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logK-files: Temperature effects

In DATABASE the logK-file contain equilibrium constants at 25°C, and 1 bar. Diagrams at other temperatures require addtional data.

These data may be entered in three different ways:

  1. Reaction data (ΔH° & ΔCp°):
  2. Analitical expressions
  3. Tables of logK°(T,P) data
See also:

Reaction data (ΔH° & ΔCp°)

In the logK-file, values for ΔH° & ΔCp° are entered inmediately after the logK° value, and before the reaction stoichiometry. For example:

CaCO3(cr);8.48;9.96;-327;2;Ca 2+;1;CO3 2-;1;1982PB /calcite InOH+2;-3.93;21.81;;In 3+;1;H+;-1;H2O;1;;;;;;;-1;SmithMart

In the second example for InOH2+ ΔH° = 21.81 kJ/mol, and ΔCp° is empty.

Below 100°C: at limited temperatures the equilibrium constant may be calculated using the van't Hoff equation if at least the value for ΔH° is available:

  logK°(T) = logK°(T0) + {ΔH° / (R ln(10))} × {(1/T0) − (1/T)}

where T and T0 are absolute temperatures in Kelvin (T0 = 298.15 K), R is the gas constant, and ΔH° is the enthalpy change of the reaction.

Below 300°C: at higher temperatures a reaction heat capacity, ΔCp°, is also needed:

  logK°(T) = logK°(T0) + {ΔH° / (R ln(10))} × {(1/T0) − (1/T)} + {ΔCp° / (R ln(10))} × {(T0/T) − 1 + ln(T/T0)}

In DATABASE the constant heat-capacity equation is used for temperatures up to 300°C if both ΔH° and ΔCp° are provided. Pressure efects are neglected in this equation.

Analytical expression

The following function may be used to calculate logK° as a function the temperature (T in Kelvin):
  logK°(T) = A1 + (A2T) + (A3T−1) + (A4 log(T)) + (A5T−2) + (A6T2)

This is the same expression as that used in the Phreeqc software. In DATABASE this equation is used at pressures of 1 bar up to 100°C and above that at the vapour-liquid equilibrium pressure (see Table) up to the critical point (373.95°C).

The parameters A1 to A6 are entered after a keyword “analytic” followed by the upper temperature limit for the equation (the lower limit is assumed to be 0°C). Examples:

HCO3-;10.329;analytic;250;107.8871;0.03252849;-5151.79;-38.92561;563713.9;0;CO3 2-;1;H+;1;;;;;;;;;1; Plummer & Busenberg 1982 O2(g);-83.1817;analytic;350;284.931;0.03166975;-41814.46;-99.87326;879333;;3;H2O;2;H+;-4;e-;-4

Tables of logK°(T,P) data

In DATABASE a “lookup table” may be used to interpolate values of logK° at the desired temperature and pressure. This makes it possible to make input files for diagrams at temperatures above the critical point (373.95°C) or at pressures above the liquid-vapor curve.

After the name of the species (reaction product) and its logK° at 25°C, and before the reaction stoichiometry, a keyword “lookUpTable” is entered followed by the upper temperature limit for the table (600°C in this software version). In the following 5 lines a grid of logK° values is given, from which values are interpolated at the desired temperature and pressure.

In this logK°-grid the rows (1 to 5) correspond to increasing pressure and the columns (1 to 14) correspond to increasing temperature. The values of temperature (°C) and pressure (bar) in the grid are: 

t=  0, 25, 50, 100,  150,  200,  250,  300,  350, 400, 450, 500, 550, 600C
p=  1,  1,  1, 1.01, 4.76, 15.6, 39.8, 85.9, 165, 300,  - ,  - ,  - ,  -
  500,500,500, 500,  500,  500,  500,  500,  500, 500, 500, 650, 900, 950
   1k, 1k, 1k,  1k,   1k,   1k,   1k,   1k,   1k,  1k,  1k,  1k,  1k,  1k
   3k, 3k, 3k,  3k,   3k,   3k,   3k,   3k,   3k,  3k,  3k,  3k,  3k,  3k
   5k, 5k, 5k,  5k,   5k,   5k,   5k,   5k,   5k,  5k,  5k,  5k,  5k,  5k

Example:

CO3 2-;-10.329;lookUpTable;600;2;H+;-1;HCO3-;1; Shock07 + Soltherm
  -10.624;-10.329;-10.169;-10.084;-10.200;-10.465;-10.871;-11.464;-12.375;-12.344;NaN;NaN;NaN;NaN;
  -10.37;-10.07;-9.92;-9.84;-9.95;-10.19;-10.54;-10.99;-11.59;-12.07;-12.88;-13.46;-13.87;-14.13;
  -10.13;-9.84;-9.69;-9.62;-9.73;-9.95;-10.26;-10.63;-11.06;-11.54;-12.07;-12.68;-13.34;-14.00;
  -9.29;-8.98;-8.85;-8.82;-8.95;-9.16;-9.42;-9.72;-10.03;-10.37;-10.72;-11.08;-11.45;-11.84;
  NaN;-8.22;-8.11;-8.12;-8.29;-8.52;-8.78;-9.05;-9.34;-9.63;-9.93;-10.23;-10.54;-10.85;

where logK° = −10.329 at 25°C and 1 bar, and = −8.22 at 5 kbar.

NOTE: For grid points where no logK° is available enter NaN (Not-a-Number), for example at temperatures above 400C and pressures below 300bar.

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