 Solution

Subtract the chlorite–gibbsite reaction from the chlorite–kaolinite reaction. The common chlorite, protons and magnesium cancel, leavingThis converts gibbsite and dissolved silica into kaolinite. Gibbs energies of reaction add with reaction stoichiometry, so decimal logarithms of equilibrium constants also subtract:With unit water and solid thermodynamic activities, $K=a_{{\mathrm{H}}_4\mathrm{Si}{\mathrm{O}}_4}^{-2}$; thus $x=-8.49/2=-4.245$, a vertical boundary. Reversing the reaction would give ${\log }_{10}K=-8.49$ and the same boundary. Its intersection with either sloping line is $(x,y)=(-4.245,13.077)$.