A solubility graph showing the solubility in grams of substance X in 100.0 g of alcohol. At 20 degrees Celsius, 24.0 grams of substance X will dissolve. At 50 degrees, 60.0 grams will dissolve.
A saturated solution of X (s) in alcohol is cooled down from 50 °C to 20 °C. 80.0 grams of X crystalize out of the solution as a solid during this process.
How much alcohol is in this solution?
A)28.8 g
B)233 g
C)180 g
D)45.0 g
80/X=(60-24)/100
X=80*100/(36)=222
The best answer is b.
To determine the amount of alcohol in the solution, we need to use the concept of solubility and the fact that the solution is saturated at both 50 °C and 20 °C.
First, let's find the change in solubility of substance X from 50 °C to 20 °C. We can calculate this by subtracting the solubility at 20 °C from the solubility at 50 °C:
Change in solubility = Solubility at 50 °C - Solubility at 20 °C
Change in solubility = 60.0 g - 24.0 g
Change in solubility = 36.0 g
This means that for every 36.0 grams of substance X, the solubility decreases by 1 °C.
Now, let's determine the amount of alcohol in the solution by subtracting the amount of substance X that crystallized out from the total amount of substance X dissolved at 50 °C:
Amount of alcohol = Total amount of substance X at 50 °C - Amount of substance X crystallized out
Amount of alcohol = 60.0 g - 80.0 g
Amount of alcohol = -20.0 g
Since the amount of alcohol cannot be negative, this means we made an error in our calculation. Let's correct it by using the change in solubility per degree Celsius.
Using the change in solubility per degree Celsius, we can calculate the difference in solubility between 50 °C and 20 °C:
Difference in solubility = Change in solubility × (50 °C - 20 °C)
Difference in solubility = 36.0 g/°C × (50 °C - 20 °C)
Difference in solubility = 36.0 g/°C × 30 °C
Difference in solubility = 1080 g
Now, we can find the total amount of substance X dissolved at 50 °C:
Total amount of substance X at 50 °C = Amount of substance X crystallized out + Difference in solubility
Total amount of substance X at 50 °C = 80.0 g + 1080 g
Total amount of substance X at 50 °C = 1160 g
Finally, we can determine the amount of alcohol in the solution:
Amount of alcohol = 1160 g - 80.0 g (amount of substance X crystallized out)
Amount of alcohol = 1080 g
Therefore, the amount of alcohol in this solution is 1080 g. None of the provided options matches this value, so there may be an error in the given information or the options.