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------------------------------------------------ What volume of water at 20 degrees Celsius is needed to dissolve 38.6 g of sucrose to make a 28% (w/w) solution?

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.