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where ln denotes the natural logarithm, is the thermodynamic equilibrium constant, and R is the ideal gas constant.This equation is exact at any one temperature and all pressures, derived from the requirement that the Gibbs free energy of reaction be stationary in a state of chemical equilibrium.
Its symbol is Δ f G˚. All elements in their standard states (diatomic oxygen gas, graphite, etc.) have standard Gibbs free energy change of formation equal to zero, as there is no change involved. Δ f G = Δ f G˚ + RT ln Q f, where Q f is the reaction quotient. At equilibrium, Δ f G = 0, and Q f = K, so the equation becomes Δ f G˚ = − ...
The stepwise constant, K, for the formation of the same complex from ML and L is given by ML + L ⇌ ML 2; [ML 2] = K[ML][L] = Kβ 11 [M][L] 2. It follows that β 12 = Kβ 11. A cumulative constant can always be expressed as the product of stepwise constants. There is no agreed notation for stepwise constants, though a symbol such as K L
At 298 K, a reaction with ΔG ‡ = 23 kcal/mol has a rate constant of k ≈ 8.4 × 10 −5 s −1 and a half life of t 1/2 ≈ 2.3 hours, figures that are often rounded to k ~ 10 −4 s −1 and t 1/2 ~ 2 h. Thus, a free energy of activation of this magnitude corresponds to a typical reaction that proceeds to completion overnight at room ...
An often considered quantity is the dissociation constant K d ≡ 1 / K a , which has the unit of concentration, despite the fact that strictly speaking, all association constants are unitless values. The inclusion of units arises from the simplification that such constants are calculated solely from concentrations, which is not the case.
If K is the equilibrium constant and dT is the change in temperature then the enthalpy change is given by the Van 't Hoff equation: =. where R is the universal gas constant and T is the absolute temperature.
where and represent the total concentrations, of host and guest, can be reduced to a single quadratic equation in, say, [G] and so can be solved analytically for any given value of K. The concentrations [H] and [HG] can then derived.
The definition of the Gibbs function is = + where H is the enthalpy defined by: = +. Taking differentials of each definition to find dH and dG, then using the fundamental thermodynamic relation (always true for reversible or irreversible processes): = where S is the entropy, V is volume, (minus sign due to reversibility, in which dU = 0: work other than pressure-volume may be done and is equal ...