SCH3U · Exam review

Chemistry Exam Review

A practice exam with questions from all 5 units, then the key facts from every lesson, unit by unit. For a deeper look at one unit, open its test review.

Unit test reviews

Practice exam

35 questions, the same number from each unit. Each one shows the lesson it comes from.

Unit 1: Atomic Models & Bohr Theory
1
What happens when an electron absorbs a photon with exactly the right amount of energy?
Unit 1: Organization of the Periodic Table
2
What does the period number of an element directly indicate?
Unit 1: Periodic Trends
3
Which is larger, a chlorine atom or a chloride ion ( $Cl^{-}$ ), and why?
Unit 1: IUPAC Nomenclature
4
Put these steps in order for naming $\text{Fe{(NO}_3)}_3$ .
1. 1Write the name: iron(III) nitrate
2. 2Conclude each iron ion is 3+
3. 3Total the anion charge: 3 × (1−) = 3−
4. 4Notice it starts with a metal, so it is ionic
5. 5Recognize NO₃ as the nitrate ion, charge 1−
Unit 1: Bond Types & Electronegativity Difference
5
Calculate ΔEN for a Mg–O bond. (Mg = 1.31, O = 3.44)
Unit 1: Intermolecular Forces
6
Which intermolecular force is present in every molecule, polar or nonpolar?
Unit 1: The Special Properties of Water
7
Match each everyday observation to the property of water that explains it.
Lakes freeze from the top down
Coastal towns have mild climates
Water climbs up a narrow glass tube
Salt disappears when stirred into water
Unit 2: Writing & Balancing Chemical Equations
8
Why is it never allowed to change a subscript to balance an equation?
Unit 2: Synthesis & Decomposition Reactions
9
Which general pattern describes a synthesis reaction?
Unit 2: Combustion Reactions
10
Which product can form during severely oxygen-limited combustion, in addition to or instead of CO?
Unit 2: Single Displacement Reactions
11
Write the correct diatomic formula for elemental nitrogen gas.
Unit 2: Double Displacement Reactions
12
Mixing aqueous NaCl and aqueous KNO₃ produces no visible reaction. Why?
Unit 2: Total & Net Ionic Equations
13
Aqueous $NH_{4} Cl$ and aqueous $NaNO_{3}$ are mixed. What is the net ionic equation?
Unit 2: Recognizing Reaction Patterns & Predicting Products
14
What are the products when copper metal is added to dilute hydrochloric acid?
Unit 3: Significant Figures & Unit Analysis
15
How many significant figures does $0.02050$ have?
Unit 3: Molar Mass
16
Calculate the molar mass of $NaCl$ .
g/mol
Unit 3: Mass, Moles & Number of Particles
17
Which $10.0 g$ sample contains the most atoms in total?
Unit 3: Empirical & Molecular Formulas
18
A hydrocarbon has the empirical formula $CH_{3}$ and a molar mass of $30.08 g/mol$ . How many hydrogen atoms are in its molecular formula?
Unit 3: Mole Ratios from Balanced Equations
19
For $2 C_{2} H_{2} + 5 O_{2} \to 4 CO_{2} + 2 H_{2} O$ , how many moles of $CO_{2}$ form from $1.5 mol C_{2} H_{2}$ ?
mol
Unit 3: Limiting & Excess Reagents
20
For $2 H_{2} + O_{2} \to 2 H_{2} O$ , $6.0 g$ of $H_{2}$ ( $M = 2.02$ ) reacts with $40.0 g$ of $O_{2}$ ( $M = 32.00 g/mol$ ). What mass of $H_{2} O$ ( $M = 18.02 g/mol$ ) forms?
g
Unit 3: Percentage Yield
21
A medicine is made in two steps with yields of $90%$ and $70%$ . What is the overall percent yield?
Unit 4: Characteristics of Solutions
22
Which best describes a supersaturated solution?
Unit 4: Solubility Curves
23
A solution's data point falls exactly on a solubility curve. The solution is:
Unit 4: Dilutions
24
Why does the dilution equation $C_{1} V_{1} = C_{2} V_{2}$ hold true?
Unit 4: Qualitative Analysis: Identifying Unknown Ions
25
Which metal ion produces a lilac (pale violet) flame test colour?
Unit 4: Solution Stoichiometry
26
Match each quantity you want to the final conversion you use.
1. A. $c = n / V$
2. B. $m = n M$
3. C. $n = c V$
4. D. $V = n / c$
Mass of product
Volume of a solution needed
Concentration of an unknown
Moles from a solution
Unit 4: Arrhenius Theory of Acids and Bases
27
Equal volumes of 0.1 mol/L HCl and 0.1 mol/L CH3COOH are tested with a conductivity tester. What is observed, and why?
Unit 4: Titration
28
Why is it acceptable for the Erlenmeyer flask to contain a little distilled water before the sample is pipetted in?
Unit 5: States of Matter & the Kinetic Molecular Theory
29
According to KMT, why do gases have much lower density than solids or liquids?
Unit 5: Pressure, Temperature, and the Kelvin Scale
30
Order these temperatures from LOWEST to HIGHEST: 0 K, 0°C, 100°C, 300 K.
1. 10°C
2. 2100°C
3. 3300 K
4. 40 K
Unit 5: Boyle's, Charles's, and Gay-Lussac's Laws
31
A student plots volume against temperature in °C for a gas at constant pressure and gets a straight line that does NOT pass through the origin. Where does the line cross the temperature axis, and what does that tell you?
Unit 5: The Ideal Gas Law
32
Find the pressure exerted by 0.750 mol of gas in a 12.0 L container at 295.0 K. Round to one decimal place.
kPa
Unit 5: Molar Volume: STP and SATP
33
How many moles of $N_{2}$ are in 11.2 L at STP?
mol
Unit 5: Gas Stoichiometry
34
Propane burns as $C_{3} H_{8} (g) + 5O_{2} (g) \to 3CO_{2} (g) + 4H_{2} O (g) .$ What volume of $O_{2}$ is needed to burn 2.00 L of propane, both at the same temperature and pressure?
L
Unit 5: Atmospheric Chemistry
35
Why were lakes on the Canadian Shield in Ontario especially vulnerable to acid rain?

