Toolbox

Molar mass calculator

Type a formula to see its molar mass and where it comes from.

Formula sheet

• Moles and particles

  $N = n \times N_A$

  N = number of particles, n = moles, Nᴀ = 6.02 × 10²³ per mole

• Moles and mass

  $n = \dfrac{m}{M}$

  n = moles (mol), m = mass (g), M = molar mass (g/mol)

• Percent composition

  $\%\,\text{element} = \dfrac{\text{mass of element}}{\text{mass of compound}} \times 100\%$

  Use the masses in one mole, or the masses measured in a sample.

• Molecular formula

  $n = \dfrac{M_{\text{molecular}}}{M_{\text{empirical}}}$

  Multiply every subscript in the empirical formula by n.

• Mole ratio

  $n_{\text{wanted}} = n_{\text{given}} \times \dfrac{\text{coefficient wanted}}{\text{coefficient given}}$

  Coefficients come from the balanced equation.

• Percent yield

  $\%\,\text{yield} = \dfrac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$

  Actual is measured in the lab; theoretical is calculated.

• Celsius to kelvin

  $T_{\text{K}} = T_{^\circ\text{C}} + 273.15$

  Gas law calculations always use kelvin.

• Percent error

  $\%\,\text{error} = \dfrac{|\text{experimental} - \text{accepted}|}{\text{accepted}} \times 100\%$

  Measures accuracy. Smaller is better.

• Molar concentration

  $c = \dfrac{n}{V}$

  c = concentration (mol/L), n = moles (mol), V = volume of solution (L)

• Percent mass/volume

  $\%\,\text{m/v} = \dfrac{m_{\text{solute}}\ (\text{g})}{V_{\text{solution}}\ (\text{mL})} \times 100\%$

  Grams of solute per 100 mL of solution.

• Dilution

  $c_1 V_1 = c_2 V_2$

  Moles of solute stay the same when you add water. V₁ and V₂ just need the same units.

• pH

  $\text{pH} = -\log[\text{H}^+] \qquad [\text{H}^+] = 10^{-\text{pH}}$

  [H⁺] in mol/L. Each pH unit is a factor of 10.

• Combined gas law

  $\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}$

  T in kelvin. Hold one quantity constant to get Boyle's, Charles's or Gay-Lussac's law.

• Ideal gas law

  $PV = nRT$

  P in kPa, V in L, n in mol, T in K, R = 8.314 kPa·L/(mol·K)

• Molar volume

  $n = \dfrac{V}{V_m}$

  Vₘ = 22.4 L/mol at STP (0 °C, 101.325 kPa); 24.8 L/mol at SATP (25 °C, 100 kPa)

• Dalton's law

  $P_{\text{total}} = P_1 + P_2 + P_3 + \dots$

  Over water, subtract water vapour pressure to find the gas's pressure.

• Light and photonsPre-AP

  $c = \lambda\nu \qquad E = h\nu$

  c = 3.00 × 10⁸ m/s, h = 6.63 × 10⁻³⁴ J·s. Wavelength in metres.

• Formal chargePre-AP

  $\text{FC} = \text{valence e}^- - \text{lone-pair e}^- - \text{bonds}$

  The best Lewis structure has formal charges closest to zero.

• Heat (calorimetry)Pre-AP

  $q = mc\Delta T \qquad \Delta H = \dfrac{q}{n}$

  c of water = 4.18 J/(g·°C). ΔH is negative when heat is released.

• pOH and KwPre-AP

  $\text{pOH} = -\log[\text{OH}^-] \qquad \text{pH} + \text{pOH} = 14.00 \qquad K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}$

  At 25 °C.

• Equilibrium constantPre-AP

  $K = \dfrac{[C]^c[D]^d}{[A]^a[B]^b}$

  For aA + bB ⇌ cC + dD. Leave out pure solids and liquids.

• Gas densityPre-AP

  $d = \dfrac{PM}{RT}$

  d in g/L. At STP, d = M ÷ 22.4.

