A water solution containing 25.0% sucrose by mass, has a density of 1.25g/mL. What volume of this solution in liters, must be in an application requiring 2.50 KG of sucrose?
So a 25% solution means 25 g in 100 g solution.
100 g soln x (2,500 g/25g) = ?? g soln required to obtain 2.5 kg.
Then mass = volume x density.
Substitute and solve for volume, then convert to L.
To find the volume of the solution needed, we can start by calculating the mass of sucrose required.
Given:
Percentage of sucrose in the solution = 25.0% = 25.0/100 = 0.25
Mass of sucrose required = 2.50 kg
To get the mass of the solution required, we can use the formula:
Mass of solution = Mass of solute + Mass of solvent
Since the solution contains 25.0% sucrose by mass, the mass of the solvent (water) can be calculated as:
Mass of sucrose = Percentage of sucrose × Mass of solution
Mass of solvent = Mass of solution - Mass of sucrose
Let's calculate the mass of the solvent:
Mass of solution = Mass of solute / (Percentage of sucrose/100)
Mass of solvent = Mass of solution - Mass of sucrose
Mass of solvent = 2.50 kg / (0.25/100) - 2.50 kg
Next, we need to find the volume of the solution by dividing the mass of the solution by its density.
Volume of solution = Mass of solution / Density
Let's calculate the volume of the solution:
Volume of solution = Mass of solvent / Density
Volume of solution = (2.50 kg / (0.25/100)) / 1.25 g/mL
Since we want the volume of the solution in liters, we need to convert the volume from milliliters to liters.
1 mL = 0.001 L
So, the final volume of the solution in liters is:
Volume of solution (in L) = (2.50 kg / (0.25/100)) / (1.25 g/mL) × (1 mL/0.001 L)
Now, we can calculate the volume of the solution required.