To determine the number of grams of sucrose needed to make 925 mL of a 32.0% (w/v) sucrose solution, we need to understand the concept of percent weight/volume (w/v).
A 32.0% (w/v) solution means that there are 32.0 grams of sucrose for every 100 mL of solution. Let's break down the steps to find the mass of sucrose required for the 925 mL solution:
1. Understand the given concentration:
- A 32.0% (w/v) sucrose solution contains 32.0 grams of sucrose per 100 mL of solution.
2. Set up the proportion:
- Since the concentration is given per 100 mL, we want to find out how much sucrose is needed for 925 mL. This can be set up as a proportion.
[tex]\[
\frac{\text{32.0 grams of sucrose}}{\text{100 mL of solution}} = \frac{\text{? grams of sucrose}}{\text{925 mL of solution}}
\][/tex]
3. Solve for the unknown:
- Let [tex]\( x \)[/tex] be the mass of sucrose required for 925 mL of solution.
[tex]\[
x = \left( \frac{32.0 \, \text{grams}}{100 \, \text{mL}} \right) \times 925 \, \text{mL}
\][/tex]
4. Perform the calculation:
- Multiplying across the ratio:
[tex]\[
x = \frac{32.0 \times 925}{100}
\][/tex]
5. Calculate the result:
- Solve the above equation to find the value of [tex]\( x \)[/tex]:
[tex]\[
x = 296.0 \, \text{grams}
\][/tex]
Therefore, you need 296.0 grams of sucrose to make 925 mL of a 32.0% (w/v) sucrose solution.
