Answer :
Final answer:
The student is seeking to determine the volume of water at 20 degrees Celsius necessary to dissolve 38.6 g of sucrose to create a 28% sucrose solution by weight. This involves calculating the total mass of the solution where 38.6 g represents 28%, subtracting the mass of sucrose to find the mass of water, and then converting this mass to volume because the density of water at 20 degrees Celsius is about 1 g/mL.
Explanation:
The question asks for the volume of water at 20 degrees Celsius needed to dissolve 38.6 g of sucrose (C12H22O11) to make a 28% (w/w) solution. To solve this, we apply the concept of percent weight/weight (% w/w), which requires us to find a total solution weight in which 38.6 g of sucrose will constitute 28%.
Here's the calculation:
- Determine the total mass of the solution using the percentage of sucrose: 38.6 g is 28% of the total mass (M), so M = 38.6 g / 0.28.
- Calculate M to find the total mass of the solution.
- Subtract the mass of sucrose from the total mass to find the mass of water needed.
- Knowing that the density of water is approximately 1 g/mL at 20 degrees Celsius, convert the mass of water to volume by using the conversion 1 g = 1 mL.
Thus, the volume of water required can be found after completing the calculations from the above steps.
