Foundations

A simple gas model relates pressure, amount, volume and temperature.

The mole counts specified entities using the exact Avogadro constant.

Balanced coefficients relate the amounts consumed and produced by a reaction.

A chemical equation must preserve each element's atom count and the total charge.

At equilibrium, opposing reactions continue without net composition change.

In the Brønsted description, an acid donates a proton and a base accepts it.

Gibbs-energy change distinguishes thermodynamic favourability from reaction speed.

Reaction rate measures change over time; a rate law describes its dependence under specified conditions.

A catalyst changes the reaction pathway and rate, while preserving the equilibrium constant for the same reaction.

Activity expresses composition relative to a specified thermodynamic standard state.

pH is an activity-based quantity realized through measurement conventions.

An acid–base pair can resist limited changes in solution pH.

An equilibrium product constrains dissolution of a specified solid phase.

Electrode potentials are specified relative to a reference half-cell.

Reversible electrochemical potential depends on activities and temperature.

A mechanism proposes steps that account for an overall chemical transformation.

Many rate constants follow an exponential temperature model over a limited range.

Reaction enthalpies can be combined because enthalpy is a state function.

Phase diagrams describe equilibrium states under stated conditions.

Quantitative analysis needs a validated relation between response and analyte amount.

Differential interactions with mobile and stationary phases separate mixture components.

Absorbance can be proportional to path length and absorbing-species concentration.

For a simple compressible equilibrium system, U(S,V,{N_i}) has differential dU=T dS−p dV+Σ_i μ_i dN_i.

The Legendre transforms H=U+pV and F=U−TS change the natural state variables: dH=T dS+V dp and dF=−S dT−p dV at fixed composition.

Equality of mixed derivatives of smooth equilibrium potentials gives (∂T/∂V)_S=−(∂p/∂S)_V, (∂T/∂p)_S=(∂V/∂S)_p, (∂S/∂V)_T=(∂p/∂T)_V and (∂S/∂p)_T=−(∂V/∂T)_p.

For a fixed amount of simple compressible matter, C_V=(∂U/∂T)_V and C_p=(∂H/∂T)_p.

Thermal equilibrium is transitive, permitting a common temperature scale.

For canonical Z=Σ_i exp(−βE_i), F=−k_BT lnZ, U=−∂_β lnZ and S=k_B(lnZ+βU).

For a system exchanging energy and particles with reservoirs at T and μ, p_i,N=exp[−β(E_i,N−μN)]/Ξ and Ξ=Σ_N,i exp[−β(E_i,N−μN)].

In a classical canonical model, each independent quadratic term in an unrestricted coordinate or momentum contributes k_BT/2 to the mean energy.