so it does not occur for every salt. Increased dissolving SPEED is distinct from increased equilibrium solubility.
4. Explain how Na⁺ and Cl⁻ are attracted to water
The δ− oxygen side of water faces Na⁺; the δ+ hydrogen side faces Cl⁻. The ions become hydrated and disperse in solution.
5. Describe 'like dissolves like'
Ionic and polar substances often dissolve in polar solvents; nonpolar substances often mix with nonpolar solvents. This is a helpful guideline with exceptions.
6. Distinguish solution, colloid and suspension
A true solution is homogeneous with molecular/ionic particles. A colloid is a heterogeneous dispersion with particles often showing Tyndall effect. A suspension has relatively large particles that tend to settle and can often be filtered.
Solved Exercise Numericals — Section D
Before you calculate
Write Given → Formula → Substitution → Answer.
Convert volume cm³ to litres by dividing by 1000.
Use final solution volume, not simply the quantity of water.
Q1. 1.25 g HCl in 30 cm³ FINAL solution
Given: m = 1.25 g; molar mass HCl = 36.5 g/mol; volume = 0.030 L.
Moles = 1.25/36.5 = 0.03425 mol. M = 0.03425/0.030 ≈ 1.14 M.
Answer: 1.14 mol/dm³.
Q2. 2.5 g KCl in 100 cm³ FINAL solution
Molar mass KCl ≈ 74.5 g/mol. Moles = 2.5/74.5 ≈ 0.03356 mol.
Volume = 0.100 L. M = 0.03356/0.100 ≈ 0.336 M.
Answer: 0.336 mol/dm³.
Q3. NaOH mass in 1 dm³ of 0.25 M solution
Molar mass NaOH = 40 g/mol. Mass = M × V × molar mass = 0.25 × 1 × 40 = 10 g.
Answer: 10 g/dm³.
Q4. 0.5 M acid to neutralize 200 mL of 4 M base
Acid and base identities are not stated, so a unique answer cannot be calculated without the reaction mole ratio.
IF acid is monoprotic, base monobasic and the reaction is 1:1: MₐVₐ = MᵦVᵦ.
Vₐ = (4 × 200)/0.5 = 1600 mL = 1.6 L.
Answer: 1.6 L only with the stated 1:1 assumption. Other acid/base combinations give different answers.
Q5. 28 mg calcium in 100 cm³; g/dm³?
28 mg = 0.028 g; 100 cm³ = 0.100 dm³. Concentration = 0.028/0.100 = 0.28 g/dm³.
Answer: 0.28 g/dm³.
Q6. 20 cm³ alcohol mixed with 80 cm³ water; % v/v?
% v/v = volume solute / FINAL solution volume × 100. The final volume is not supplied; alcohol–water mixtures can contract.
If volumes are assumed additive: Vfinal ≈ 20 + 80 = 100 cm³; percentage ≈ 20/100 × 100 = 20% v/v.
Answer: approximately 20% v/v if the two volumes are assumed to add directly; exact % needs measured final volume.
Q7. NaOH needed for 400 cm³ of 0.3 M solution
V = 0.400 L. Moles = M × V = 0.3 × 0.400 = 0.120 mol.
Mass = 0.120 × 40 = 4.8 g.
Answer: 4.8 g NaOH, made up to 400 cm³ FINAL solution.