Key facts by unit

Unit 1: Matter, Chemical Trends & Bonding

Atomic Models & Bohr Theory

Electron energy is quantized — only specific energy levels ( $n = 1, 2, 3, \dots$ ) are allowed.
Absorbing a photon of the right energy moves an electron to a higher level (excited state).
Falling back to a lower level releases a photon — this produces an element's unique line spectrum.
Shell capacities (elements 1–20): shell 1 holds 2, shell 2 holds 8, shell 3 holds 8, shell 4 holds up to 2.
A neutral atom has electrons = protons = atomic number $Z$ .

Isotopes, Atomic Mass & Isotopic Abundance

Atomic number $Z$ = protons; mass number $A$ = protons + neutrons.
Isotopes: same protons, different neutrons, different mass number.
Number of neutrons $= A - Z$ .
Average atomic mass = weighted average of all natural isotopes, based on their percent abundance.
The average atomic mass always lies closer to the more abundant isotope's mass.

Organization of the Periodic Table

Period number = number of electron shells in use.
Group number (main groups) = number of valence electrons (subtract 10 for groups 13–18).
Metals lose electrons to form positive ions (cations); nonmetals gain electrons to form negative ions (anions).
Metalloids sit along the staircase line and have intermediate, semiconductor-like properties.
Elements in the same family share similar chemical properties because they share the same valence electron count.

Periodic Trends

$Z_{e ff}$ increases across a period (more protons, same shielding); shielding increases down a group (more shells).
Atomic radius: decreases across a period, increases down a group.
Ionization energy: increases across a period, decreases down a group.
Electronegativity: increases across a period, decreases down a group; fluorine (3.98) is the highest of all elements.
Noble gases have the highest ionization energy in each period (the peak of the trend) but are left out of electron affinity and electronegativity because their shell is already full.
Cations are smaller than their parent atoms; anions are larger. Metal reactivity increases down a group; nonmetal reactivity increases up a group.

Ionic Bonding & Compounds

The octet rule: atoms are most stable with 8 valence electrons (2 for H/He), matching the nearest noble gas.
Metals lose electrons to form cations; nonmetals gain electrons to form anions.
Ionic bonds form from electrostatic attraction between oppositely charged ions.
Ionic compounds form repeating crystal lattices, not individual molecules.
Ionic compounds conduct electricity only when molten or dissolved (ions must be free to move).

IUPAC Nomenclature

Binary ionic: metal name + nonmetal root + "-ide"; no prefixes.
Multivalent metal: Roman numeral in brackets shows the cation's charge, found by working backward from the anion.
Polyatomic ion names and charges must be memorized (e.g. sulfate SO₄²⁻, carbonate CO₃²⁻, ammonium NH₄⁺).
Hydrate names use a Greek prefix + "hydrate" for the attached water molecules (e.g. pentahydrate = 5 H₂O).
Binary molecular compounds use Greek prefixes on both elements to state exact atom counts; "mono-" is dropped on the first element only.

