Q141CP - Chemistry: Molecular Nature Of Matter And Change

Question

Although other solvents are available, dichloromethane $\mathbf{\left(}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}\mathbf{\right)}$ is still often used to “decaffeinate” drinks because the solubility of caffeine in ${\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$ is $\mathbf{\text{8.35}}$ times that in water.

(a) A $\mathbf{\text{100.0 mL}}$  sample of cola containing $\mathbf{\text{10.0 mg}}$ of caffeine is extracted with $\mathbf{\text{60.0 mL}}$  of ${\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$. What mass of caffeine remains in the aqueous phase?

(b) A second identical cola sample is extracted with two successive $\mathbf{\text{30.0 mL}}$ portions of  ${\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$. What mass of caffeine remains in the aqueous phase after each extraction?

(c) Which approach extracts more caffeine?

Step-by-Step Solution

Answer

(a) Mass of caffeine extracted with $60\text{ mL}$ of dichloromethane is $1.66\text{ mg}$.

(b) Mass of caffeine with first extraction of 30mL dichloromethane is  $2.85\text{ mg}$ and with second extraction is $\text{3.41 mg}$.

(c) Two successive extraction $30\text{ mL}$ dichloromethane extracts more caffeine.

Decaffeination:

An organic solvent called dichloromethane (also known as methylene chloride) is often used to remove caffeine from green tea and coffee. The coffee beans come into direct contact with the solvent during the decaffeination process, and the solvent is then removed by evaporation. Caffeine is more soluble in dichloromethane than in water.

(a) Mass of caffeine:

In the first part volume of sample, mass of caffeine and volume of caffein is given.

Volume of sample, $V_1=100\text{ mL}$   

Amount of caffeine is $10\text{ mg}$.

Volume of dichloromethane, data-custom-editor="chemistry" $V_2=60\text{ mL}$

The fraction of caffeine in the aqueous phase can be calculated by the following formula,

$f=\frac{V_1}{V_1+D{V}_2}$ 

Where, $f$  is fraction of caffein,  $V_1$ is volume of sample, $V_2$ is volume of dichloromethane, and  $d$ is the solubility of caffeine in dichloromethane.

 

Substitute known values in the above equation.

$\begin{array}{rcl}f& =& \frac{100\text{ mL}}{100\text{ mL}+8.35\times 60\text{ mL}}\\ & =& 0.166\end{array}$

Therefore, mass of caffeine can be calculated as,

$\begin{array}{rcl}\text{Mass of caffeine}& =& \text{fraction}\times \text{amount\hspace{0.17em}of\hspace{0.17em}caffeine}\\ & =& 0.166\times 10\text{ mg}\\ & =& 1.66\text{ mg}\end{array}$

Hence, the mass of caffeine remains in aqueous phase is $1.66\text{ mg}$.

(b) Mass of caffeine:

In the second part $100\text{ mL}$  sample of cola is extracted with $30\text{ mL}$  of dichloromethane.

Volume of sample, $V_1=100\text{ mL}$

Volume of dichloromethane, $V_2=30\text{ mL}$ 

 

The fraction of caffeine in the aqueous phase can be calculated by the following formula.

$f=\frac{V_1}{V_1+D{V}_2}$ 

Where, $f$  is fraction of caffein, $V_1$ is volume of sample, $V_2$  is volume of dichloromethane, and $D$ is the solubility of caffeine in dichloromethane.

 

Substitute known values in the above equation, and you get

$\begin{array}{rcl}f& =& \frac{100\text{ mL}}{100\text{ mL}+8.35\times 30\text{ mL}}\\ & =& 0.285\end{array}$ 

 

Therefore, mass of caffeine can be calculated as;

$\begin{array}{rcl}\text{Mass of caffeine}& =& \text{fraction}\times \text{amount\hspace{0.17em}of\hspace{0.17em}caffeine}\\ & =& 0.285\times 10\text{ mg}\\ & =& 2.85\text{ mg}\end{array}$ 

Thus, the mass of caffeine remains in aqueous phase after first extraction is $\begin{array}{rcl}& & 2.85\text{ mg}\end{array}$.

After first extraction the volume of is increased in becomes,

$\begin{array}{rcl}V& =& V_1+V_2\\ & =& 100\text{ mL}+30\text{ mL}\\ & =& 130\text{ mL}\end{array}$ 

 

Hence, fraction for second extraction can be calculated as below.

$f=\frac{V}{V+D{V}_2}$

Where, $f$  is fraction of caffeine, $V$  is volume of sample after first extraction which is  $130\text{ mL}$,   $V_2$ is volume of dichloromethane which is $30\text{ mL}$, and $D$  is the solubility of caffeine in dichloromethane.  

 

$\begin{array}{rcl}f& =& \frac{130\text{ mL}}{130\text{ mL}+8.35\times 30\text{ mL}}\\ & =& 0.341\end{array}$ 

Therefore, mass of caffeine can be defined as,

$\begin{array}{rcl}\text{Mass of caffeine}& =& \text{fraction}\times \text{amount\hspace{0.17em}of\hspace{0.17em}caffeine}\\ & =& 0.341\times 10\text{ mg}\\ & =& 3.41\text{ mg}\end{array}$

Thus, the mass of caffeine remains in aqueous phase after second extraction is  $3.41\text{ mg}$.

(c) More caffeine extraction:

From the above calculations it is clear that the mass of caffeine with single extraction is less than the mass of caffeine with two successive extraction method.

 

Hence, Cola sample is extracted with two successive  $30\text{ mL}$ of chloromethane extracts more caffeine.