Problem 10 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

A solute has a partition coefficient of 28.7 between trichloromethane \(\left(\mathrm{CHCl}_{2}\right)\) and water. \(20 \mathrm{cm}^{3}\) of \(\mathrm{CHCl}_{3}\) were added to \(100 \mathrm{cm}^{3}\) of an aqueous solution of the solute. At equilibrium, the aqueous layer contained a concentration of \(0.005 \mathrm{moldm}^{-3} .\) What was the concentration of the organic layer? (Assume \(k=1\).) (Section 11.3 )

Step-by-Step Solution

Answer

The concentration of the organic layer was 0.1435 mol/dm^3.

Step 1: Understand the Partition Coefficient Formula

The partition coefficient (k) between two solvents, such as trichloromethane and water, indicates how a solute distributes itself between the two solutions. The formula is \( k = \frac{C_{organic}}{C_{aqueous}} \), where \( C_{organic} \) is the concentration of the solute in the organic layer and \( C_{aqueous} \) is the concentration in the aqueous layer.

Step 2: Substitute Known Values into Formula

We know \( k = 28.7 \) and \( C_{aqueous} = 0.005 \text{ mol/dm}^3 \). We need to find \( C_{organic} \). Substitute these values into the partition coefficient formula: \( 28.7 = \frac{C_{organic}}{0.005} \).

Step 3: Solve for Organic Layer Concentration

To find \( C_{organic} \), rearrange the equation \( C_{organic} = 28.7 \times 0.005 \). Calculate the product to find the concentration of the organic layer.

Step 4: Calculate the Final Value

Perform the multiplication: \( C_{organic} = 0.1435 \text{ mol/dm}^3 \). Thus, the concentration of the organic layer is \( 0.1435 \text{ mol/dm}^3 \).

Key Concepts

Extraction Process

The extraction process is a vital technique in chemistry used to separate compounds based on their different solubilities in two immiscible liquids, typically an organic solvent and water. In our example, trichloromethane (also known as chloroform) and water are the two solvents involved. The solute moves between these two layers until it reaches equilibrium, meaning it distributes itself according to its relative affinity for each solvent.
If a solute is more soluble in one solvent, it will be found in higher concentration there. This separation is crucial for purifying compounds or isolating specific components from mixtures.
Understanding the extraction process helps chemists predict how a solute distributes itself across different phases and design experiments to harness this behavior effectively.

Chemical Equilibrium

Chemical equilibrium plays a central role in the extraction process. In our exercise, equilibrium is reached when the rate at which the solute moves from the aqueous phase to the organic phase equals the rate at which it moves back. At this point, the concentrations of the solute in both solvents become constant, even though molecules continue to move between the phases.
The concept of equilibrium is essential for calculating the concentrations correctly. It allows us to use the partition coefficient, a constant value describing the ratio of solute concentration between the organic and aqueous phases at equilibrium. Having a clear understanding of equilibrium dynamics aids in anticipating how variables like temperature or pressure might influence the extraction outcome.

Organic Chemistry

In organic chemistry, extractions are often used because many organic compounds are more soluble in organic solvents like trichloromethane than in water. This is due to the non-polar nature of many organic compounds compared to the polar nature of water.
Organic chemistry emphasizes the importance of solvent choice. The solvent should selectively dissolve the target compound without dissolving impurities. Additionally, the organic solvent should not mix with water to form a single phase, as this would hinder effective separation.
Understanding the nature of the solute, such as whether it is polar or non-polar, helps chemists select the appropriate organic solvent for efficient extractions, ensuring high yields and pure products.

Concentration Calculations

Accurate concentration calculations are fundamental when performing extractions since they determine how much of a solute is present in each phase. In our exercise, we use the partition coefficient to calculate the concentration of the solute in the organic layer.
The partition coefficient formula is:

• \( k = \frac{C_{organic}}{C_{aqueous}} \)

Knowing the partition coefficient and the concentration in the aqueous layer allows for straightforward calculations of the concentration in the organic layer. This is done by rearranging the formula:

• \( C_{organic} = k \times C_{aqueous} \)

This approach ensures precision, reducing errors in practical experimentation and verifying our understanding of the system's equilibrium state. Calculations like these are pivotal in both laboratory and industrial settings to achieve desirable outcomes.