Covalent Bonding & Lewis Structures

A covalent bond is a shared pair of electrons; a bonding line represents 2 electrons.
Total valence electrons = sum of group-number electrons per atom, adjusted for ion charge.
Central atom: usually the one that forms the most bonds; hydrogen is always terminal.
If the central atom lacks an octet after single bonds, convert a lone pair to a double/triple bond.
Exceptions to the octet rule: H/He (duet), B/Be (deficient), period 3+ elements (expanded octet), odd-electron species.

Bond Types & Electronegativity Difference

$Δ EN = ∣ E N_{A} - E N_{B} ∣$ , using Pauling electronegativity values.
ΔEN 0.0–0.4: nonpolar covalent. ΔEN 0.4–1.7: polar covalent. ΔEN ≥ 1.7: ionic.
In a polar covalent bond, the more electronegative atom carries a partial negative charge ( $δ^{-}$ ).
A coordinate covalent bond has both shared electrons donated by the same atom (e.g. forming NH₄⁺ or H₃O⁺).
Once formed, a coordinate covalent bond behaves identically to any other covalent bond of the same type.

Molecular Shape (VSEPR) & Polarity

VSEPR: electron domains (bonds + lone pairs) repel and spread to minimize repulsion, setting molecular shape.
Lone pairs compress bond angles slightly compared to the same domain count with no lone pairs.
A molecule is nonpolar only if its shape is symmetric AND every outer atom attached to the central atom is identical.
Lone pairs on the central atom always break symmetry and tend to produce a net dipole.
CH₂Cl₂ is polar (asymmetric substitution); CCl₄ is nonpolar (identical Cl atoms, perfectly symmetric tetrahedron).

Intermolecular Forces

London dispersion forces exist in every molecule and are the only IMF in nonpolar molecules; strength increases with molar mass/electron count.
Dipole-dipole forces act between molecules with a permanent net dipole (polar molecules).
Hydrogen bonding is an especially strong dipole-dipole attraction, requiring H bonded directly to N, O, or F.
Overall IMF strength ranking: hydrogen bonding > dipole-dipole > London dispersion (for similarly sized molecules).
Stronger IMFs mean more energy (higher temperature) is needed to separate molecules — higher boiling/melting points.

The Special Properties of Water

All of water's unusual properties trace back to its bent shape, polarity, and extensive hydrogen bonding.
Ice is less dense than liquid water because hydrogen bonds lock molecules into an open hexagonal lattice — ice floats.
Water has a high specific heat capacity because energy is absorbed breaking/reforming hydrogen bonds rather than raising temperature.
High surface tension comes from unbalanced hydrogen-bond pulling on molecules at the surface.
Water dissolves ionic and polar substances via ion-dipole and hydrogen-bonding interactions ('like dissolves like'); nonpolar substances remain insoluble.

Unit 2: Chemical Reactions

Writing & Balancing Chemical Equations

Word equation (names) → skeleton equation (formulas) → balanced equation (coefficients added).
Law of conservation of mass: atoms are conserved — the same count of each element on both sides.
Only coefficients may be changed to balance an equation; subscripts define the substance and must never change.
Balancing order that usually works well: metals, then other nonmetals, then hydrogen, then oxygen last.
State symbols: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).

Synthesis & Decomposition Reactions

Synthesis: $A + B \to A B$ — multiple reactants combine into a single product.
Decomposition: $A B \to A + B$ — a single reactant breaks into multiple products.
Metal oxide + water → metal hydroxide (base); nonmetal oxide + water → acid.
Metal carbonates decompose (with heat) into a metal oxide + carbon dioxide gas.
Metal hydroxides decompose (with heat) into a metal oxide + water.

Combustion Reactions

Complete combustion (excess O₂): hydrocarbon + O₂ → CO₂ + H₂O.
Incomplete combustion (limited O₂): hydrocarbon + O₂ → CO + H₂O, and possibly soot (C) in severe oxygen shortage.
Carbon monoxide (CO) is toxic because it binds to hemoglobin more strongly than oxygen, blocking oxygen transport in the blood.
A blue flame indicates efficient, complete combustion; a yellow/orange sooty flame indicates incomplete combustion.
Combustion reactions release energy as heat and light.