• Graham's lawPre-AP

  $\dfrac{\text{rate}_1}{\text{rate}_2} = \sqrt{\dfrac{M_2}{M_1}}$

  Lighter gases effuse faster.

• Constants

  Avogadro's number: Nᴀ = 6.02 × 10²³ per mole

Common atomic masses

In g/mol, rounded to two decimals as on your periodic table.

• 1H1.01
• 6C12.01
• 7N14.01
• 8O16.00
• 11Na22.99
• 12Mg24.31
• 13Al26.98
• 16S32.07
• 17Cl35.45
• 19K39.10
• 20Ca40.08
• 26Fe55.85
• 29Cu63.55
• 30Zn65.38
• 47Ag107.87
• 56Ba137.33

Glossary

absolute zero

0 K, or −273.15 °C — the lowest possible temperature, where particles have the least possible motion.

accuracy

How close a measurement is to the accepted value.

acid

A compound that produces hydrogen ions, H⁺, when dissolved in water. Acids taste sour and turn blue litmus red.

acid rain

Rain made acidic by sulfur and nitrogen oxides from burning fuels and smelting.

acidic oxide

A non-metal oxide. It reacts with water to form an acid.

activation energy

The energy needed to start a reaction — the hump on an energy diagram.

activity series

A list of metals from most to least reactive. A metal can replace any metal below it in a compound.

actual yield

The amount of product you really collect in the lab.

alkali metals

The very reactive metals in group 1, such as sodium and potassium.

amphiprotic

Able to act as an acid or a base, like H₂O and HCO₃⁻.

anion

A negative ion, formed when an atom gains electrons. Non-metals form anions.

aqueous (aq)

Dissolved in water.

atomic mass

The average mass of one atom of an element, shown on the periodic table. In g/mol it is also the molar mass of that element.

atomic number (Z)

The number of protons in an atom. It decides which element the atom is.

atomic radius

The size of an atom, measured from the nucleus to the outer electrons.

Aufbau principle

Electrons fill the lowest-energy sublevels first — 1s, 2s, 2p, 3s, 3p, 4s, 3d, and so on.

Avogadro's hypothesis

Equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

Avogadro's number (Nᴀ)

6.02 × 10²³ — the number of particles in one mole.

base

A compound that produces hydroxide ions, OH⁻, in water. Bases taste bitter, feel slippery and turn red litmus blue.

basic oxide

A metal oxide. It reacts with water to form a base.

binary compound

A compound made of exactly two elements, like NaCl or CO₂.

Bohr–Rutherford diagram

A drawing of an atom showing the protons and neutrons in the nucleus and the electrons in each shell.

bonding capacity

The number of covalent bonds an atom usually forms — enough to reach 8 valence electrons (2 for hydrogen).

Boyle's law

At constant temperature, a gas's volume is inversely proportional to its pressure. P₁V₁ = P₂V₂.

Brønsted–Lowry theory

An acid is a proton (H⁺) donor; a base is a proton acceptor.

cation

A positive ion, formed when an atom loses electrons. Metals form cations.

Charles's law

At constant pressure, a gas's volume is directly proportional to its kelvin temperature. V₁/T₁ = V₂/T₂.

chemical reaction

A change in which substances rearrange their atoms to form new substances.

coefficient

The big number in front of a formula in a balanced equation. It tells you how many moles react or form.

combined gas law

P₁V₁/T₁ = P₂V₂/T₂, for a fixed amount of gas when pressure, volume and temperature can all change.

combustion

A fast reaction of a substance with oxygen that releases heat and light.

combustion analysis

Finding a compound's empirical formula by burning it and weighing the CO₂ and H₂O produced.

concentration

The amount of solute in a given volume of solution, often in mol/L.

conjugate acid–base pair

Two species that differ by exactly one H⁺, like HCl and Cl⁻.

controlled variable

A variable you keep the same so the test is fair.

conversion factor

A fraction equal to 1, like 1 L / 1000 mL, used to change units without changing the amount.

covalent bond

A pair of electrons shared between two non-metal atoms.

crystal lattice

The repeating 3-D pattern of ions in an ionic solid.

