Defining equation (physical chemistry)

In physical chemistry, there are numerous quantities associated with chemical compounds and reactions; notably in terms of amounts of substance, activity or concentration of a substance, and the rate of reaction. This article uses SI units.

Introduction

Theoretical chemistry requires quantities from core physics, such as time, volume, temperature, and pressure. But the highly quantitative nature of physical chemistry, in a more specialized way than core physics, uses molar amounts of substance rather than simply counting numbers; this leads to the specialized definitions in this article. Core physics itself rarely uses the mole, except in areas overlapping thermodynamics and chemistry.

Quantification

General basic quantities

Quantity	Symbol/s	SI Units	Dimension
Number of molecules	N	dimensionless	dimensionless
Mass	m	kg
Number of moles, amount of substance, amount	n	mol
Volume of mixture or solvent, unless otherwise stated	V	m³	³

General derived quantities

Quantity	Symbol/s	Defining Equation	SI Units	Dimension
Relative atomic mass of an element	A_r, A, m_ram	The average mass is the average of the T masses m_i corresponding the T isotopes of X :	dimensionless	dimensionless
Relative formula mass of a compound, containing elements X_j	M_r, M, m_rfm	j = index labelling each element, N = number of atoms of each element X_i.	dimensionless	dimensionless
Molar concentration, concentration, molarity of a component i in a mixture	c_i,		mol dm⁻³ = 10⁻³ mol m⁻³	⁻³
Molality of a component i in a mixture	b_i, b	where solv = solvent.	mol kg⁻¹	⁻¹
Mole fraction of a component i in a mixture	x_i, x	where Mix = mixture.	dimensionless	dimensionless
Partial pressure of a gaseous component i in a gas mixture	p_i, p	where mix = gaseous mixture.	Pa = N m⁻²	⁻¹
Density, mass concentration	ρ_i, γ_i, ρ		kg m⁻³	³
Number density, number concentration	C_i, C		m^{− 3}	^{− 3}
Volume fraction, volume concentration	ϕ_i, ϕ		dimensionless	dimensionless
Mixing ratio, mole ratio	r_i, r		dimensionless	dimensionless
Mass fraction	w_i, w	m = mass of X_i	dimensionless	dimensionless
Mixing ratio, mass ratio	ζ_i, ζ	m = mass of X_i	dimensionless	dimensionless

Kinetics and equilibria

The defining formulae for the equilibrium constants K_c and K_p apply to the general chemical reaction:
+ + \cdots + \nu_\mathit X_\mathit <=> + + \cdots + \eta_\mathit _\mathit
and the defining equation for the rate constant k applies to the simpler synthesis reaction :
+ + \cdots + \nu_\mathit X_\mathit -> \eta
where:

i = dummy index labelling component i of reactant mixture,
j = dummy index labelling component i of product mixture,
X_i = component i of the reactant mixture,
Y_j = reactant component j of the product mixture,
r = number of reactant components,
p = number of product components,
ν_i = stoichiometry number for component i in product mixture,
η_j = stoichiometry number for component j in product mixture,
σ_i = order of reaction for component i in reactant mixture.

The dummy indices on the substances X and Y ''label the components ; they are not the numbers of each component molecules as in usual chemistry notation.
The units for the chemical constants are unusual since they can vary depending on the stoichiometry of the reaction, and the number of reactant and product components. The general units for equilibrium constants can be determined by usual methods of dimensional analysis. For the generality of the kinetics and equilibria units below, let the indices for the units be;
For the constant K_c;
Substitute the concentration units into the equation and simplify:,
The procedure is exactly identical for K_p.
For the constant k''

Quantity	Symbol/s	Defining Equation	SI Units	Dimension
Reaction progress variable, extent of reaction	ξ		dimensionless	dimensionless
Stoichiometric coefficient of a component i in a mixture, in reaction j	ν_i	where N_i = number of molecules of component i.	dimensionless	dimensionless
Chemical affinity	A		J	²⁻²
Reaction rate with respect to component i	r, R		mol dm⁻³ s⁻¹ = 10⁻³ mol m⁻³ s⁻¹	⁻³ ⁻¹
Activity of a component i in a mixture	a_i		dimensionless	dimensionless
Mole fraction, molality, and molar concentration activity coefficients	γ_xi for mole fraction, γ_bi for molality, γ_ci for molar concentration.	Three coefficients are used;	dimensionless	dimensionless
Rate constant	k		s⁻¹	⁻¹
General equilibrium constant	K_c
General thermodynamic activity constant	K₀	a and a are activities of X_i and Y_j respectively.
Equilibrium constant for gaseous reactions, using Partial pressures	K_p		Pa
Logarithm of any equilibrium constant	pK_c		dimensionless	dimensionless
Logarithm of dissociation constant	pK		dimensionless	dimensionless
Logarithm of hydrogen ion activity, pH	pH		dimensionless	dimensionless
Logarithm of hydroxide ion activity, pOH	pOH		dimensionless	dimensionless

Electrochemistry

Notation for half-reaction standard electrode potentials is as follows. The redox reaction
A + BX <=> B + AX
split into:

a reduction reaction: B+ + e^- <=> B
and an oxidation reaction: A+ + e^- <=> A

the electrode potential for the half reactions are written as and respectively.
For the case of a metal-metal half electrode, letting M represent the metal and z be its valency, the half reaction takes the form of a reduction reaction:
+ \mathit e^- <=> M

Quantity	Symbol/s	Defining Equation	SI Units	Dimension
Standard EMF of an electrode		where Def is the standard electrode of definition, defined to have zero potential. The chosen one is hydrogen:	V	²⁻¹
Standard EMF of an electrochemical cell		where Cat is the cathode substance and An is the anode substance.	V	²⁻¹
Ionic strength	I	Two definitions are used, one using molarity concentration, and one using molality, The sum is taken over all ions in the solution.	mol dm⁻³ or mol dm⁻³ kg⁻¹	⁻³ ⁻¹
Electrochemical potential		φ = local electrostatic potential z_i = valency of the ion i	J	²⁻²

Quantum chemistry

Quantity	Symbol/s	Defining Equation	SI Units	Dimension
Electronegativity	χ	Pauling : Mulliken : Energies E_d = Bond dissociation E_I = Ionization E_EA = Electron affinity	dimensionless	dimensionless