Single Displacement Reactions

Single displacement: $A + BC \to A C + B$ , but only if A is more reactive than B.
The activity series ranks metals from most to least reactive; a metal can only displace a less reactive metal below it.
Metals above hydrogen in the activity series react with acids to release H₂ gas; metals below hydrogen do not react with acids.
HOFBrINCl elements (H₂, O₂, F₂, Br₂, I₂, N₂, Cl₂) exist as diatomic molecules in their elemental form.
Halogen reactivity order: F₂ > Cl₂ > Br₂ > I₂ (decreases down the group, opposite to metals).

Double Displacement Reactions

Double displacement: $A B + C D \to A D + CB$ — cations and anions trade partners.
A double displacement reaction "happens" (is worth writing) only if a precipitate, gas, or water forms.
Group 1 and ammonium compounds are always soluble; nitrates and acetates are always soluble.
Silver, lead(II), and mercury(I) halides (Cl⁻, Br⁻, I⁻) are the classic insoluble exceptions to the halide rule.
Carbonates, phosphates, and hydroxides are insoluble except with Group 1 metals and ammonium.
Neutralization, acid + base → salt + water, is a double displacement driven by $H^{+}$ and $OH^{-}$ forming water.

Total & Net Ionic Equations

Formula equation → total ionic equation (dissociate all soluble aqueous ionic compounds) → net ionic equation (cancel spectator ions).
Only (aq) ionic compounds are split into ions; (s), (l), and (g) substances are kept as whole formulas.
Spectator ions appear identically on both sides and are removed in the net ionic equation.
A net ionic equation must be balanced for both atoms and total charge.
The net ionic equation shows only the ions/substances that actually undergo chemical change.

Recognizing Reaction Patterns & Predicting Products

Acid + base → salt + water (neutralization; technically a double displacement).
Acid + metal carbonate → salt + water + CO₂ gas (recognized by fizzing).
Acid + reactive metal (above H) → salt + H₂ gas (a single displacement reaction).
Hydrocarbon + O₂ → combustion products (CO₂/H₂O if excess O₂; CO or soot/H₂O if limited O₂).
General strategy: identify reactant types, match to a known pattern, predict products, check states, then balance.

Unit 3: Quantities in Chemical Reactions

Significant Figures & Unit Analysis

Multiplication/division: round the answer to the same number of sig figs as the measurement with the fewest sig figs.
Addition/subtraction: round the answer to the same number of decimal places as the measurement with the fewest decimal places.
Zeros between nonzero digits are always significant; leading zeros never are.
Trailing zeros are significant only when a decimal point is present — use scientific notation to remove ambiguity, e.g. $1.5 \times 1 0^{3}$ has 2 sig figs.
Exact numbers (counted items, defined conversions such as $1 m = 100 cm$ ) have unlimited sig figs and never limit an answer.
Carry guard digits through every intermediate step and round only the final answer.

The Mole Concept

$1 mol = 6.022 \times 1 0^{23}$ particles (atoms, molecules, ions, or formula units) — Avogadro's number, $N_{A}$ .
$n = \frac{N}{N _{A}}$ converts a particle count to moles.
$N = n \times N_{A}$ converts moles to a particle count.
The mole is the SI base unit for amount of substance — conceptually identical to "a dozen," just for an enormously larger group size.
$N_{A} \times 1 u = 1 g$ , so a particle's mass in u equals the mass of one mole of those particles in grams.
Atoms or ions inside a compound: moles of that atom = moles of compound × its subscript (e.g. $1 mol CaCl_{2}$ has $2 mol Cl^{-}$ ).

Molar Mass

Molar mass $M$ (g/mol) numerically equals the average atomic mass (amu) from the periodic table, summed for every atom in the formula.
$M (compound) = \sum (number of atoms \times atomic mass)$
A subscript outside a bracket multiplies every atom inside it: $Mg (OH)_{2}$ has 1 Mg, 2 O, and 2 H.
Molar mass always has units of g/mol.
Periodic-table atomic masses are weighted averages of an element's isotopes, which is why they are rarely whole numbers.
Diatomic elements ( $H_{2}, N_{2}, O_{2}, F_{2}, Cl_{2}, Br_{2}, I_{2})$ have double the atomic molar mass, e.g. $M (O_{2}) = 32.00 g/mol$ .

