A 5 mol/L solution of uranyl nitrate (UN) in water is treated with tributyl phosphate (TBP) to remove uranyl nitrate in batchwise equilibrium contacts. Assume that water and TBP are mutually insoluble. The distribution coefficient for UN is K”DB = (cB)C / (cB)A = 3.5, where (cB)C = concentration of UN in TBP and (cB)A = concentration of UN in water, both in mol/L.
a) If 10L of UN in water is fed into a single batch extraction, what is the percent of UN obtained if 10L of TBP is used. (Hint: start with a mass balance!)
b) If instead you used three batch extractions with one-third of the solvent (TBP) used in each batch, how much total solvent is needed to achieve the same percent of UN extracted in part a, keeping the amount of feed the same.
Now, assume that we operate with N stages under crosscurrent flow, but with an uneven distribution of solvent over the various stages (i.e. solvent fed into stage i is fiS, where S is the total amount of solvent used, and fi is the fraction of solvent fed to stage i, such that Sigma 1N fi = 1).
c) Derive an expression to determine the percent extraction for a given solvent to feed ratio S/F and distribution coefficient K”DB.
d) Calculate the percent extraction of UN if three batch extractions are done with 3L solvent in the first, 4L solvent in the second, and 3L solvent in the third batch. Feed is still 10L.
e) Calculate the percent extraction for a continuous countercurrent process with three stages, assuming the same flow rate of solvent calculated in part b was used.
f) Calculate the amount of solvent used in a continuous countercurrent process with infinite stages, using the same percent extraction found in part e.