Question

The solubility of benzoic acid in water is 6.80g per 100 mL at 100 ℃, and 0.34g per 100 mL at 25 ℃.

(a) Calculate the min. volume of water needed to dissolve 1.00g of benzoic acid at 100 ℃. 

(b) Calculate the maximum theoretical percent recovery from the recrystallization of 1.00g benzoic acid from 15 mL of water assuming the solution is filtered at 25 ℃?

Answer 1

Concepts and reason

This is based upon the concept of the solubility of solute in a solvent. The solubility increases with increase in temperature.

Fundamentals

Solubility is the amount of solute that can be dissolved in a particular amount of solvent at a particular temperature.

Unitary method:

If x quantity have y units

Then, z quantity will have $\frac{y}{x} \times z$units

Part a

Solubilityof benzoic acid in water at ${100^o}{\rm{ C}}$$\left( {{s_{100}}} \right)$is 6.80 g in 100 mL

Amount of water needed to dissolve 6.8 g benzoic acid is 100 mL

Applying unitary method

Amount of water needed to dissolve 1 g benzoic acid$\left( v \right)$is

$\begin{array}{c}\\v = \frac{{100{\rm{ mL}}}}{{6.84{\rm{ g}}}} \times 1{\rm{ g}}\\\\{\rm{ = 14}}{\rm{.7 mL}}\\\end{array}$

Part b

Solubility of benzoic acid in water at ${25^o}{\rm{ C}}$$\left( {{s_{25}}} \right)$is 0.34 g in 100 mL

Amount of benzoic acid soluble in 100 mL water is 0.34 g

Applying unitary method

Amount ofbenzoic acidsoluble in 15 mL water$\left( a \right)$is

$\begin{array}{c}\\a = \frac{{0.34{\rm{ g}}}}{{100{\rm{ mL}}}} \times 15{\rm{ mL}}\\\\{\rm{ = 0}}{\rm{.051 g}}\\\end{array}$

Amount of benzoic acid that remains undissolved$\left( {{a_{un}}} \right)$out of total amount$\left( {{a_t}} \right)$ when a is dissolved amount is

${a_{un}} = {a_t} - a$

Substitute 0.051 g for a and 1 g for ${a_t}$

$\begin{array}{c}\\{a_{un}} = 1{\rm{ }}g{\rm{ }}--{\rm{ }}0.051{\rm{ }}g{\rm{ }}\\\\ = {\rm{ }}0.949{\rm{ }}g\\\end{array}$

Theoretical percentrecovery$\left( {{r_\% }} \right)$ from the recrystallization of 1.00g benzoic acid from 15mL

${r_\% } = \frac{{{a_{un}}}}{{{a_t}}} \times 100$

Substitute 1 g for ${a_t}$and 0.949 g for ${a_{un}}$

$\begin{array}{c}\\{r_\% } = \frac{{0.949{\rm{ g}}}}{{1{\rm{ g}}}} \times 100\% \\\\ = 94.9\% \\\end{array}$

Ans: Part a

Minimum amount of water needed to dissolve 1 g benzoic acid is 14.7 mL

Part b

Maximum theoretical percent recovery from the recrystallization of 1.00g benzoic acid from 15 mL of water is 94.9%