Chapter 6, Problem 6.109P

Various amounts of activated carbon were added to a ?xed amount of raw cane sugar solution (48 wt% sucrose in water) at 80°C. A colorimeter was used to measure the color of the solutions, R, which is proportional to the concentration of trace unknown impurities in the solution. The following data were obtained (adapted from the reference in Footnote 20, p. 652):

kg carbon/kg dry sucrose	0	0.005	0.010	0.015	0.020	0.030
R (color units/kg sucrose)	20.0	10.6	6.0	3.4	2.0	1.0

The reduction in color units is a measure of the mass of impurities (the adsorbate) adsorbed on the carbon (the adsorbent).

1. The general form of the Freundlich isotherm is

   $X_i^{*}=K_{\text{F}}{c}_i^{\beta }$

where $X_i^{*}$is the mass of i adsorbed/mass of adsorbent and c_iis the concentration of i in solution. Demonstrate that the Freundlich isotherm may be formulated for the system described above as

   $\vartheta ={K^{\prime }}_F{R}^{\beta }$

where $\vartheta$is the % removal of color/[mass of carbon/mass of dissolved sucrose]. Then determine $K^{\prime }$. and $\beta$by ?tting this expression to the given data, using one of the methods in Section 2.7.

1. Calculate the amount of carbon that would have to be added to a vat containing 1000 kg of the 48 wt% sugar solution at 80°C for a reduction in color content to 2.5% of the original value.