Dalton's law of partial pressures

The total pressure of a gas mixture equals the sum of the partial pressures of its gases.

decomposition reaction

One compound breaks down into two or more simpler substances. AB → A + B.

delocalized electrons

Electrons not tied to one atom, free to move through a structure — like the "sea of electrons" in a metal.

dependent variable

The variable you measure to see the effect of the change.

diatomic molecule

A molecule of two atoms. The diatomic elements are H₂, N₂, O₂, F₂, Cl₂, Br₂ and I₂.

diffusion

A gas spreading out and mixing with another gas.

dipole–dipole force

The attraction between the δ+ end of one polar molecule and the δ− end of another.

dissociation

The separation of an ionic compound into its ions as it dissolves.

double displacement reaction

Two ionic compounds swap ions. AB + CD → AD + CB.

dynamic equilibrium

The state where forward and reverse reactions run at the same rate, so amounts stay constant.

effective nuclear charge

The pull of the nucleus that an atom's outer electrons actually feel, after inner electrons shield some of it.

effusion

A gas escaping through a tiny hole.

electrolyte

A substance that forms ions in water, so its solution conducts electricity.

electron

A tiny particle with a −1 charge that moves around the nucleus. Its mass is almost zero.

electron affinity

The energy released when an atom gains an electron. A larger value means a stronger attraction for an extra electron.

electronegativity

How strongly an atom attracts the shared electrons in a bond. Fluorine is highest at 3.98.

empirical formula

The simplest whole-number ratio of atoms in a compound. CH₂O is the empirical formula of glucose.

endothermic

Absorbing heat from the surroundings. ΔH is positive.

energy level (shell)

A region around the nucleus where electrons are found. For the first 20 elements the shells hold 2, 8, 8 and 2 electrons.

enthalpy change (ΔH)

The heat released or absorbed by a reaction at constant pressure.

equivalence point

The point in a titration where the reactants have been added in exactly the ratio of the balanced equation.

excess reagent

The reactant left over when the limiting reagent is used up.

exothermic

Releasing heat to the surroundings. ΔH is negative.

formal charge

Valence electrons minus lone-pair electrons minus bonds. Used to pick the best Lewis structure.

formula unit

The smallest repeating group in an ionic compound, like one Na⁺ with one Cl⁻ in NaCl.

frequency (ν)

How many wave peaks pass a point each second, in hertz (Hz).

Gay-Lussac's law

At constant volume, a gas's pressure is directly proportional to its kelvin temperature. P₁/T₁ = P₂/T₂.

Graham's law

Rate of effusion is inversely proportional to the square root of molar mass.

group

A column of the periodic table. Elements in a group have the same number of valence electrons and similar properties.

halogens

The very reactive non-metals in group 17, such as fluorine and chlorine.

hard water

Water containing dissolved calcium and magnesium ions.

hydrate

An ionic compound with water molecules held in its crystals, like CuSO₄·5H₂O.

hydrocarbon

A compound made only of hydrogen and carbon, like methane, CH₄.

hydrogen bonding

A strong dipole–dipole attraction between molecules where H is bonded to N, O or F.

hydronium ion

H₃O⁺, a water molecule carrying an extra proton. H⁺(aq) is shorthand for it.

ideal gas

An imaginary gas that follows the kinetic molecular theory exactly. Real gases behave almost ideally at normal conditions.

ideal gas law

PV = nRT, with R = 8.314 kPa·L/(mol·K).

independent variable

The variable you change on purpose in an investigation.

indicator

A substance that changes colour depending on whether a solution is acidic or basic, like litmus.

intermolecular force

An attraction between separate molecules. Much weaker than a covalent bond.

ion

An atom or group of atoms that has gained or lost electrons, so it has a charge.

ion product of water (Kw)

[H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C.

ionic bond

The attraction between positive and negative ions, formed when a metal transfers electrons to a non-metal.

ionization

The formation of ions when a molecular substance, such as an acid, reacts with water.

ionization energy

The energy needed to remove an electron from an atom.

isotope

Atoms of the same element with different numbers of neutrons, like chlorine-35 and chlorine-37.

isotopic abundance

The percentage of an element's atoms that are a particular isotope.

