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

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

General derived quantities

The average mass is the average of the T masses mi corresponding the T isotopes of X :dimensionlessdimensionlessRelative formula mass of a compound, containing elements XjMr, M, mrfm
j = index labelling each element,

N = number of atoms of each element Xi.dimensionlessdimensionlessMolar concentration, concentration, molarity of a component i in a mixtureci, mol dm−3 = 10−3 mol m−3 −3Molality of a component i in a mixturebi, b
where solv = solvent.mol kg−1 −1Mole fraction of a component i in a mixturexi, x
where Mix = mixture.dimensionlessdimensionlessPartial pressure of a gaseous component i in a gas mixturepi, p
where mix = gaseous mixture.Pa = N m−2−1Density, mass concentrationρi, γi, ρkg m−3 3Number density, number concentrationCi, Cm− 3− 3Volume fraction, volume concentrationϕi, ϕdimensionlessdimensionlessMixing ratio, mole ratiori, rdimensionlessdimensionlessMass fractionwi, w
m = mass of XidimensionlessdimensionlessMixing ratio, mass ratioζi, ζ
m = mass of Xidimensionlessdimensionless

Kinetics and equilibria

The defining formulae for the equilibrium constants Kc and Kp apply to the general chemical reaction:
and the defining equation for the rate constant k applies to the simpler synthesis reaction :
where:
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 Kc;
Substitute the concentration units into the equation and simplify:,
The procedure is exactly identical for Kp.
For the constant k
where Ni = number of molecules of component i.dimensionlessdimensionlessChemical affinityAJ2−2Reaction rate with respect to component ir, Rmol dm−3 s−1 = 10−3 mol m−3 s−1 −3 −1Activity of a component i in a mixtureaidimensionlessdimensionlessMole fraction, molality, and molar concentration activity coefficientsγxi for mole fraction, γbi for molality, γci for molar concentration.Three coefficients are used;





dimensionlessdimensionlessRate constantk s−1 −1General equilibrium constantKcGeneral thermodynamic activity constantK0
a and a are activities of Xi and Yj respectively.Equilibrium constant for gaseous reactions, using Partial pressuresKpPaLogarithm of any equilibrium constantpKcdimensionlessdimensionlessLogarithm of dissociation constantpKdimensionlessdimensionlessLogarithm of hydrogen ion activity, pHpHdimensionlessdimensionlessLogarithm of hydroxide ion activity, pOHpOHdimensionlessdimensionless

Electrochemistry

Notation for half-reaction standard electrode potentials is as follows. The redox reaction
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:
where Def is the standard electrode of definition, defined to have zero potential. The chosen one is hydrogen:V2−1Standard EMF of an electrochemical cell
where Cat is the cathode substance and An is the anode substance.V2−1Ionic strengthITwo 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 −1Electrochemical potential
φ = local electrostatic potential
zi = valency
of the ion iJ2−2

Quantum chemistry

Mulliken :

Energies
Ed = Bond dissociation
EI = Ionization
EEA = Electron affinitydimensionlessdimensionless