Mass, Moles & Number of Particles

$n = \frac{m}{M}$ — moles from mass, using molar mass.
$m = n \times M$ — mass from moles.
$N = n \times N_{A}$ — particles from moles.
$n = \frac{N}{N _{A}}$ — moles from particles.
Atoms of one element in a compound: moles of that atom = moles of compound × its subscript.
Mass of one particle $= \frac{M}{N _{A}}$ , e.g. one $H_{2} O$ molecule is $2.992 \times 1 0^{- 23} g$ .

Percentage Composition

$% element = \frac{mass of element in 1 mol of compound}{molar mass of compound} \times 100%$
The percentages of every element in a compound always sum to $100%$ (within rounding).
$mass of element in sample = % element \times mass of sample$
Percent composition is fixed for a given compound — it doesn't depend on sample size.
From lab data: $% element = \frac{measured mass of element}{measured mass of compound} \times 100% .$
Law of definite proportions: a pure compound always has the same composition by mass, so percent composition can identify it.

Empirical & Molecular Formulas

Assume a $100 g$ sample so each percent becomes grams directly.
Convert grams of each element to moles using $n = m / M$ .
Divide every mole value by the smallest mole value to get a ratio close to whole numbers.
A ratio ending in $.5$ needs every subscript doubled; $.33$ or $.67$ needs every subscript tripled.
Molecular formula = empirical formula $\times n$ , where $n = \frac{molar mass given}{empirical formula mass} .$
Combustion analysis: $m (C) = m (CO_{2}) \times \frac{12.01}{44.01}$ , $m (H) = m (H_{2} O) \times \frac{2.02}{18.02}$ ; oxygen is found by difference.

Hydrates

A hydrate's formula is $salt \cdot x H_{2} O$ ; the dot means "combined with," not multiplication.
Mass of water lost on heating = mass of hydrate $-$ mass of anhydrous salt remaining.
$x = \frac{mol H _{2} O lost}{mol anhydrous salt},$ rounded to the nearest whole number.
$% H_{2} O = \frac{mass H _{2} O}{mass hydrate} \times 100%$
$M (hydrate) = M (anhydrous salt) + x (18.02 g/mol)$
Water left behind makes $x$ too low; any other mass lost (spattering, decomposition) makes $x$ too high.

Mole Ratios from Balanced Equations

Coefficients in a balanced equation give the mole ratio between any two substances directly.
$mol wanted = mol given \times \frac{coefficient wanted}{coefficient given}$
The equation must be balanced before its coefficients can be trusted as a mole ratio.
Stoichiometry roadmap: given substance $\to$ mol given $\to$ mol wanted $\to$ wanted substance.
Mass is always conserved in a reaction, but the total number of moles is not (e.g. $2 H_{2} + O_{2} \to 2 H_{2} O$ : 3 mol become 2 mol).
Mole ratios apply equally to numbers of particles, since particles are proportional to moles.

Mass-to-Mass Stoichiometry

Roadmap: mass given $\to$ mol given ( $\div M_{given}$ ) $\to$ mol wanted (mole ratio) $\to$ mass wanted ( $\times M_{wanted}$ ).
$n = m / M$ and $m = n \times M$ are used once on each side of the mole-ratio step.
Masses of two different substances can never be compared or scaled directly — only their moles are related by the equation's coefficients.
The chemical equation must be balanced before any of this works.
Check with conservation of mass: total mass of reactants used = total mass of products formed.
Keep extra digits in intermediate values; round only the final answer to the sig figs of the given data.

Limiting & Excess Reagents

Divide each reactant's moles by its own coefficient; the smaller result identifies the limiting reagent.
All product-yield calculations must be based on the limiting reagent, never the excess reagent.
Excess remaining = starting mol of excess reagent $-$ mol of excess reagent consumed (via the mole ratio with the limiting reagent).
The limiting reagent is determined by the required ratio, not simply by which reactant has less starting mass or fewer moles.
After the reaction, the limiting reagent is at zero; mass is conserved, so mass of reactants used = mass of products formed.
Stoichiometric amounts: reactants mixed in exactly the equation's mole ratio, leaving no excess.

Percentage Yield

$% yield = \frac{actual yield}{theoretical yield} \times 100%$
Theoretical yield is calculated from stoichiometry, always based on the limiting reagent.
Actual yield is measured experimentally and is normally less than theoretical due to side reactions, incomplete reactions, or loss during transfer/purification.
A percent yield over 100% signals a measurement or purity error, not an unusually efficient reaction.
Planning: $theoretical needed = \frac{actual wanted}{% yield /100%};$ predicting: $actual = \frac{% yield}{100%} \times theoretical .$
For a multi-step process, overall yield = product of the step yields (as decimals).

