IMAT Chemistry · Formula sheet

Solutions and Concentration formulas

12 formulas, 4 reference tables and 17 common traps for IMAT Chemistry Solutions and Concentration, grouped by subtopic.

Full notes with worked examples

Solutions, Mixtures and How to Separate Them

Learn this subtopic in the notes

Solutions and mixtures: the key terms

Term	Meaning	Example
Solution	Homogeneous mixture; particles too small to see or settle	Sugar dissolved in water
Suspension	Heterogeneous; particles large enough to settle or be filtered	Muddy water
Colloid	Particles about 1 to 1000 nm across; they scatter light and do not settle	Milk, fog
Miscible liquids	Mix completely to give one layer	Water and ethanol
Immiscible liquids	Separate into two layers	Hexane and water
Blood	Heterogeneous: cells suspended in plasma, which is itself a solution	Spinning blood separates the cells

Separation techniques and when to use each

Technique	Separates	Based on	Example
Filtration	Insoluble solid from a liquid	Particle size	Sand from water
Evaporation or crystallisation	Dissolved solid from its solution	Solvent evaporates, solid stays	Salt from sea water
Simple distillation	Solvent from a solution	Large difference in boiling point	Pure water from sea water
Fractional distillation	Miscible liquids	Close boiling points	Ethanol from water; crude oil fractions
Separating funnel	Immiscible liquids	Density; liquids do not mix	Oil from water
Chromatography	Dissolved substances in a mixture	Different attraction to the paper and the solvent	Plant pigments, ink dyes
Centrifugation	Suspended particles from a liquid	Density	Blood cells from plasma

Common traps

Homogeneous does not mean pure, and blood is not homogeneous

Salt water is homogeneous but still a mixture of two substances. Blood looks uniform but is heterogeneous: its cells can be separated by spinning. Options calling blood homogeneous, or calling a solution a pure substance, are wrong.

Filtration cannot remove a dissolved substance

Dissolved particles pass through filter paper with the solvent. Salt cannot be filtered out of salt water; it needs evaporation, or distillation to recover the water. Two miscible liquids need fractional distillation, not filtration or a separating funnel.

Like Dissolves Like, Electrolytes and Saturation

Learn this subtopic in the notes

Solubility, saturation and crystals formed on cooling

Mass of crystals formed on cooling

m_{\text{crystals}} = (S_{\text{hot}} - S_{\text{cold}}) \times \frac{m_{\text{water}}}{100}

$S_{\text{hot}}, S_{\text{cold}}$ solubility at each temperature, in g per 100 g of water
$m_{\text{water}}$ mass of water, in g

Like dissolves like: polar and non-polar solvents

Solute	In water (polar)	In hexane (non-polar)	Reason
Most ionic salts (NaCl, KNO₃)	Dissolve	Do not dissolve	Water's dipoles attract the ions
Small polar molecules (ethanol, glucose, sucrose)	Dissolve	Dissolve poorly	Hydrogen bonds with water
Non-polar molecules (I₂, Br₂, oils, alkanes)	Barely dissolve	Dissolve	Only weak dispersion forces on both sides
Non-polar gases (O₂, N₂, H₂)	Very slightly	Slightly	Weak attractions to any solvent
Giant covalent solids (SiO₂, diamond)	Insoluble	Insoluble	Strong covalent network cannot be broken

Electrolytes and non-electrolytes: which particles are in a solution

Solute type	Particles in water	Conducts?	Examples
Strong electrolyte	Ions only, plus water molecules	Well	NaCl, HCl, KOH, MgCl₂
Weak electrolyte	Mostly molecules, a few ions	Weakly	Ethanoic acid, ammonia
Non-electrolyte	Solute molecules and water molecules	No	Glucose, sucrose, ethanol, urea
Undissolved ionic solid	Ions fixed in a lattice	No	Solid sodium chloride

Common traps

Ionic does not always mean soluble, covalent does not always mean insoluble

Calcium carbonate and silver chloride are ionic but insoluble in water. Sugar and ethanol are covalent but very soluble, because they are polar and form hydrogen bonds. Statements starting with all ionic or all covalent are wrong.

A salt solution contains ions and molecules, not atoms

Sodium chloride solution contains

\mathrm{Na^+}

and

\mathrm{Cl^-}

ions among water molecules. There are no free sodium or chlorine atoms, and no NaCl units. Options that include single atoms are wrong.

Cooling removes solute, not solvent

When a saturated solution of a solid cools, crystals form but the mass of water is unchanged. The remaining solution is still saturated, and its concentration is lower. Statements saying the concentration stays the same, or that water is lost, are wrong.

Gases dissolve less in warm water

The rule that solubility rises with temperature is for most solids only. For gases it is the reverse, which is why warm water holds less oxygen for fish.

Molarity, Mass Concentration and Other Units

Learn this subtopic in the notes

Molarity: moles of solute per litre of solution

Molarity

c = \frac{n}{V} \qquad n = c\,V

$c$ concentration, in mol/L
$n$ moles of solute, in mol
$V$ volume of solution, in L

Mass concentration in g/L and converting it to mol/L

Mass concentration

\rho_{\text{solute}} = c \times M

$\rho_{\text{solute}}$ mass concentration, in g/L
$c$ molar concentration, in mol/L
$M$ molar mass of the solute, in g/mol

Percentage concentrations and parts per million

Percentage by mass and by volume

\%\,w/w = \frac{m_{\text{solute}}}{m_{\text{solution}}} \times 100 \qquad \%\,w/v = \frac{m_{\text{solute}}\,(\text{g})}{V_{\text{solution}}\,(\text{mL})} \times 100

$m_{\text{solution}}$ mass of solute plus solvent
$V_{\text{solution}}$ volume of the solution, in mL

Molality, mole fraction and converting with density

Molality and mole fraction

b = \frac{n_{\text{solute}}}{m_{\text{solvent}}\,(\text{kg})} \qquad x_A = \frac{n_A}{n_A + n_B}

$b$ molality, in mol/kg
$m_{\text{solvent}}$ mass of solvent only, in kg
$x_A$ mole fraction of A

Common traps

Millilitres must become litres

Molarity is per litre. Multiplying 0.30 mol/L by 200 (mL) instead of 0.200 (L) gives an answer 1000 times too large. Convert the volume first.

g/L and mol/L differ by the molar mass

A 0.1 mol/L solution of a substance with

M = 40

is 4 g/L, not 0.1 g/L. Check which unit the question asks for; options often give the right number in the wrong unit.

