The solubility of compound A in ethanol is 0.4 g per 100 mL at 0C and 5.0 g per 100 mL at 78C. What is the minimum amount of solvent needed to recrystallize an 8.0 g sample of compound A? How much would be lost in the recrystallization? Show your work.
The minimum amount will be the amount ethanol needed to dissolve 8.0 g at 100 C.
That will be 100 mL x (8/5) = 160 mL ethanol needed.
How much is lost.
0.4g x (160/100) = solubility of A in 160 mL ethanol at zero C.
159.36
Well, I must say, recrystallization sounds like a truly mesmerizing process. But before we dive into the calculation, let's try to keep things light, shall we?
So, we have compound A, a substance that's a bit shy and doesn't like to mingle with just any solvent. In this case, it prefers ethanol, which I guess makes it a bit of a party animal, huh?
We are given that at 0°C, 0.4 g of compound A can dissolve in 100 mL of ethanol. And at a balmy 78°C, it can tolerate up to 5.0 g, feeling all loose and giggly.
Now, if we want to recrystallize our 8.0 g sample of compound A, we need to figure out the minimum amount of ethanol needed, as well as how much of our precious compound will be lost. I hope it doesn't get too emotional about it, or we might need some tissues.
First, let's determine how much ethanol we need for 8.0 g of compound A at 0°C. We can set up a simple proportion:
0.4 g / 100 mL = 8.0 g / x mL
Cross-multiplying, we find:
0.4x = 8.0 * 100
Now, let's solve for x:
x = (8.0 * 100) / 0.4
So, the minimum amount of ethanol needed at 0°C is... drumroll, please... 2000 mL, or 2.0 L. Cheers to that! We couldn't possibly disappoint our precious compound, right?
But wait, as with any party, there are always a few casualties. The difference between the original amount of compound A (8.0 g) and the amount dissolved at 0°C (0.4 g) tells us how much ends up lost, like forgotten car keys at the end of a wild night:
Loss = 8.0 g - 0.4 g
And the grand total of loss in the recrystallization process is... ta-da! It's 7.6 g.
So, I hope you enjoyed this little journey through the world of solubility and recrystallization. And remember, even in chemistry, a touch of humor can make everything a little brighter!
To determine the minimum amount of solvent needed to recrystallize compound A, we need to find the solubility of compound A at a temperature between 0°C and 78°C.
First, let's calculate the difference in solubility for every 1°C increase in temperature. The solubility of compound A increases by (5.0 g - 0.4 g) = 4.6 g for every (78°C - 0°C) = 78°C increase in temperature.
Therefore, the solubility of compound A increases by 4.6 g / 78°C = 0.059 g/°C.
Next, we need to determine the temperature at which the solubility of compound A equals the mass of the sample (8.0 g).
Let's set up the equation:
0.4 g + (0.059 g/°C) * ΔT = 8.0 g,
where ΔT is the temperature increase in degrees Celsius needed to recrystallize the sample.
Simplifying the equation:
0.059 g/°C * ΔT = 8.0 g - 0.4 g,
0.059 g/°C * ΔT = 7.6 g.
Dividing both sides of the equation by 0.059 g/°C:
ΔT = 7.6 g / 0.059 g/°C,
ΔT = 128.81°C.
Therefore, to recrystallize the 8.0 g sample of compound A, we need to increase the temperature by 128.81°C.
Now, let's calculate the amount of solvent needed to recrystallize the sample. At 78°C, the solubility of compound A is 5.0 g per 100 mL. We can set up a proportion:
5.0 g x mL
------- = --------
100 mL 128.81°C.
Cross-multiplying and solving for x:
5.0 g * 128.81°C = 100 mL * x mL,
x = (5.0 g * 128.81°C) / 100 mL,
x ≈ 6.44 g/mL.
Therefore, the minimum amount of solvent needed to recrystallize the 8.0 g sample of compound A is approximately 6.44 g/mL.
To determine the amount lost in recrystallization, we subtract the amount of compound A that can remain dissolved in the minimum amount of solvent from the original 8.0 g sample.
Amount lost = 8.0 g - (6.44 g/mL * 0.100 L),
Amount lost ≈ 8.0 g - 0.644 g,
Amount lost ≈ 7.356 g.
Therefore, approximately 7.356 grams would be lost in the recrystallization process.