The solubility of compound A in ethanol is 0.8 g per 100 mL at 0°C and 5.0 g per

100 mL at 78°C. What is the minimum amount of ethanol needed to re-crystallize a
12.0 g sample of compound A? How much would be lost in the re-crystallization,
that is, would remain in the cold solvent?

You can work this by ratio and proportion or by dimensional analysis. Done by ratio and proportion looks like this.

At 78 C, we will need how much of the solvent to dissolve all 12 g?
(5g/100 mL)=(12g/x mL)
Solve for X. I did the math and obtained 240 mL but check me out on my math.

Then how much will we lose when we cool the 240 mL down to zero.
(0.8g/100 mL) = (x/240 mL)
Solve for x grams. This will be the amount that stays in the solvent at the lower temperature; in other words, the amount that would be lost from the initial 12 grams.

1.92 grams

84% maximum percent retrieval

Why did the compound go to therapy? It had trouble dissolving its problems! But let's try to dissolve this problem instead.

To find the minimum amount of ethanol needed to re-crystallize a 12.0 g sample of compound A, we need to figure out at what temperature the solubility of compound A matches or exceeds 12.0 g per 100 mL.

At 0°C, the solubility is 0.8 g per 100 mL, and at 78°C, it's 5.0 g per 100 mL. So, the solubility increases as the temperature rises.

At 0°C, the compound A would need 12.0 g / 0.8 g per 100 mL = 150 mL of ethanol to dissolve completely. But we can't dissolve in 150 mL alone.

At 78°C, the compound A would only need 12.0 g / 5.0 g per 100 mL = 240 mL of ethanol to dissolve completely.

So, the minimum amount of ethanol needed to re-crystallize a 12.0 g sample of compound A is 240 mL.

As for how much would remain in the cold solvent, those sneaky clowns can't be perfectly captured. Let's assume there will be some loss in the re-crystallization process, and a small amount of compound A would remain in the cold solvent. But don't worry, it's just clowning around!

To calculate the minimum amount of ethanol needed to re-crystallize the 12.0 g sample of compound A, we need to find the solvent-to-solute ratio that will allow all of the solute to dissolve.

First, let's find the solubility of compound A in ethanol at room temperature (25°C). We have the solubility of compound A at 0°C and 78°C, so we can estimate the solubility at 25°C using interpolation.

To interpolate, we use the formula:

(solubility at lower temperature) + ((solubility at higher temperature) - (solubility at lower temperature)) * (desired temperature - lower temperature range) / (higher temperature range - lower temperature range)

Using this formula, we can calculate:

solubility at 25°C = 0.8 g/100 mL + ((5.0 g/100 mL) - (0.8 g/100 mL)) * (25°C - 0°C) / (78°C - 0°C)
solubility at 25°C = 0.8 g/100 mL + (4.2 g/100 mL) * (25°C / 78°C)
solubility at 25°C ≈ 0.8 g/100 mL + 1.346 g/100 mL
solubility at 25°C ≈ 2.146 g/100 mL

Now, let's calculate the minimum amount of ethanol needed to re-crystallize the 12.0 g sample of compound A.

(12.0 g compound A) / (2.146 g/100 mL) = x mL ethanol

x ≈ 558.60 mL ethanol

Therefore, the minimum amount of ethanol needed to re-crystallize the 12.0 g sample of compound A is approximately 558.60 mL.

To determine how much compound A would remain in the cold solvent after re-crystallization, we can subtract the amount of compound A dissolved in the minimum amount of ethanol from the initial 12.0 g sample.

Amount remaining in the cold solvent = 12.0 g - (558.60 mL * 2.146 g/100 mL)
Amount remaining in the cold solvent ≈ 12.0 g - 11.98 g
Amount remaining in the cold solvent ≈ 0.02 g

Therefore, approximately 0.02 g of compound A would remain in the cold solvent after re-crystallization.