Suppose you need to extract an organic substance S from water into ether, where the distribution constant Kdist = [S]org/[S]aq is at first unknown.
a) By testing the solubility of the material in each solvent under saturating conditions at room temperature, you find that it has a solubility in water of 12 g L–1 but it is 36 g L–1 in ether. What is the value of Kdist for this solvent pair? Hint: Assume you start with 48 g.
b. If you use equal volumes of water and ether in your extraction, what percentage of the material will be transferred to the ether phase? Hint: Suppose you have 48 g of substance and use 1 L of each solvent, then use the solubilities in each phase and the Kdist value from part (a).
(c) What is the minimum volume of water required to dissolve 7.2 g of your substance?
d.Suppose now that you have a saturated solution in water. If you then extract this with one sixth the volume of ether as you have water, what percentage of the material will find itself in the ether phase? Hint: The Kdist value will still apply.
a) To find the value of the distribution constant (Kdist), we can use the formula:
Kdist = [S]org / [S]aq
Given that the solubility of the substance (S) in water is 12 g/L and in ether is 36 g/L, we can substitute these values into the equation:
Kdist = (36 g/L) / (12 g/L)
Kdist = 3
Therefore, the value of Kdist for this solvent pair is 3.
b) If equal volumes of water and ether are used in the extraction and you have 48 g of substance, we can calculate the percentage of the material transferred to the ether phase as follows:
Percentage in ether phase = (solubility in ether / total solubility) * 100
Solubility in ether = 36 g/L
Total solubility = (solubility in water + solubility in ether) = (12 g/L + 36 g/L) = 48 g/L
Percentage in ether phase = (36 g/L / 48 g/L) * 100
Percentage in ether phase = 75%
Therefore, 75% of the material will be transferred to the ether phase.
c) To find the minimum volume of water required to dissolve 7.2 g of the substance, we can use the solubility in water of 12 g/L:
Minimum volume of water = (mass of substance / solubility in water)
Minimum volume of water = 7.2 g / 12 g/L
Minimum volume of water = 0.6 L
Therefore, the minimum volume of water required to dissolve 7.2 g of the substance is 0.6 L.
d) If we extract a saturated solution in water with one sixth the volume of ether as water, we can calculate the percentage of the material transferred to the ether phase using the Kdist value:
Percentage in ether phase = (volume of ether / volume of water) * Kdist * 100
Given that we have one sixth the volume of ether as water, the volume of ether is:
Volume of ether = (1/6) * volume of water
Using the Kdist value from part (a) as 3:
Percentage in ether phase = ((1/6) * volume of water / volume of water) * 3 * 100
Percentage in ether phase = (1/6) * 3 * 100
Percentage in ether phase = 50%
Therefore, 50% of the material will be transferred to the ether phase.
To solve these questions, we need to calculate the distribution constant (Kdist) and use it to determine the percentage of the material transferred to the ether phase. Let's go step by step:
a) To find the value of Kdist, we need to calculate the concentration of the substance in each solvent:
Concentration of S in water = 12 g/L
Concentration of S in ether = 36 g/L
Now, divide the concentration of S in ether by the concentration of S in water to find Kdist:
Kdist = (36 g/L) / (12 g/L)
Kdist = 3
So, the value of Kdist for this solvent pair is 3.
b) If equal volumes of water and ether are used in the extraction, we can consider the volume of both solvents as 1 liter. Using the solubilities in each phase and the Kdist value from part (a), we can calculate the percentage of the material transferred to the ether phase:
Amount of substance in water = solubility in water × volume of water
= (12 g/L) × 1 L
= 12 g
Amount of substance in ether = solubility in ether × volume of ether
= (36 g/L) × 1 L
= 36 g
Percentage transferred to ether phase = (Amount of substance in ether / Total amount of substance) × 100
= (36 g / (36 g + 12 g)) × 100
= (36 g / 48 g) × 100
= 75%
Therefore, 75% of the material will be transferred to the ether phase.
c) To calculate the minimum volume of water required to dissolve 7.2 g of the substance, we can use the solubility in water:
Minimum volume of water = Mass of substance / Solubility in water
= 7.2 g / (12 g/L)
= 0.6 L
Therefore, the minimum volume of water required to dissolve 7.2 g of the substance is 0.6 liters.
d) If we start with a saturated solution in water and extract it with one-sixth the volume of ether as we have water, we can use the Kdist value to determine the percentage of the material in the ether phase:
Amount of substance in water = solubility in water × volume of water
= (12 g/L) × 1 L
= 12 g
Volume of ether = (1/6) × volume of water
= (1/6) × 1 L
= 1/6 L
Amount of substance in ether = Kdist × (Amount of substance in water)
= 3 × 12 g
= 36 g
Percentage transferred to ether phase = (Amount of substance in ether / Total amount of substance) × 100
= (36 g / (36 g + 12 g)) × 100
= (36 g / 48 g) × 100
= 75%
Therefore, 75% of the material will find itself in the ether phase.