To prepare a 500-gram aqueous solution containing 15% by mass of sucrose, you would need to follow these steps:

1. Determine the mass of sucrose needed:
Given that the desired solution contains 15% sucrose, we can calculate the mass of sucrose needed using the formula:
Mass of sucrose = Percentage of sucrose × Total mass of solution
Mass of sucrose = 15% × 500 grams
Mass of sucrose = 0.15 × 500 grams
Mass of sucrose = 75 grams

2. Determine the mass of water needed:
The remaining mass of the solution will be water since sucrose is the only solute present. We can calculate the mass of water using the formula:
Mass of water = Total mass of solution - Mass of sucrose
Mass of water = 500 grams - 75 grams
Mass of water = 425 grams

3. Prepare the solution:
Now that we know the mass of sucrose (75 grams) and the mass of water (425 grams) needed, we can proceed to prepare the solution. Here's how you can do it:

- Take a clean container or beaker.
- Weigh out 75 grams of sucrose using a weighing scale.
- Add the 75 grams of sucrose to the container.
- Measure out 425 grams of water using a measuring cylinder or a graduated cylinder.
- Slowly add the water to the container containing the sucrose.
- Stir the mixture gently until all the sucrose dissolves completely in the water.
- Continue stirring until you obtain a homogeneous solution.

4. Final check:
After preparing the solution, you can double-check if the final solution indeed contains 15% sucrose by calculating the mass percent of sucrose. The formula for mass percent is:
Mass percent of sucrose = (Mass of sucrose / Total mass of solution) × 100%
Mass percent of sucrose = (75 grams / 500 grams) × 100%
Mass percent of sucrose = 15%

If the mass percent of sucrose is 15%, then you have successfully prepared a 500-gram aqueous solution containing 15% by mass of sucrose.