# What is K (Equilibrium Constant)? Geochemistry quick tips!

What is K (Equilibrium Constant)? Geochemistry quick tips!

In principle, any chemical equilibrium reaction can be described by the mass – action law.

$\alpha A +\beta B ... \rightleftharpoons \sigma S+\tau T ...$
$K=\frac{{\{S\}} ^\sigma {\{T\}}^\tau ... } {{\{A\}}^\alpha {\{B\}}^\beta ...}$

Where
K = Thermodynamic equilibrium or dissolution constant

K is truly defined based on the type of reaction in hand. For example:

1. Dissolution / Precipitation reaction: K= Ks = Solubility product constant.
2. Sorption: K = Kd = Distribution constant or; K=Kx =Selectivity Co -efficient
3. Redox reactions; K=Stability constant
4. Complex formation: K = Complexation constant

Note: If you reverse the reaction, K(reverse) = 1/K(forward)! So always write the reaction for any K.
Note: K is dependent on Temperature. K for various temperatures can be calculated using Van’t Hoff Equation.
Note: If a process consists of subsequent reactions, the equilibrium constants are numbered in order 9K1, K2, K3…). Example carbonate dissolution.

# Van ‘t Hoff equation

The Van ‘t Hoff equation in chemical thermodynamics relates the change in temperature (T) to the change in the equilibrium constant (K) given the enthalpy change (?H). The equation was first derived by Jacobus Henricus van ‘t Hoff.

$\frac{d \mbox{ ln K}}{dT} = \frac{\Delta H^\ominus}{RT^2}$

If the enthalpy change of reaction is assumed to be constant with temperature, the definite integral of this differential equation between temperatures T1 and T2 is given by

$\ln \left( {\frac{{K_2 }}{{K_1 }}} \right) = \frac{{ - \Delta H^\ominus }}{R}\left( {\frac{1}{{T_2 }} - \frac{1}{{T_1 }}} \right)$ ——–Equation A ( USE THIS EQUATION TO CALCULATE K at DIFFERENT TEMPERATURES)

In this equation K1 is the equilibrium constant at absolute temperature T1 and K2 is the equilibrium constant at absolute temperature T2. ?Ho is the enthalpy change and R is the gas constant.

Since

$\Delta G^\ominus = \Delta H^\ominus - T\Delta S^\ominus$

and

$\Delta G^\ominus = -RT \ln K$

it follows that

$\ln K = - \frac{{\Delta H^\ominus}}{RT}+ \frac{{\Delta S^\ominus }}{R}$

Therefore, a plot of the natural logarithm of the equilibrium constant versus the reciprocal temperature gives a straight line. The slope of the line is equal to minus the standard enthalpy change divided by the gas constant, ?Ho/R and the intercept is equal to the standard entropy change divided by the gas constant, ?So/R. Differentiation of this expression yields the van ‘t Hoff equation.