IUPAC

The International Union of Pure and Applied Chemistry, which sets the official rules for naming compounds.

kelvin (K)

The SI temperature scale. It starts at absolute zero. K = °C + 273.15.

kinetic molecular theory

A model of gases as tiny particles in constant, random motion, with no attractions, whose average energy depends on temperature.

law of conservation of mass

In a chemical reaction, the total mass of the products equals the total mass of the reactants.

law of definite proportions

A compound always contains the same elements in the same proportions by mass.

Le Châtelier's principle

A system at equilibrium shifts to partly undo any change made to it.

Lewis dot diagram

An element's symbol surrounded by dots, one for each valence electron.

Lewis structure

A diagram of a molecule showing bonds as lines and lone pairs as dots.

limiting reagent

The reactant that runs out first. It decides how much product can form.

line spectrum

The set of specific colours an element gives off when its electrons drop between energy levels. Each element's is unique.

London dispersion force

A weak, brief attraction between all molecules. It's stronger for bigger molecules.

lone pair

A pair of valence electrons that is not shared in a bond.

mass number (A)

The number of protons plus neutrons in an atom's nucleus.

Maxwell–Boltzmann distribution

A graph of how many gas particles have each speed at a given temperature.

metric prefix

A word part in front of a unit that multiplies it, like kilo- (× 1000) or milli- (× 0.001).

molar mass (M)

The mass of one mole of a substance, in g/mol. Add up the atomic masses in the formula.

molar volume

The volume of one mole of a gas — 22.4 L/mol at STP and 24.8 L/mol at SATP.

mole (mol)

A counting unit for particles. One mole is 6.02 × 10²³ particles, the way one dozen is 12.

mole ratio

The ratio of coefficients between two substances in a balanced equation, such as 2 mol H₂ : 1 mol O₂.

molecular formula

The actual number of each atom in one molecule. C₆H₁₂O₆ for glucose.

molecule

A group of atoms joined by covalent bonds, like H₂O.

multivalent metal

A metal that can form ions with different charges, like iron (Fe²⁺ and Fe³⁺).

net ionic equation

An equation showing only the ions and substances that actually change in a reaction.

neutralization

The reaction of an acid with a base to form a salt and water.

neutron

A particle in the nucleus with no charge and a mass of about 1 u.

noble gases

The unreactive gases in group 18, which have a full outer shell.

nucleus

The tiny, dense centre of an atom, made of protons and neutrons.

orbital

A region around the nucleus where up to two electrons are likely to be found. s, p, d and f sublevels have 1, 3, 5 and 7 orbitals.

oxidation

Losing electrons. The oxidation number goes up.

oxidation number

A number tracking an atom's electrons, as if every bond were ionic. Used to spot oxidation and reduction.

oxidizing agent

The substance that is reduced, taking electrons from another substance. The one that is oxidized is the reducing agent.

partial charge (δ+ / δ−)

A small charge on the end of a polar bond. The atom with higher electronegativity is δ−.

partial pressure

The pressure one gas in a mixture would exert if it were alone.

particle

Whatever you are counting — an atom, a molecule, an ion or a formula unit. Always say which.

parts per million (ppm)

A unit for very small concentrations. In water, 1 ppm = 1 mg/L.

percent composition

The percentage of a compound's mass that comes from each element.

percent error

How far a result is from the accepted value, as a percentage of the accepted value.

percent uncertainty

The uncertainty divided by the measurement, × 100%.

percent yield

Actual yield ÷ theoretical yield × 100%. How close the experiment came to the calculation.

period

A row of the periodic table. Elements in the same period have the same number of electron shells.

periodic law

When elements are arranged by atomic number, their properties repeat in a regular pattern.

pH

A scale from about 0 to 14 for how acidic or basic a solution is. Below 7 is acidic, 7 is neutral, above 7 is basic.

photon

A packet of light energy. Its energy is E = hν.

pictogram

A hazard symbol in a red diamond on a WHMIS label.

