Question

What is the meaning of the term a ^x as used in equilibrium constant?

Answer 1

The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no tendency towards further change. At any given time, the reaction quotient is a number defined by taking the product of effective concentrations (chemical activities) for species appearing on the right-hand side of a chemical equation and dividing by the corresponding product for species appearing on the left-hand side. As the chemical reaction progresses, the reaction quotient changes and tends to the value of the equilibrium constant.
For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.
A knowledge of equilibrium constants is essential for the understanding of many chemical systems, as well as biochemical processes such as oxygen transport by hemoglobin in blood and acid-base homeostasis in the human body.
Stability constants, formation constants, binding constants, association constants and dissociation constants are all types of equilibrium constants. (See also the article on the determination of equilibrium constants for experimental and computational methods.)
Basic definitions and properties
For a system undergoing a reversible reaction described by the general chemical equation
{\displaystyle \alpha \,\mathrm {A} +\beta \,\mathrm {B} +\cdots \rightleftharpoons \rho \,\mathrm {R} +\sigma \,\mathrm {S} +\cdots }
the standard or thermodynamic equilibrium constant, denoted by
{\displaystyle K^{\ominus }}
(or simply as K), is defined to be the value of the reaction quotient Q at chemical equilibrium, when forward and reverse reactions occur at the same rate, and the chemical composition of the mixture remains constant over time. (It is important to note that chemical equilibrium is an idealized state and is approached asymptotically as the forward and reverse reaction rates converge.[1][2] In practice, the reaction is considered to reach equilibrium when the ongoing change in composition becomes too small to be measured by the chosen analytical technique.)
As a thermodynamic criterion, the Gibbs free energy change of reaction at chemical equilibrium is zero:
{\displaystyle \Delta _{\mathrm {r} }G=0}
. The equilibrium constant
{\displaystyle K^{\ominus }}
is related to the standard Gibbs free energy change of reaction
{\displaystyle \Delta _{\mathrm {r} }G^{\ominus }}
by
{\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\,\ln K^{\ominus }}
,
where R is the universal gas constant, T is the temperature in kelvins, and ln is the natural logarithm function.
An equilibrium constant is related to the composition of the mixture at equilibrium by [3] [4]
{\displaystyle K^{\ominus }={\frac {\mathrm {\{R\}} ^{\rho }\mathrm {\{S\}} ^{\sigma }...}{\mathrm {\{A\}} ^{\alpha }\mathrm {\{B\}} ^{\beta }...}}={\frac {{[\mathrm {R} ]}^{\rho }{[\mathrm {S} ]}^{\sigma }...}{{[\mathrm {A} ]}^{\alpha }{[\mathrm {B} ]}^{\beta }...}}\times \Gamma \times (c^{\ominus })^{(\alpha +\beta +\cdots )-(\rho +\sigma +\cdots )}}
(
{\displaystyle \Gamma ={\frac {\gamma _{\mathrm {R} }^{\rho }\gamma _{\mathrm {S} }^{\sigma }...}{\gamma _{\mathrm {A} }^{\alpha }\gamma _{\mathrm {B} }^{\beta }...}}}
and
{\displaystyle c^{\ominus }=1\ \mathrm {mol} \cdot \mathrm {L} ^{-1}}
),
where {X} denotes the thermodynamic activity of reagent X at equilibrium, [X] the corresponding concentration, and γ the corresponding activity coefficient. If it can be assumed that the quotient of activity coefficients,
{\displaystyle \Gamma }
, is constant over a range of experimental conditions, such as pH, then an equilibrium constant can be approximated by a quotient of concentrations, with concentrations of pure solids, liquids, and solvents omitted (since their activity is unity or nearly so), all other numerical values expressed in mol/L, and units omitted.[5] The related concentration equilibrium constant Kc is defined by the IUPAC[6][7] as
{\displaystyle K_{\mathrm {c} }={\frac {{[\mathrm {R} ]}^{\rho }{[\mathrm {S} ]}^{\sigma }...}{{[\mathrm {A} ]}^{\alpha }{[\mathrm {B} ]}^{\beta }...}}}
.
For an equilibrium mixture of gases, an equilibrium constant can be defined in terms of partial pressure or fugacity.
The law of mass action relates the equilibrium constant to the forward and backward rate constants, k and k', and serves as a link to connect chemical thermodynamics and chemical kinetics:[8]