Divide by the mass of solution, not of solvent

In % w/w the bottom of the fraction is solute plus solvent. 20 g of sugar in 80 g of water is 20%, not 25%. The same rule applies to ppm.

Molality uses kilograms of solvent, molarity uses litres of solution

Molality divides by the mass of the solvent alone, in kilograms. Molarity divides by the volume of the whole solution, in litres. Using grams, or the mass of the solution, gives a wrong molality.

Preparing, Diluting, Mixing and Reacting Solutions

Learn this subtopic in the notes

Preparing a solution of known concentration

Mass of solute needed

m = c \times V \times M

$m$ mass of solute to weigh, in g
$c$ concentration wanted, in mol/L
$V$ final volume of solution, in L
$M$ molar mass, in g/mol

Dilution: c₁V₁ = c₂V₂

Dilution

c_1 V_1 = c_2 V_2

$c_1, V_1$ concentration and volume before adding water
$c_2, V_2$ concentration and total volume after

Mixing two solutions of the same solute

Concentration after mixing

c = \frac{c_1V_1 + c_2V_2}{V_1 + V_2}

$c_1, V_1$ first solution
$c_2, V_2$ second solution

Reacting volumes and titration

At the equivalence point

\frac{c_A V_A}{a} = \frac{c_B V_B}{b}

$c_A, V_A$ concentration and volume of solution A
$a, b$ coefficients of A and B in the balanced equation

Common traps

Made up to 1 L is not the same as dissolved in 1 L

Molarity is per litre of solution. Adding a solid to 1 L of water gives more than 1 L of solution, so the concentration is slightly below the target. Correct preparation always makes the solution up to the mark.

Water added is not the final volume

c_1V_1 = c_2V_2

gives the final volume. If the question asks how much water to add, subtract the starting volume. The final volume itself is usually one of the wrong options.

Concentrations do not add

Mixing 0.1 mol/L with 0.1 mol/L gives 0.1 mol/L, not 0.2. Add moles and volumes separately, then divide.

Check the ratio before using c₁V₁ = c₂V₂

The dilution formula only works for reactions in a 1 : 1 ratio. Sulfuric acid needs twice its moles of sodium hydroxide, and a carbonate needs twice its moles of hydrochloric acid. Use the coefficients of the balanced equation.

Boiling Point, Freezing Point and Osmotic Pressure

Learn this subtopic in the notes

Colligative properties and the van 't Hoff factor

Concentration of dissolved particles

c_{\text{particles}} = i \times c

$i$ van 't Hoff factor: particles per formula unit
$c$ concentration of the solute

Boiling point elevation and freezing point depression

Boiling and freezing point changes

\Delta T_b = i\,K_b\,b \qquad \Delta T_f = i\,K_f\,b

$\Delta T_b, \Delta T_f$ rise in boiling point, fall in freezing point, in K
$K_b, K_f$ constants of the solvent, in K kg/mol
$b$ molality of the solute, in mol/kg
$i$ van 't Hoff factor

Osmosis and osmotic pressure

Osmotic pressure

\pi = i\,c\,R\,T

$c$ molar concentration of the solute (mol/L with R = 0.0821 L atm/(mol K), or mol/m³ with R = 8.314 J/(mol K))
$T$ absolute temperature, in K
$i$ van 't Hoff factor

Common traps

Count particles, not formula units

At the same concentration, a sodium chloride solution has twice the effect of a glucose solution, because each NaCl gives two ions. Comparing solute concentrations without multiplying by

i

picks the wrong solution.

A solution boils higher and freezes lower

Dissolving a solute raises the boiling point and lowers the freezing point. A saturated sugar solution does not freeze at 0 °C; it freezes below it. Options with the change in the wrong direction are common.

Water moves towards the more concentrated solution

In osmosis it is water, not solute, that moves, and it moves towards the side with more dissolved particles. Count particles: 0.15 mol/L NaCl matches 0.30 mol/L glucose, not 0.15 mol/L glucose.

Solutions and Concentration formulas

Solutions, Mixtures and How to Separate Them

Solutions and mixtures: the key terms

Separation techniques and when to use each

Common traps

Like Dissolves Like, Electrolytes and Saturation

Solubility, saturation and crystals formed on cooling

Like dissolves like: polar and non-polar solvents

Electrolytes and non-electrolytes: which particles are in a solution

Common traps

Molarity, Mass Concentration and Other Units

Molarity: moles of solute per litre of solution

Mass concentration in g/L and converting it to mol/L

Percentage concentrations and parts per million

Molality, mole fraction and converting with density

Common traps

Preparing, Diluting, Mixing and Reacting Solutions

Preparing a solution of known concentration

Dilution: c₁V₁ = c₂V₂

Mixing two solutions of the same solute

Reacting volumes and titration

Common traps

Boiling Point, Freezing Point and Osmotic Pressure

Colligative properties and the van 't Hoff factor

Boiling point elevation and freezing point depression

Osmosis and osmotic pressure

Common traps

More IMAT Chemistry formula sheets