1. You are given a mixture containing two compounds, A and B. Both compounds have a solubility of 1 g/ 100 mL of solvent at 20 °C and 16 g/ 100 mL of solvent at 100 °C. The sample is composed of 3.5 g of A and 10 g of B. At 100 °C the entire sample just dissolves in a minimum amount of solvent. The solution is cooled to 20 °C and crystals are collected. Calculate the composition of the crystals and the yield of the process. What is the composition of the mother liquor?
2. If the crystals obtained in question (2) are recrystallized from 100 mL of solvent, what will be the yield and composition of the crystals obtained?
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At 100 degrees celsius Compound B (Has the greater mass): 10g x 100mL/16g = 62.5mL When cooled to 20 degrees celsius Compound A: 62.5mL x 1g/100mL = 0.625g Compound B: 62.5mL x 1g/100mL = 0.625g Therefore the mother liquor contains 0.625g of each. Composition of crystal Compound A = 3.5g - 0.625g = 2.875g Compound B = 10g – 0.625g = 9.375g Percent Yield Compound A = 2.875g/(2.875+9.375)g x 100% = 23.5% Compound B = 9.375g/(2.875+9.375)g x 100% = 76.5% % yield of process = (2.875+9.375)g/(3.5+10)g x 100% = 12.5g/13.5g x 100% = 90.7%
To solve these questions, we'll need to consider the solubility of the compounds A and B at different temperatures. Let's break down each question step by step:
Question 1: Calculate the composition of the crystals and the yield of the process. What is the composition of the mother liquor?
Step 1: Determine the solubility of compounds A and B at 20 °C and 100 °C:
- At 20 °C: Both A and B have a solubility of 1 g/100 mL.
- At 100 °C: Both A and B have a solubility of 16 g/100 mL.
Step 2: Calculate the amount of solvent required:
- The sample contains 3.5 grams of compound A and 10 grams of compound B.
- Since the entire sample dissolves in a minimum amount of solvent at 100 °C, the total mass of the solution is 3.5g + 10g = 13.5g.
Step 3: Determine the maximum solubility at 100 °C:
- Given that the entire sample dissolves in a minimum amount of solvent at 100 °C, the total mass of the solution is the same as the solubility at that temperature.
- At 100 °C, the solubility is 16 g/100 mL. Therefore, the solvent volume required to dissolve the sample is 13.5g / 16g/100 mL = 84.375 mL.
Step 4: Calculate the composition of the crystals:
- The crystals formed upon cooling contain the excess amount of compound A that couldn't stay in solution.
- The amount of compound A in the solution at 20 °C is given by the difference between the initial sample and the solubility at 20 °C: 3.5g - (1g/100 mL * 84.375 mL) = 2.125 g.
- The composition of the crystals is 2.125 g of compound A (100%) and 0 g of compound B.
Step 5: Calculate the yield of the process:
- The yield is the mass of the crystals obtained divided by the mass of the initial sample, then multiplied by 100%.
- The mass of the crystals obtained is 2.125 g.
- The yield is (2.125 g / (3.5 g + 10 g)) * 100% = 15.074%.
Step 6: Determine the composition of the mother liquor:
- Since all of compound A has precipitated as crystals, the composition of the mother liquor is 10 g of compound B and 0 g of compound A.
Question 2: If the crystals obtained in question (1) are recrystallized from 100 mL of solvent, what will be the yield and composition of the crystals obtained?
Step 1: Determine the solubility at 20 °C and 100 °C (same as in question 1).
Step 2: Calculate the amount of solvent required for recrystallization:
- The amount of crystals obtained in question 1 (2.125 g) is used for recrystallization.
- The crystals are dissolved in 100 mL of solvent.
Step 3: Calculate the composition of the crystals obtained:
- Since the recrystallization was performed from a saturated solution at 20 °C, the composition of the crystals will be the same as compound A's solubility at that temperature: 1 g.
Step 4: Calculate the yield of the process:
- The yield is the mass of the crystals obtained divided by the mass of the initial crystals used for recrystallization, then multiplied by 100%.
- The mass of the crystals obtained is 1 g.
- The yield is (1 g / 2.125 g) * 100% = 47.06%.
I hope this helps you understand the process of solving these questions! Let me know if you have any further inquiries.