88.4 Surface adsorption of solution 8.4.2 Gibbs adsorption isotherm d=-S++al+∑om Ad+∑ndA=0 Let n, be the excess amount of the solute(2) At constant T and p in the surface layer compared to that in a solution of uniform composition. Then the dgo=odA+>u dn lowering of free energy due to the adsorption of solute at the interface is n, du, Integration gives This lowering of free energy in the surface G=a4+∑n is equivalent to -Ado, hence do Further differentiation Ado au2 dG=ad4+Aa+∑om+∑i i i dG SdT Vdp dA dn   = − + + +    At constant T and p = + i dG dA i dni     = +   G A i ni i i i i dG dA Ad dn n d    = + + +       Integration gives 0 Ad n di i    + =  Let n2 be the excess amount of the solute (2) in the surface layer compared to that in a solution of uniform composition. Then the lowering of free energy due to the adsorption of solute at the interface is n2 d2 . 8.4.2 Gibbs adsorption isotherm Further differentiation n2 d2 = −Ad This lowering of free energy in the surface is equivalent to - Ad, hence: 2 2 T       = −    §8.4 Surface adsorption of solution