Answer:
The volume of water containing 150g of sucrose is 600 mL.
Step by step explanation:
To solve this problem, we need to first determine the total mass of the solution. We know that the mass fraction of water is 0.8, which means that water makes up 80% of the solution.
Therefore, the mass fraction of the other component (sucrose) is 0.2, or 20%.
Let's assume we have a total mass of 1 kg (1000 grams) of solution, then the mass of water in the solution would be:
Mass of water = 0.8 x 1000 grams = 800 gramsSince the mass of sucrose is 20% of the total mass,
we can calculate it as:
Mass of sucrose = 0.2 x 1000 grams = 200 grams
Now we can use the density of water to calculate the volume of water that contains 800 grams.
The density of water is approximately 1 gram per milliliter (g/mL).
Therefore, the volume of water that contains 800 grams is:
Volume of water = 800 grams / 1 g/mL = 800 mL
Finally, we can calculate the volume of water that contains 150 grams of sucrose by using the mass ratio of sucrose to water, which is:
150 grams of sucrose / 200 grams of sucrose = 0.75
This means that the volume of water containing 150 grams of sucrose is 0.75 times the volume of water in the entire solution:
Volume of water containing 150g of sucrose = 0.75 x 800 mL = 600 mL
Therefore, the volume of water containing 150g of sucrose is 600 mL.