Chemistry Formulas Cheat Sheet: Moles, Concentration, Acids, and Equilibrium

Overview

Formula questions become easier when you identify the quantity being asked for before choosing an equation. Start by writing down the known values, convert units where necessary, substitute carefully, and then check whether the answer is chemically sensible. A formula sheet is most useful as a decision tool, not as a list to memorize without context.

Keep these habits in mind:

• Write the chemical equation and balance it before using mole ratios.
• Use a consistent unit system, especially for volume and concentration.
• Keep extra digits during working and round only at the end.
• Include units in every line of a calculation, then check the final unit.
• Distinguish between mass concentration, amount concentration, and the mass of a solute.

For broader planning, combine this reference with a science exam revision planner. For additional problem-solving practice, see the step-by-step guide to molarity and dilution problems.

Checklist by scenario

1. Moles and particle calculations

The mole connects measurable quantities, such as mass, with the number of particles in a sample.

Amount from mass:

n = m / M

• n = amount of substance in mol
• m = mass in g
• M = molar mass in g mol⁻¹

Example: What amount of calcium carbonate is in 10.0 g? The molar mass of CaCO₃ is approximately 100.1 g mol⁻¹.

n = 10.0 g ÷ 100.1 g mol⁻¹ = 0.0999 mol, which may be reported as 0.100 mol depending on the required significant figures.

Particles from moles:

N = nN_A, where N is the number of particles and N_A is Avogadro's constant, approximately 6.02 × 10²³ mol⁻¹. Confirm which particles are requested: atoms, molecules, ions, or formula units.

Checklist: calculate molar mass from the correct chemical formula; use grams, not kilograms, unless you convert; and label whether the result refers to molecules or atoms.

2. Stoichiometry and reacting quantities

For a balanced equation, the coefficients give mole ratios. For example:

2H₂ + O₂ → 2H₂O

Two moles of hydrogen react with one mole of oxygen to produce two moles of water. To solve a mass-to-mass problem:

1. Convert the known mass to moles using n = m / M.
2. Apply the coefficient ratio from the balanced equation.
3. Convert the resulting moles into the requested unit.

Do not compare masses directly using equation coefficients. Coefficients describe amounts in moles, not grams.

3. Concentration and dilution

Molar concentration:

c = n / V

• c = concentration in mol dm⁻³ or mol L⁻¹
• n = amount in mol
• V = volume in dm³ or L

Because 1 dm³ equals 1 L, these concentration units are numerically equivalent. However, 100 cm³ equals 0.100 dm³, not 100 dm³.

Example: A solution contains 0.0500 mol of solute in 250 cm³. Convert the volume: 250 cm³ = 0.250 dm³. Then c = 0.0500 ÷ 0.250 = 0.200 mol dm⁻³.

Dilution:

c₁V₁ = c₂V₂

This works when the amount of dissolved solute stays constant. Use matching volume units on both sides. If a solution is diluted from 1.00 mol dm⁻³ to 0.200 mol dm⁻³ and the final volume is 500 cm³, then V₁ = (0.200 × 500) ÷ 1.00 = 100 cm³. The remaining volume is made up with solvent.

4. Acids, bases, and pH

pH:

pH = −log₁₀[H⁺]

Here, [H⁺] is the hydrogen ion concentration, usually expressed in mol dm⁻³. If [H⁺] = 1.0 × 10⁻³ mol dm⁻³, pH = 3.00.

pOH:

pOH = −log₁₀[OH⁻]

At the commonly used reference temperature of 25°C, pH + pOH = 14.00. If a course uses a different temperature or convention, follow the value specified in the question.

Acid dissociation constant:

For HA ⇌ H⁺ + A⁻,

K_a = [H⁺][A⁻] / [HA]

For a base equilibrium, the corresponding expression is:

K_b = [BH⁺][OH⁻] / [B]

Use equilibrium concentrations, not initial concentrations, in the final expression unless the question specifically asks for an approximation or gives an assumption. Water and pure solids are not normally included in an equilibrium expression.

5. Equilibrium calculations

For a general reaction aA + bB ⇌ cC + dD, the concentration equilibrium constant is:

K_c = [C]^c[D]^d / [A]^a[B]^b

The balanced equation supplies the powers. A coefficient of 2 becomes a squared concentration; it is not multiplied outside the brackets. K_c has no units in some exam conventions, although the numerical expression may appear to produce units depending on the reaction and course framework. Use the convention required by your specification.

Checklist: balance the equation first; write the products in the numerator; apply coefficients as powers; omit pure solids and liquids; and use equilibrium values consistently.

What to double-check

• Volume conversion: convert cm³ to dm³ by dividing by 1,000 when using mol dm⁻³.
• Molar mass: count every atom, including brackets and subscript numbers.
• Equation balance: never use mole ratios from an unbalanced equation.
• Logarithms: enter negative powers correctly and check whether the answer should be acidic, neutral, or alkaline.
• Significant figures: match the precision of the data rather than reporting unjustified decimal places.
• State symbols and phases: check whether a substance is aqueous, gaseous, solid, or liquid before writing an equilibrium expression.
• Temperature and pressure: gas-law questions require absolute temperature in kelvin, not degrees Celsius. For an ideal gas, use PV = nRT with units that match the value of R provided or expected.

When a calculation feels unclear, write the units beside each quantity. Units often reveal whether the wrong rearrangement or conversion has been used.

Common mistakes

Using mass ratios instead of mole ratios: balanced coefficients compare particles or moles. Convert to moles before applying them.

Forgetting the final dilution volume: c = n/V uses the total volume of the solution, not just the volume of solvent added.

Confusing strong and concentrated: strength describes how completely an acid or base ionizes; concentration describes how much solute is present per volume. They are not interchangeable.

Including solids in K_c: pure solids and liquids are generally omitted because their effective concentrations are treated as constant.

Rounding too early: early rounding can change a titration, pH, or equilibrium result. Keep a few extra digits until the final answer.

Memorizing without explaining: In an exam, define the symbols, show substitutions, and include units. Clear working can expose an error and make partial reasoning easier to follow. For a wider approach to chemistry revision, read how to study chemistry without memorizing everything.

When to revisit

Return to this chemistry formulas cheat sheet before starting a new topic, beginning a timed practice set, or reviewing mistakes from a marked assignment. Revisit the concentration and dilution section before practical work or titration questions, and review acids and equilibrium before an assessment that includes logarithms or ICE-table style calculations.

Use this short pre-exam checklist:

1. Write the formulas you are expected to use from memory, then compare them with this reference.
2. Complete one problem each on moles, stoichiometry, concentration, dilution, pH, and equilibrium.
3. Mark every unit conversion and equation-balance error separately.
4. Redo incorrect questions without looking at the worked solution.
5. Build a one-page personal formula sheet using the notation and units used in your course.

Update your personal notes whenever your class introduces a new convention, such as a different equilibrium notation or required number of significant figures. The formulas remain useful, but the expected presentation can vary between courses and exam specifications.