Unit 4: Solutions & Solubility

Characteristics of Solutions

Solute = dissolved substance (smaller amount); solvent = dissolving medium (larger amount).
Saturated solution: dissolving and recrystallizing occur at equal rates (dynamic equilibrium).
Supersaturated solutions are unstable and will crystallize out excess solute if disturbed.
Strong electrolytes produce many ions and conduct well; non-electrolytes produce no ions and do not conduct.
Solutions can be gaseous (air), liquid (salt water) or solid (alloys such as brass); miscible liquids mix in all proportions.
Predict conductivity from the formula: soluble ionic compounds and strong acids/bases → strong electrolytes; weak acids and $NH_{3}$ → weak electrolytes; sugars and alcohols → non-electrolytes.

How Dissolving Happens

"Like dissolves like": polar/ionic solutes dissolve in polar solvents; non-polar solutes dissolve in non-polar solvents.
Dissociation: an ionic compound separates into ions that already existed, e.g. $NaCl (s) \to Na^{+} (aq) + Cl^{-} (aq) .$
Ionization: a molecular compound reacts with water to form new ions, e.g. $HCl (g) + H_{2} O (l) \to H_{3} O^{+} (aq) + Cl^{-} (aq) .$
Water is polar because oxygen is more electronegative than hydrogen, giving it a bent shape with $δ^{-}$ at O and $δ^{+}$ at each H.
Hydration is the process of polar water molecules surrounding a freed ion or polar molecule in solution.
Stirring, crushing and heating speed up dissolving; only temperature (and pressure, for gases) changes how much can dissolve.

Solubility Curves

A point ON the solubility curve = saturated; BELOW the curve = unsaturated; ABOVE the curve = supersaturated.
Most solids: solubility increases as temperature increases (though the rate of increase varies a lot between compounds).
Gases: solubility decreases as temperature increases, because faster-moving gas particles escape the liquid more easily.
Mass of solute that crystallizes on cooling = (solubility at higher T − solubility at lower T) scaled to the actual mass of water present.
Scale solubility to the real mass of water: $m_{max} = S \times \frac{m _{water}}{100 g}$ .
Gas solubility increases with pressure — which is why an opened soft drink goes flat.

Concentration

Molar concentration: $c = \frac{n}{V}$ , where $n$ is moles of solute and $V$ is volume of solution in litres.
Rearranged forms: $n = c V$ and $V = \frac{n}{c}$ .
$1 ppm \approx 1 mg solute per L of dilute aqueous solution .$
% w/v = (grams of solute ÷ mL of solution) × 100%, which is simply the grams of solute in every 100 mL of solution.
A standard solution's volume (V) is always the TOTAL solution volume, fixed by a volumetric flask's calibration line — never just the solvent added.
$ppm = \frac{m _{solute}}{m _{solution}} \times 1 0^{6};$ in water 1 ppm ≈ 1 mg/L and 1 ppb ≈ 1 µg/L. Convert mol/L to g/L by multiplying by molar mass.

Dilutions

Dilution equation: $C_{1} V_{1} = C_{2} V_{2}$ (moles of solute are conserved during dilution).
$C_{1}, V_{1}$ = concentration and volume BEFORE dilution (the stock); $C_{2}, V_{2}$ = concentration and volume AFTER dilution.
Diluting always means adding solvent, never adding solute.
Rearranged to solve for any unknown: e.g. $V_{1} = \frac{C _{2} V _{2}}{C _{1}}$ .
Dilution factor $= \frac{V _{2}}{V _{1}} = \frac{C _{1}}{C _{2}}$ ; in a serial dilution the overall factor is the PRODUCT of the step factors.
Mixing two solutions of the same solute: $C_{final} = \frac{C _{a} V _{a} + C _{b} V _{b}}{V _{a} + V _{b}}$ (add moles, divide by total volume).

Ions in Solution & Precipitation Reactions

All Group 1 and NH4+ compounds are soluble; all nitrates and acetates are soluble — no exceptions.
AgCl, PbI2, PbCl2, Hg2Cl2 type halides are insoluble; BaSO4, PbSO4, SrSO4 are insoluble sulfates.
Carbonates, phosphates, hydroxides, and sulfides are generally insoluble (except with Group 1/NH4+).
Total ionic equation: split every aqueous (soluble) compound into ions; keep solids/liquids/gases whole.
Net ionic equation: cancel spectator ions (identical ions unchanged on both sides) from the total ionic equation.

