Step 1: Identify the number of moles of solute. In this case, it is given as 0.5 mol.
Step 2: Identify the mass of the solvent (water) given in the problem, which is 1 kg.
Step 3: Convert the mass of water to moles. The molar mass of water (H2O) is approximately 18 g/mol. Since 1 kg = 1000 g, we calculate the moles of water: 1000 g / 18 g/mol = 55.5 mol.
Step 4: Use the formula for vapor pressure lowering: Vapor pressure lowering = (n_solute / n_solvent) * P°_solvent.
Step 5: Substitute the values into the formula: n_solute = 0.5 mol, n_solvent = 55.5 mol, and P°_solvent = 23.76 mmHg.
