Math Problem Statement
Solution
Let's analyze the given problem step by step:
Fiona mixed 10.10 g of compound A with an unknown amount of compound B, resulting in a total mixture of 5.9 g after some compound was lost. The task is to determine how much of the recrystallized mixture Fiona would recover after recrystallizing the compounds.
Solubility Data in Water:
- The table shows solubility in 50 mL of water at different temperatures for both compounds A and B.
- At cold solvent (~5°C):
- Compound A: 0.1 g
- Compound B: 1.5 g
- At hot solvent (100°C):
- Compound A: 9.4 g
- Compound B: 2.1 g
- At cold solvent (~5°C):
Total solution prepared:
Fiona dissolved 10.10 g of compound A in 100 mL of water. However, the total mixture found after her partner added compound B weighs 5.9 g. Now, let's focus on the recrystallization step to figure out the amount of mixture that Fiona would recover.
Recrystallization Process:
-
Hot solvent at 100°C dissolves a significant portion of compound A and some compound B.
- Compound A: At 100°C, 9.4 g dissolves in 50 mL of water, meaning in 100 mL of water, 18.8 g of compound A would dissolve (but she only has 10.10 g of A).
- Compound B: At 100°C, 2.1 g dissolves in 50 mL, meaning in 100 mL, 4.2 g would dissolve (but there is only about 5.9 g total mixed material).
-
Cold solvent at ~5°C recrystallizes the compounds as follows:
- Compound A: At 5°C, 0.1 g of A dissolves in 50 mL, so in 100 mL, 0.2 g dissolves, and the remaining A recrystallizes.
- Compound B: At 5°C, 1.5 g dissolves in 50 mL, so in 100 mL, 3.0 g of B dissolves, and the rest stays dissolved.
Recovery of Compound A:
- At cold temperature (5°C), 0.2 g of compound A remains dissolved in 100 mL water. Therefore, the recrystallized amount of compound A will be:
Recovery of Compound B:
- At cold temperature (5°C), 3.0 g of compound B remains dissolved in 100 mL water, which means no significant amount of B will recrystallize.
Conclusion:
The total amount of recrystallized mixture will mostly consist of compound A, and Fiona should recover 9.9 g, corresponding to option C.
Let me know if you need further clarification or additional details!
Related Questions:
- What is recrystallization, and why is it useful for purifying compounds?
- How does solubility vary with temperature in different compounds?
- Why does compound B not recrystallize as much as compound A in this scenario?
- What would happen if Fiona used less water in the recrystallization process?
- Could the solubility of compounds in solvents other than water affect recrystallization efficiency?
Tip: Always ensure that the solution is cooled gradually to maximize the recovery of recrystallized compounds.
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Math Problem Analysis
Mathematical Concepts
Recrystallization
Solubility
Temperature Effects on Solubility
Formulas
Recrystallized Amount = Total Compound A - Solubility at Cold Temperature
Theorems
Solubility rules related to temperature in chemical solutions
Suitable Grade Level
Grades 11-12
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