Question

The capacity factor of a give solute in a water-chloroform system is 10. calculate the percentage of the solute from 50ml of water by 200ml of chloroform where: a) the chloroform was used all at once. b) the 100ml chloroform is divided into five 20ml portions which are used one after the other.

Answer 1

a)

$$r = {V_{water} \over V_{chloroform}} = {200 \over 50} = 4$$

$$r = {1 - R \over R}$$

$$4R = 1 - R$$

$$R = 0.2$$

$$P = {r*R \over 1 -R_{A}} = {4*0.2 \over 1 - R_{A}} = 10$$

$$R_{A} = 0.92 = 92\%$$

b)

$$r = {20 \over 50} = 0.4$$

$$R_1 = {P \over P + r} = {10 \over 10+0.4} = 0.9615 = 96.15\%$$

$$R_2 = (100 - 96.15)*0.9615 = 3.7\%$$

$$R_3 = (100-96.15 - 3.7)*0.9615 = 0.14\%$$

$$R_4 = (100 - 96.15 - 3.7 - 0.14)*0.9615 = 0.0096\%$$

$$R_5 = (100 - 96.15 - 3.7 - 0.14 - 0.0096)*0.9615 = 0.00038\%$$

$$R = R_1 + R_2 + R_3 + R_4 + R_5 = 99.99998\% \approx 99.99\%$$