Question

Although other solvents are available, dichloromethane \(\left(\mathrm{CH}_{2} \mathrm{Cl}_{2}\right)\) is still often used to "decaffeinate" drinks because the solubility of caffeine in \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) is 8.35 times that in water. (a) A 100.0 -mL sample of cola containing 10.0 mg of caffeine is extracted with \(60.0 \mathrm{~mL}\) of \(\mathrm{CH}_{2} \mathrm{Cl}_{2} .\) What mass of caffeine remains in the aqueous phase? (b) A second identical cola sample is extracted with two successive \(30.0-\mathrm{mL}\) portions of \(\mathrm{CH}_{2} \mathrm{Cl}_{2} .\) What mass of caffeine remains in the aqueous phase after each extraction? (c) Which approach extracts more caffeine?

Short answer

Part (a): 1.67 mg of caffeine remains in the aqueous phase. Part (b): 0.81 mg of caffeine remains after two extractions. Part (c): Two successive extractions extract more caffeine.

Step-by-step solution

- Determine Distribution Coefficient (Part a)

The distribution coefficient (D) is the ratio of the solubility of caffeine in dichloromethane to that in water. Given: D = 8.35.

- Calculate Remaining Caffeine After Single Extraction (Part a)

Use the formula for single extraction: \[ \text{remaining caffeine} = \frac{10.0\text{ mg}}{1 + \frac{60 \text{ mL} \times 8.35}{100 \text{ mL}}} \] Solve: \[ \text{remaining caffeine} = \frac{10.0 \text{ mg}}{1 + 5.01} = 1.67 \text{ mg} \]

- Calculate Remaining Caffeine After First Extraction (Part b)

For two successive extractions, first calculate the caffeine remaining after the first extraction using 30 mL of CH2Cl2: \[ \text{remaining caffeine} = \frac{10.0 \text{ mg}}{1 + \frac{30 \text{ mL} \times 8.35}{100 \text{ mL}}} \] Solve: \[ \text{remaining caffeine} = \frac{10.0 \text{ mg}}{1 + 2.505} = 2.85 \text{ mg} \]

- Calculate Remaining Caffeine After Second Extraction (Part b)

Use the remaining caffeine from the first extraction as the initial amount for the second extraction: \[ \text{remaining caffeine} = \frac{2.85 \text{ mg}}{1 + \frac{30 \text{ mL} \times 8.35}{100 \text{ mL}}} \] Solve: \[ \text{remaining caffeine} = \frac{2.85 \text{ mg}}{1 + 2.505} = 0.81 \text{ mg} \]

- Compare the Extraction Methods (Part c)

Compare the results of the single extraction and the two successive extractions. The single extraction leaves 1.67 mg of caffeine, while two successive extractions leave 0.81 mg, showing that the two-successive extraction method is more efficient.

Key concepts

distribution coefficient

The distribution coefficient, often represented as \(D\), is a ratio that describes how a compound is distributed between two immiscible solvents. In this exercise, the distribution coefficient of caffeine between dichloromethane \((CH_2Cl_2)\) and water is given as 8.35. This tells us that caffeine is 8.35 times more soluble in dichloromethane than in water. Understanding the distribution coefficient helps in predicting how much compound will remain in each phase after extraction.
Here's how it's calculated and used:

• Determine the solubility of caffeine in both solvents.
• Calculate the ratio of these solubilities to find \(D\).
• Apply this coefficient in extraction formulas to find how much caffeine remains in each phase.

Using \(D\) simplifies the calculations and provides a clear picture of the efficiency of the extraction process.

solubility

Solubility refers to the amount of a substance (solute) that can dissolve in a given volume of solvent. In extraction processes, understanding solubility is crucial because it dictates how much of the compound will dissolve in each solvent. When caffeine's solubility is 8.35 times higher in dichloromethane \((CH_2Cl_2)\) than in water, it means that dichloromethane is a far better solvent for extracting caffeine from cola.
Key points to remember about solubility in this context:

• Higher solubility in a solvent means that more of the solute can be dissolved in it.
• The comparison of solubilities in two solvents helps determine the distribution coefficient.
• Solubility data is essential for predicting how a substance will behave in different extraction scenarios.

In the exercise, using the given solubility ratio was instrumental in determining how much caffeine could be efficiently extracted using dichloromethane.

aqueous phase

The aqueous phase is the water-containing layer in a liquid-liquid extraction process. In this case, it's the phase where the cola (an aqueous solution) holds dissolved caffeine. After extracting the caffeine with dichloromethane, we need to determine how much caffeine remains in this aqueous phase.

• Starting with a known caffeine amount in the aqueous phase.
• Applying the distribution coefficient to calculate how caffeine redistributes between the aqueous and organic phases.
• Using formulas to find the concentration of caffeine left in the aqueous phase post-extraction.

This process helps to understand the efficiency of the extraction method and how much of the target compound would remain in the water layer.

dichloromethane

Dichloromethane \(CH_2Cl_2\), also known as methylene chloride, is a common organic solvent used in chemical extractions. It is particularly chosen for caffeine extraction due to its high solubility for caffeine.

• It's immiscible with water which allows for clear separation of layers.
• High caffeine solubility means it can pull more caffeine out of the aqueous phase in each extraction step.
• Safe handling and disposal are crucial due to its volatility and potential health risks.

In this exercise, dichloromethane's role is pivotal as it determines how effectively caffeine can be extracted from the cola. The repeated use of smaller volumes of dichloromethane in successive extractions was demonstrated to be more efficient than a single extraction with a larger volume, highlighting the practical aspects of choosing optimal extraction methods.