The adsorption of a dye from a solution on charcoal is governed by Freundlich's isotherm in which 1n=2 and k=6.8 If 10 g of charcoal be shaken with 0.1 M solution of the dye, equilibrium concentration of the solution will be (concentration of dye is in millimoles/cc and the amount adsorbed in millimoles/g)

Let x be millimoles of dye be adsorbed by 10 g charcoal. Initial concentration of dye = 0.1mol L-1=0.1×1000 millimol 1000cc=0.1millimol/ccThus, equilibrium concentration = (0.1 x) millimol/cc xm=k(C)1/n Given, k=6.8 and 1n=2x millimol/10 g=6.8(0.1−x)2x=68(0.1−x)2=68(0.1)2+x2−0.2x=680.01+x2−0.2x68 x2−14.6x+0.68=0x=+14.6±(14.6)2−4×68×0.682×68= 0.07∴ Equilibrium concentration =0.1−0.07= 0.03 M