Qualitative Analysis: Identifying Unknown Ions

Selective precipitation: choose a reagent that precipitates only some possible ions, narrowing down the unknown.
Flame test colours: Li+ = crimson red, Na+ = bright yellow, K+ = lilac, Ca2+ = orange-red, Sr2+ = red, Ba2+ = pale green, Cu2+ = blue-green.
Flame colour arises from electrons absorbing heat energy then releasing it as light of specific wavelengths on falling back down.
A single test is rarely conclusive — combine flame tests, selective precipitation, and solubility rules for confident identification.
In a separation scheme, add the MOST selective reagent first (e.g. Cl- before SO4 2- before OH-) and filter after each step.
Anion tests: Cl- + Ag+ → white AgCl; SO4 2- + Ba2+ → white BaSO4; CO3 2- + acid → CO2 bubbles that turn limewater milky. Cu2+ solutions are blue.

Solution Stoichiometry

First step for any solution stoichiometry problem: $n = c V$ to get moles from concentration and volume.
Mole ratio comes from the coefficients of the balanced chemical equation.
Limiting reagent = whichever reactant produces the LESS product when each is assumed to react completely.
Excess reagent's leftover amount = initial moles − moles actually consumed (found using the mole ratio with the limiting reagent).
To find an unknown concentration, get moles of the unknown from the reaction, then $c = \frac{n}{V}$ using the volume of the unknown sample.
After two solutions are mixed, concentrations of leftover ions use the TOTAL volume $V_{1} + V_{2}$ .

Properties & Naming of Acids and Bases

Acids: sour, turn litmus red, react with metals/carbonates, conduct electricity.
Bases: bitter, slippery, turn litmus blue, conduct electricity.
Binary acid naming: hydro- + nonmetal root + -ic acid (e.g. HCl = hydrochloric acid).
Oxyacid naming: -ate ion → -ic acid; -ite ion → -ous acid (e.g. sulfate → sulfuric acid, sulfite → sulfurous acid).
Bases (metal hydroxides) are named like standard ionic compounds: metal name + hydroxide.
In an acid formula, the number of H atoms equals the size of the anion's charge (sulfate $SO_{4}^{2 -}$ → $H_{2} SO_{4}$ ); acid names apply to the (aq) solution.

Arrhenius Theory of Acids and Bases

Arrhenius acid: produces H+(aq) / H3O+(aq) in water. Arrhenius base: produces OH-(aq) in water.
Bases (ionic hydroxides) dissociate: existing OH- ions separate from the solid lattice.
Acids (molecular) ionize: they react with water to form new H3O+ ions.
Strong acid/base = ionizes/dissociates (nearly) completely. Weak acid/base = only partially ionizes/dissociates.
Strong/weak (degree of ionization) is completely independent from concentrated/dilute (amount of solute present).

The pH Scale

$pH = - lo g [H^{+}]$ and $pOH = - lo g [OH^{-}]$ .
$pH + pOH = 14$ at 25°C (from $K_{w} = [H^{+}] [OH^{-}] = 1.0 \times 1 0^{- 14}).$
$[H^{+}] = 1 0^{- pH}$ — use this to reverse a pH value back into a concentration.
pH < 7 acidic, pH = 7 neutral, pH > 7 basic (at 25°C).
Each 1-unit drop in pH means a 10× increase in [H+].

Titration

Neutralization: acid + base → salt + water.
Equivalence point = the theoretical stoichiometric match point (moles acid = moles base, scaled by mole ratio); endpoint = the observed indicator colour change.
A well-chosen indicator makes the endpoint occur very close to the equivalence point.
Core calculation: $n_{a c i d} = c_{a c i d} V_{a c i d}$ , then apply the mole ratio, then solve for the unknown $c$ or $V$ .
Phenolphthalein: colourless below ~pH 8.2, pink above ~pH 10. Litmus: red below ~pH 4.5, blue above ~pH 8.3.

Unit 5: Gases & Atmospheric Chemistry

States of Matter & the Kinetic Molecular Theory

KMT postulate: particles are in constant, random, straight-line motion.
KMT postulate: particle volume is negligible compared to the container's volume.
KMT postulate: no attractive/repulsive forces act between ideal gas particles.
KMT postulate: collisions are perfectly elastic (no net kinetic energy lost).
KMT postulate: average kinetic energy $\propto$ absolute (Kelvin) temperature.

