Question

Organic chemistry question

4. Benzoic acid is almost 12 times more soluble in dichloromethane than in water at room temperature (the distribution coefficient (K) is 11.7). a) Approximately how many grams of benzoic acid would be recovered in the organic layer if 10.0 g of benzoic acid dissolved in 100 mL of water was extracted with 100 mL of dichloromethane? Show calculations. b) Approximately how many grams of benzoic acid would be recovered if the water layer was extracted a second time with an additional 100 mL of dichloromethane? Show calculations. Is doing a second extraction important? Explain.

Answer 1

4.

a)

We have 10.0 g of benzoic acid in 100 mL of water(phase 1).

VH2O 100 mL

It is given that the distribution coefficient between water and dichloromethane is 11.7

SCH2Cl2 K CHCl = 11.7 SHO

Where are the solubility of benozoic acid in dichloromethane and water respectively.

SCH2C and SH2O

Now, for extraction 100 mL of dichloromethane(phase 2) is being used.

VCHC=100 mL

A equilibrium will be established as some of the benzoic acid becomes soluble in dichloromethane.

Let the fraction of benzoic acid that is soluble in water be x and total amount of the solute be m.

Hence, we can write solubility in water as

VH2O

Hence, the fraction that is soluble in dichloromethane is 1-x.

Hence, the solubility of the solute in dichloromethane can be written as

SCH.Cl(1-) XVH.Ch VCH2CI2

The fraction x is related to
VCH2CL
and
Нао
and K as follows

К- Sсн.C, SH2O Vн-0 т — К 3 (1-т)X VсH:Clz ххт Vн-0 VсH,Cl — VсH,CI, X Кхд%3D Vн,о - а х Vн,с — г(Vн2О + К x Vсн,Cl) 3D Ин,0 1 — х — К-

о'НА Vн,0 + К x Vсн,Ci, 100 тL 100 100 mL + 11.7x 100 тL 1270

Since the amount of benzoic acid originally present = 10.0 g

The amount of benzoic acid left in water after extraction with 100 mL dichloromethane is

100 x 10.0 g 0.787 g 1270 x 10.0 g

Hence, the amount of benzoic acid recovered in the dichloromethane layer(organic layer) is

10.0 g 0.787 g 9.21 g

b)

Now, we know that 0.787 g of benzoic acid is left in the aqueous layer. Hence, after a second extraction with another 100 mL of dichloromethane, the amount of benzoic acid left in the aqueous layer will be x times the amount left.

Hence, amount left in aqueous layer after second extraction is

$0.787 \ g \times x = 0.787 \ g \times \frac{100}{1270} \approx 0.0620 \ g$

Hence, the amount recovered will be

$10.0 \ g- 0.062 \ g \approx 9.94 \ g$

Hence, we have recovered 99.4% of the benzoic acid with 2 extractions as opposed to 92.1% after 1 extraction.

Hence, certainly doing a second extraction is important as we are able to increase our recovery by at least 7.3% which is great where the yield in a reaction is small. It is also better to do 2 extraction of 100 mL each than an extraction with 200 mL of dichloromethane which can be easily shown using a similar calculation as done in part a).