Laws of Diffusion, Chemistry & Physics
A reference library of 30 fundamental scientific laws and equations. Each one has a plain-language statement, its formula and an interactive calculator.
- Fick's First Law of Diffusion
- Fick's Second Law of Diffusion
- Arrhenius Equation for Diffusion
- Stokes–Einstein Relation
- Einstein–Smoluchowski Diffusion Relation
- Graham's Law of Effusion
- Membrane Permeation (Solution–Diffusion Model)
- Einstein Relation (Nernst–Einstein)
- Heat Equation (Heat Diffusion)
- Ideal Gas Law
- Combined Gas Law
- Molar Concentration
- Dilution Equation
- pH Definition (Sørensen)
- Law of Radioactive Decay
- Arrhenius Equation
- Nernst Equation
- van 't Hoff Law of Osmotic Pressure
- Beer–Lambert Law
- Henry's Law
- Ohm's Law
- Newton's Second Law of Motion
- Kinetic Energy
- Gravitational Potential Energy
- Hooke's Law
- Coulomb's Law
- Newton's Law of Universal Gravitation
- Fourier's Law of Heat Conduction
- Density
- Pressure
Diffusion laws
Fick's laws, diffusion coefficients, diffusion length and mass transport.
Fick's First Law of Diffusion
The diffusion flux is proportional to the negative concentration gradient: matter flows from high to low concentration at a rate set by the diffusion coefficient. (Adolf Fick, 1855)
Open the Fick's First Law calculator →Fick's Second Law of Diffusion
The rate of change of concentration at a point equals the diffusion coefficient times the curvature of the concentration profile. (Adolf Fick, 1855)
Open the Fick's Second Law calculator →Arrhenius Equation for Diffusion
Diffusion in solids is thermally activated: the diffusion coefficient increases exponentially with absolute temperature.
Open the Diffusion Coefficient vs Temperature calculator →Stokes–Einstein Relation
A sphere undergoing Brownian motion in a viscous fluid has a diffusion coefficient equal to the thermal energy divided by its Stokes friction coefficient. (Albert Einstein, 1905; William Sutherland, 1905)
Open the Stokes–Einstein Equation calculator →Einstein–Smoluchowski Diffusion Relation
For a random walk, the mean squared displacement grows linearly with time: ⟨r²⟩ = 2nDt in n dimensions. (Einstein 1905, Smoluchowski 1906)
Open the Diffusion Length & Time calculator →Graham's Law of Effusion
The rate of effusion of a gas is inversely proportional to the square root of its molar mass. (Thomas Graham, 1848)
Open the Graham's Law of Effusion calculator →Membrane Permeation (Solution–Diffusion Model)
Steady-state flux through a membrane equals the permeability coefficient times the concentration difference across it, where permeability = D·K/L.
Open the Membrane Diffusion & Permeability calculator →Einstein Relation (Nernst–Einstein)
For particles in thermal equilibrium, the diffusion coefficient is proportional to the mobility, with the thermal voltage kT/q as the constant. (Albert Einstein, 1905)
Open the Einstein Relation calculator →Heat Equation (Heat Diffusion)
Temperature diffuses just like concentration: ∂T/∂t = α∇²T. The thermal diffusivity α plays the role of Fick's D. (Joseph Fourier, 1822)
Open the Thermal Diffusivity calculator →Chemistry laws
Gas laws, solutions, pH, kinetics, electrochemistry and spectroscopy.
Ideal Gas Law
For an ideal gas, the product of pressure and volume equals the amount of gas times the gas constant times the absolute temperature. (Émile Clapeyron, 1834)
Open the Ideal Gas Law calculator →Combined Gas Law
For a fixed amount of gas, PV/T is constant. Holding T constant gives Boyle's law, holding P constant gives Charles's law, and holding V constant gives Gay-Lussac's law.
Open the Combined Gas Law calculator →Molar Concentration
Molarity is the amount of solute in moles per litre of solution.
Open the Molarity calculator →Dilution Equation
Diluting a solution does not change the amount of solute: the concentration times the volume is the same before and after.
Open the Dilution calculator →pH Definition (Sørensen)
pH is the negative base-10 logarithm of the hydrogen-ion activity, approximately −log₁₀[H⁺] in dilute solutions. (S. P. L. Sørensen, 1909)
Open the pH calculator →Law of Radioactive Decay
The number of undecayed nuclei decreases exponentially with time; in each half-life, half of what remains decays. (Ernest Rutherford & Frederick Soddy, 1902)
Open the Half-Life & Radioactive Decay calculator →Arrhenius Equation
The rate constant of a chemical reaction increases exponentially with temperature, governed by the activation energy. (Svante Arrhenius, 1889)
Open the Arrhenius Equation calculator →Nernst Equation
The potential of an electrochemical cell depends on the standard potential, the temperature, and the ratio of product to reactant activities. (Walther Nernst, 1889)
Open the Nernst Equation calculator →van 't Hoff Law of Osmotic Pressure
The osmotic pressure of a dilute solution equals the pressure the solute particles would exert as an ideal gas occupying the same volume. (Jacobus van 't Hoff, 1887)
Open the Osmotic Pressure calculator →Beer–Lambert Law
The absorbance of light by a solution is proportional to the concentration of the absorbing species and the path length. (Bouguer 1729, Lambert 1760, Beer 1852)
Open the Beer–Lambert Law calculator →Henry's Law
At constant temperature, the amount of a gas that dissolves in a liquid is proportional to its partial pressure above the liquid. (William Henry, 1803)
Open the Henry's Law calculator →Physics laws
Mechanics, energy, electricity, gravitation and heat transfer.
Ohm's Law
The current through a conductor is directly proportional to the voltage across it, with resistance as the constant of proportionality. (Georg Simon Ohm, 1827)
Open the Ohm's Law calculator →Newton's Second Law of Motion
The net force on a body equals its mass times its acceleration; equivalently, force equals the rate of change of momentum. (Isaac Newton, 1687)
Open the Newton's Second Law calculator →Kinetic Energy
The energy of motion of a body equals one half its mass times the square of its speed.
Open the Kinetic Energy calculator →Gravitational Potential Energy
Near a planet's surface, the potential energy gained by raising a mass equals its weight times the height raised.
Open the Gravitational Potential Energy calculator →Hooke's Law
The force needed to stretch or compress a spring is proportional to the displacement from its natural length. (Robert Hooke, 1678)
Open the Hooke's Law calculator →Coulomb's Law
The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. (Charles-Augustin de Coulomb, 1785)
Open the Coulomb's Law calculator →Newton's Law of Universal Gravitation
Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres. (Isaac Newton, 1687)
Open the Newton's Law of Universal Gravitation calculator →Fourier's Law of Heat Conduction
The rate of heat flow through a material is proportional to the negative temperature gradient and to the area through which heat flows. (Joseph Fourier, 1822)
Open the Fourier's Law of Heat Conduction calculator →Density
Density is mass per unit volume, an intrinsic property of a material at a given temperature and pressure.
Open the Density calculator →Pressure
Pressure is the force acting perpendicular to a surface divided by the area over which it acts.
Open the Pressure calculator →