Pressure, Temperature, and the Kelvin Scale

$1 atm = 101.325 kPa = 760 mmHg = 760 torr$
$T (K) = T (° C) + 273.15$ (or $+ 273$ for typical sig figs)
Gas pressure results from particle collisions with container walls: $P = F / A$ .
Kelvin is the only valid temperature scale for gas law ratios/proportions — 0 K corresponds to minimum particle motion, with no negative values.
Gauges read pressure above the atmosphere: $P_{absolute} = P_{gauge} + P_{atmosphere} .$ Gas laws always use absolute pressure.

Boyle's, Charles's, and Gay-Lussac's Laws

Boyle's law: $P_{1} V_{1} = P_{2} V_{2}$ at constant $T, n$ (inverse relationship).
Charles's law: $\frac{V _{1}}{T _{1}} = \frac{V _{2}}{T _{2}}$ at constant $P, n$ (direct relationship, $T$ in Kelvin).
Gay-Lussac's law: $\frac{P _{1}}{T _{1}} = \frac{P _{2}}{T _{2}}$ at constant $V, n$ (direct relationship, $T$ in Kelvin).
$P$ vs. $V$ graphs (Boyle's law) are hyperbolas; $P$ vs. $1/ V$ is linear.
$V$ vs. $T$ (K) and $P$ vs. $T$ (K) graphs are straight lines through the origin.

The Combined Gas Law

Combined gas law: $\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$ (constant $n$ ).
Reduces to Boyle's law when $T$ is constant, Charles's law when $P$ is constant, Gay-Lussac's law when $V$ is constant.
Always convert temperature to Kelvin before substituting.
$P_{1}, P_{2}$ must share units; $V_{1}, V_{2}$ must share units (any consistent pair works).
Correction-factor check: $V_{2} = V_{1} \times \frac{P _{1}}{P _{2}} \times \frac{T _{2}}{T _{1}}$ . Each ratio should be above 1 if that change makes the gas expand and below 1 if it squeezes it.

The Ideal Gas Law

$P V = n RT$
$R = 8.314 kPa \cdot L / (mol \cdot K)$ (use with $P$ in kPa, $V$ in L, $T$ in K)
Rearranged forms: $P = n RT / V$ , $V = n RT / P$ , $n = P V / (RT)$ , $T = P V / (n R)$
Ideal behaviour is best approximated at low pressure and high temperature.
Real gases deviate from ideal at high pressure (particle volume matters) and low temperature (intermolecular forces matter).

Molar Volume: STP and SATP

STP: 0°C (273.15 K), 101.325 kPa, $V_{m} = 22.4$ L/mol.
SATP: 25°C (298.15 K), 100.0 kPa, $V_{m} = 24.8$ L/mol.
STP and SATP are different standards — do not interchange their molar volumes.
Avogadro's law: equal volumes of gas at the same $T, P$ contain equal moles, regardless of gas identity.
$n = V / V_{m}$ and $V = n \times V_{m}$ — valid only exactly at STP or SATP.

Gas Stoichiometry

Gas stoichiometry road map: given quantity → moles (molar mass, molar volume, or ideal gas law) → mole ratio → moles of target → target quantity.
Use $V_{m}$ = 22.4 L/mol (STP) or 24.8 L/mol (SATP) only when the gas is exactly at that standard condition.
Use $n = P V / (RT)$ for gases at non-standard conditions.
For two gases at the SAME $T, P$ , their volume ratio equals their mole ratio (from the balanced equation's coefficients), by Avogadro's law.
Dalton's law: $P_{total} = P_{1} + P_{2} + \dots$ ; for a gas collected over water, $P_{gas} = P_{atm} - P_{H_{2} O}$ .

Atmospheric Chemistry

Dry air composition (by volume): $N_{2} \approx 78.08%$ , $O_{2} \approx 20.95%$ , Ar $\approx 0.93%$ , $CO_{2} \approx 0.04%$ (≈420 ppm, rising).
Greenhouse gases ( $CO_{2}$ , $CH_{4}$ , $H_{2} O$ (g)) absorb and re-radiate infrared energy, warming the lower atmosphere.
Stratospheric ozone ( $O_{3}$ ) absorbs harmful UV radiation; CFCs catalytically destroy this protective ozone layer.
Acid rain forms when $SO_{2}$ / $NO_{x}$ from fossil fuel combustion react with atmospheric water to form sulfuric/nitric acid.
Ground-level ozone and particulate matter (from vehicle/industrial emissions) cause smog; the AQHI summarizes public health risk from air pollution.