Chemistry is a quantitative science that relies heavily on mathematical expressions and equations to describe various phenomena and relationships between different chemical entities. These key formulas and equations provide a quick reference for essential concepts in chemistry, aiding in calculations, problem-solving, and understanding fundamental principles. Here, we present a compilation of some of the most important and commonly used formulas and equations across different branches of chemistry.

1. General Chemistry Formulas:

a. Mass-Volume Relationships (Density):

Density (ρ) = Mass (m) / Volume (V)

b. Mole Concept:

Number of moles (n) = Mass (m) / Molar mass (M)

Number of particles (N) = Number of moles (n) * Avogadro’s number (6.022 x 10^23)

c. Ideal Gas Law:

PV = nRT

where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (8.314 J/(mol*K)), and T is the temperature in Kelvin.

d. Stoichiometry:

Coefficients in a balanced chemical equation represent the mole ratios of reactants and products.

2. Thermodynamics and Energetics Formulas:

a. Enthalpy Change (ΔH) for a Reaction:

ΔH = ΣH(products) – ΣH(reactants)

b. Gibbs Free Energy Change (ΔG) for a Reaction:

ΔG = ΔH – TΔS

where ΔS is the change in entropy.

c. Hess’s Law:

The total enthalpy change of a reaction is independent of the pathway taken.

3. Acid-Base Equilibria Formulas:

a. pH and pOH:

pH = -log[H+]

pOH = -log[OH-]

b. Acid Dissociation Constant (Ka) and Base Dissociation Constant (Kb):

Ka = [H+][A-] / [HA]

Kb = [OH-][BH+] / [B]

c. pH of Strong Acid or Base Solutions:

pH of strong acid = -log[acid concentration]

pH of strong base = 14 + log[base concentration]

4. Electrochemistry Formulas:

a. Nernst Equation:

Ecell = E°cell – (RT / nF) * ln(Q)

where E°cell is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday’s constant (96,485 C/mol), and Q is the reaction quotient.

b. Faraday’s Law of Electrolysis:

Amount of substance (in moles) = (Electric charge (in Coulombs) / Faraday’s constant) * (Molar mass)

5. Organic Chemistry Formulas:

a. Nomenclature:

Naming conventions for different functional groups, such as alkanes, alkenes, alkynes, alcohols, etc.

b. Isomerism:

Different types of isomers, including structural isomers, geometric isomers (cis-trans isomers), and enantiomers.

c. Reaction Mechanisms:

Mechanisms of organic reactions, such as addition, elimination, substitution, and rearrangement reactions.

6. Kinetics Formulas:

a. Rate of Reaction:

Rate = k[A]^m[B]^n

where k is the rate constant and m and n are the reaction orders with respect to reactants A and B, respectively.

b. Arrhenius Equation:

k = A * e^(-Ea / RT)

where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

7. Spectroscopy Formulas:

a. Wavelength and Frequency Relationship:

c = λ * ν

where c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength in meters, and ν is the frequency in Hz.

b. Energy of a Photon:

E = h * ν

where E is the energy of a photon, h is Planck’s constant (6.63 x 10^-34 J·s), and ν is the frequency in Hz.

In conclusion, this collection of key formulas and equations serves as a valuable quick reference guide for various concepts in chemistry. From basic stoichiometry and thermodynamics to electrochemistry and spectroscopy, these formulas play a pivotal role in solving problems, predicting outcomes, and understanding the principles governing chemical reactions and properties. By having these equations at hand, students, researchers, and professionals can navigate the quantitative aspects of chemistry with ease and efficiency.