Final answer:
To make a 0.75 molal solution of table sugar in 5.00 L of water, calculate the mass of sucrose needed based on its molar mass and dissolve in enough water to make the total mass 5.00 kg.
Step-by-step explanation:
To prepare 5.00 L of a 0.75 molal solution of table sugar (C12H22O11), we need to take the concepts of molality into account. Molality is defined as the number of moles of solute per kilogram of solvent. For table sugar, which is sucrose, we need to calculate the amount of sucrose needed for this solution.
First, we calculate the mass in grams of sucrose required for the molal solution:
- Find the molar mass of sucrose (C12H22O11) by adding the atomic masses of its constituent elements: (12 × 12.01) + (22 × 1.01) + (11 × 16.00) = 342.30 g/mol.
- Calculate the mass of sucrose needed: 0.75 mol/kg × 5 kg = 3.75 moles. Multiply by the molar mass of sucrose: 3.75 moles × 342.30 g/mol = 1283.63 grams of sucrose.
Finally, dissolve the calculated amount of sucrose in enough water to make the total mass of the solution equal to 5.00 kg (since 5.00 L of water approximately equals 5.00 kg, assuming the density of water is 1 g/mL).