Answer :
About 138.214 mL of water at 20°C is required to dissolve 38.6 g of sucrose for a 28% (w/w) solution.
To calculate the volume of water needed to dissolve 38.6 g of sucrose to make a 28% (w/w) solution, we first need to understand that the given percentage is a weight-to-weight percentage. This means that 28% of the total weight of the solution will be sucrose.
So, if the total weight of the solution is \(W\), then 28% of \(W\) will be sucrose. Mathematically, we can express this as:
[tex]\[ \text{Weight of sucrose} = 0.28 \times W \][/tex]
Given that the weight of sucrose is 38.6 g, we can solve for \(W\):
[tex]\[ 0.28 \times W = 38.6 \][/tex]
[tex]\[ W = \frac{38.6}{0.28} \][/tex]
[tex]\[ W ≈ 138.214 \text{ g} \][/tex]
Now, to find the volume of water needed, we can use the density of water (1 g/mL at 20°C) to convert the weight of water to volume:
[tex]\[ \text{Volume of water} = \frac{\text{Weight of water}}{\text{Density of water}} \][/tex]
[tex]\[ \text{Volume of water} = \frac{138.214 \text{ g}}{1 \text{ g/mL}} \][/tex]
[tex]\[ \text{Volume of water} ≈ 138.214 \text{ mL} \][/tex]
So, approximately 138.214 mL of water at 20°C is needed to dissolve 38.6 g of sucrose to make a 28% (w/w) solution.
