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The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
Equilibrium constants are determined in order to quantify chemical equilibria.When an equilibrium constant K is expressed as a concentration quotient, = [] [] [] [] it is implied that the activity quotient is constant.
The decrease in zero-point energy due to deuterium substitution will then be more important for R'–H than for R–H, and R'–D will be stabilized more than R–D, so that the equilibrium constant K D for R' + D–R ⇌ R'–D + R is greater than K H. This is summarized in the rule the heavier atom favors the stronger bond. [19]
In particular, equilibrium constants for species in aqueous solution are dependent on ionic strength, as the quotient of activity coefficients varies with the ionic strength of the solution. The values of the standard free energy change and of the equilibrium constant are temperature dependent.
However, the equilibrium constant will no longer be dimensionless and will have units of reciprocal concentration instead. The difference between the kinetic and thermodynamic derivations of the Langmuir model is that the thermodynamic uses activities as a starting point while the kinetic derivation uses rates of reaction.
The role of water in the association equilibrium is ignored as in all but the most concentrated solutions the activity of water is constant. K is defined here as an association constant, the reciprocal of an acid dissociation constant. Each activity term { } can be expressed as the product of a concentration [ ] and an activity coefficient γ ...
The affinity constants, k + and k −, of the 1879 paper can now be recognised as rate constants. The equilibrium constant, K, was derived by setting the rates of forward and backward reactions to be equal. This also meant that the chemical affinities for the forward and backward reactions are equal. The resultant expression
where k f is the rate constant for the forward reaction and k b is the rate constant for the backward reaction and the square brackets, […], denote concentration. If only A is present at the beginning, time t = 0 , with a concentration [A] 0 , the sum of the two concentrations, [A] t and [B] t , at time t , will be equal to [A] 0 .