polar covalent bond

A covalent bond where electrons are shared unequally because the atoms have different electronegativities.

polar molecule

A molecule with a slightly negative side and a slightly positive side, like H₂O.

polyatomic ion

A group of atoms bonded together that has an overall charge, like NO₃⁻ or NH₄⁺.

precipitate

An insoluble solid that forms when two solutions are mixed.

precision

How finely a measurement was made. 2.00 g is more precise than 2 g.

pressure

Force per unit area. For gases, it comes from particles hitting the walls of their container. Measured in kPa.

product

A substance formed in a chemical reaction, written on the right of the arrow.

proton

A particle in the nucleus with a +1 charge and a mass of about 1 u.

qualitative analysis

Identifying which ions are in a sample, using tests like precipitation and flame colours.

qualitative observation

A description without numbers, like a colour change or bubbles forming.

quantitative observation

A measurement with a number and a unit, like 2.31 g.

radioisotope

An isotope with an unstable nucleus that breaks down and gives off radiation.

reactant

A substance you start with in a chemical reaction, written on the left of the arrow.

reduction

Gaining electrons. The oxidation number goes down.

resonance structures

Two or more valid Lewis structures for one molecule or ion. The real structure is a blend of them.

reversible reaction

A reaction that can run in both directions, written with ⇌.

safety data sheet (SDS)

A document that comes with a chemical and explains its hazards, safe handling, first aid and spill clean-up.

salt

An ionic compound formed from the positive ion of a base and the negative ion of an acid.

SATP

Standard ambient temperature and pressure — 25 °C (298.15 K) and 100 kPa. Molar volume is 24.8 L/mol.

saturated solution

A solution holding the maximum amount of solute at that temperature.

scientific notation

Writing a number as a × 10ⁿ, where a is between 1 and 10. Example 6.02 × 10²³.

significant figures

The digits in a measurement that carry real meaning about its precision — all the certain digits plus one estimated digit.

single displacement reaction

An element replaces another element in a compound. A + BC → AC + B.

skeleton equation

A chemical equation written with formulas but not yet balanced.

solubility

The maximum amount of solute that dissolves in a given amount of solvent at a given temperature.

solute

The substance that gets dissolved in a solution.

solution

A uniform mixture of two or more substances, like salt dissolved in water.

solvent

The substance that does the dissolving. In aqueous solutions, it's water.

spectator ion

An ion that is present in a reaction but doesn't change. It appears on both sides of a total ionic equation.

standard solution

A solution whose concentration is known precisely.

stoichiometry

Using a balanced equation to calculate amounts of reactants and products.

STP

Standard temperature and pressure — 0 °C (273.15 K) and 101.325 kPa. Molar volume is 22.4 L/mol.

strong acid

An acid that ionizes completely in water, like HCl.

structural formula

A diagram showing which atoms are bonded to which, with each bond drawn as a line.

supersaturated solution

An unstable solution holding more solute than its normal maximum.

synthesis reaction

Two or more simple substances combine to form one compound. A + B → AB.

theoretical yield

The amount of product you calculate should form, using stoichiometry.

titrant

The solution of known concentration added from the burette in a titration.

titration

A lab method that finds an unknown concentration by reacting it with a measured volume of a solution of known concentration.

total ionic equation

An equation that shows all dissolved ionic compounds as separate ions.

uncertainty

The range a measurement could reasonably be off by, written with ±.

unsaturated solution

A solution holding less solute than the maximum. More can still dissolve.

valence electron

An electron in the outermost shell of an atom. Valence electrons take part in bonding.

vapour pressure

The pressure of a vapour above its liquid in a closed container. Weaker intermolecular forces give higher vapour pressure.

VSEPR theory

Valence-shell electron-pair repulsion — electron groups around a central atom spread as far apart as possible, setting the molecule's shape.

wavelength (λ)

The distance from one wave peak to the next. For visible light, about 400–700 nm.

weak acid

An acid that only partly ionizes in water, like acetic acid.

WHMIS

Workplace Hazardous Materials Information System — Canada's system of labels, pictograms and safety data sheets for hazardous products.