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)

Question

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)

Infinity Learn · Accepted Answer

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

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