Method for predicting the conductivity of a liquid mixture

Abstract

In a method of preparing a liquid solution by mixing ingredients according to a predetermined recipe, wherein at least one pair of species of the liquid solution is derived from a weak electrolyte and corresponds to an acid-base pair, the conductivity of the liquid solution is predicted by: (i) for each pair of species derived from a weak electrolyte, solving a respective equilibrium equation to calculate the actual molar concentration of each such species at equilibrium in the liquid solution, (ii) calculating for each ionic species of said plurality of species the molar conductivity by the formula: Λ=Λ 0 −K× Sqrt( c ) wherein Λ is the molar conductivity, Λ 0 is the molar conductivity at infinite dilution, c is the concentration, and K is the Kohlrausch coefficient, and wherein K and Λ 0 are predetermined values for K and Λ 0 for each ionic species, (iii) calculating the conductivity x for each ionic species by the formula: κ= c×Λ and (iv) adding up the conductivities determined in step (iii) for the different ionic species to obtain a predicted conductivity of the liquid solution. A computer program product comprises instructions for causing a computer to perform the method steps.

1 . A method of preparing a liquid solution by mixing ingredients according to a predetermined recipe, wherein the liquid solution comprises a plurality of species, at least one pair of species being derived from a weak electrolyte and corresponding to an acid-base pair, and wherein the conductivity of the liquid solution is predicted by:
 (i) for each pair of species derived from a weak electrolyte, solving a respective equilibrium equation to calculate from said predetermined recipe the actual molar concentration of each such species, including all ionic species derived from the weak electrolyte, at equilibrium in the liquid solution,   (ii) calculating for each ionic species of said plurality of species the molar conductivity by the formula:
   Λ=Λ 0   −K× Sqrt( c )
 
   wherein Λ is the molar conductivity, Λ 0  is the molar conductivity at infinite dilution, c is the concentration of the ionic species, and K is the Kohlrausch coefficient, and wherein K and Λ 0  are obtained from a data set comprising predetermined values for K and Λ 0  for each ionic species,   (iii) calculating the conductivity K for each ionic species by the formula:
   κ= ×Λ 
 
   wherein c and Λ are as defined above, and   (iv) adding up the conductivities determined in step (iii) for the different ionic species to obtain a predicted conductivity of the liquid solution.   
     
     
         2 . The method of  claim 1 , wherein the data set comprises values for the Kohlrausch coefficient K obtained by measuring the conductivity of a solution containing the ionic species at a plurality of different concentrations of the ionic species and different pH values, and optionally different temperatures, and fitting the resulting data to the formula in step (ii) of  claim 1  to obtain K. 
     
     
         3 . The method of  claim 2 , wherein said data set further comprises values for Λ 0  obtained by said fitting. 
     
     
         4 . The method of  claim 2 , wherein the Kohlrausch coefficient is expressed as K=A+B×Λ 0 , wherein A and B are temperature-dependent constants and Λ 0  is as previously defined, and wherein the predetermined values for K in the data set are calculated from values for A and B obtained by said fitting. 
     
     
         5 . The method of  claim 2 , wherein the Kohlrausch coefficient is expressed as K=A+B+w×Λ 0 , wherein A and B are temperature-dependent constants, w is the Onsager factor, and Λ 0  is as previously defined, and wherein the predetermined values for K in the data set are calculated from values for A, B and w obtained by said fitting. 
     
     
         6 . The method of  claim 1 , wherein the concentration of each ionic species is calculated by an algorithm comprising the equation of Debye-Hückel, wherein the ionic strength of each species is used as a weighting parameter in the calculation of an average hydrated radius of the ionic species. 
     
     
         7 . The method of  claim 1 , wherein the liquid solution is a buffer. 
     
     
         8 . The method of  claim 1 , which is computer-implemented. 
     
     
         9 - 11 . (canceled) 
     
     
         12 . A computer program product comprising instructions for causing a computer to perform the method steps of  claim 1 . 
     
     
         13 . A device for measuring pH, comprising a conductivity sensor and means for calculating pH from measured conductivity using the conductivity prediction steps of  claim 1 , in a backwards calculation mode. 
     
     
         14 . A method of predicting the conductivity of a liquid solution containing ingredients according to a predetermined recipe, wherein the liquid solution comprises a plurality of species, at least one pair of species being derived from a weak electrolyte and corresponding to an acid-base pair, comprising the steps of:
 (i) for each pair of species derived from a weak electrolyte, solving a respective equilibrium equation to calculate from said predetermined recipe the actual molar concentration of each such species, including all ionic species derived from the weak electrolyte, at equilibrium in the liquid solution,   (ii) calculating for each ionic species of said plurality of species the molar conductivity by the formula:
   Λ=Λ 0   −K× Sqrt( c )
 
   wherein Λ is the molar conductivity, Λ 0  is the molar conductivity at infinite dilution, c is the concentration of the ionic species, and K is the Kohlrausch coefficient, and wherein K and Λ 0  are obtained from a data set comprising predetermined values for K and Λ 0  for each ionic species,   (iii) calculating the conductivity K for each ionic species by the formula:
   κ= c×Λ 
 
   wherein c and Λ are as defined above, and   (iv) adding up the conductivities determined in step (iii) for the different ionic species to obtain a predicted conductivity of the liquid solution.