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A speciation calculation is one in which concentrations of all the species in an equilibrium system are calculated, knowing the analytical concentrations, T A, T B etc. of the reactants A, B etc. This means solving a set of nonlinear equations of mass-balance
The calculation of K at a particular temperature from a known K at another given temperature can be approached as follows if standard thermodynamic properties are available. The effect of temperature on equilibrium constant is equivalent to the effect of temperature on Gibbs energy because:
The equilibrium constant for the protonation of a base, B, + H + ⇌ + is an association constant, K b, which is simply related to the dissociation constant of the conjugate acid, BH +. = The value of is ca. 14 at 25 °C. This approximation can be used when the correct value is not known.
At any equilibrium, the concentrations are unchanging, hence the left hand sides of these equations are zero. Then, from the first of these four equations, the ratio of reaction 1's rate constants equals the ratio of its equilibrium concentrations, and this ratio, called K 1, is called the equilibrium constant for reaction 1, i.e.
where quantities in square brackets represent the molar concentrations of the species at equilibrium. [c] [2] For example, a hypothetical weak acid having K a = 10 −5, the value of log K a is the exponent (−5), giving pK a = 5. For acetic acid, K a = 1.8 x 10 −5, so pK a is 4.7.
where: k 1 is the rate coefficient for the reaction that consumes A and B; k −1 is the rate coefficient for the backwards reaction, which consumes P and Q and produces A and B. The constants k 1 and k −1 are related to the equilibrium coefficient for the reaction (K) by the following relationship (set v=0 in balance):
The ratio of the mass–action ratio to the equilibrium constant is often called the disequilibrium ratio, denoted by the symbol . ρ = Γ K e q {\displaystyle \rho ={\frac {\Gamma }{K_{eq}}}} and is a useful measure for indicating how from equilibrium a given reaction is.
For a reversible reaction, the equilibrium constant can be measured at a variety of temperatures. This data can be plotted on a graph with ln K eq on the y-axis and 1 / T on the x axis. The data should have a linear relationship, the equation for which can be found by fitting the data using the linear form of the Van 't Hoff equation