Final answer:
To find the molality of a solution, divide the moles of solute by the kilograms of solvent. After calculating the moles of sucrose and converting the mass of water to kilograms, the resulting molality does not match any of the provided options. An error may exist in the question or calculation, necessitating a review of the details.
Step-by-step explanation:
To calculate the molality of a solution made by dissolving 145g of sucrose (C12H22O11) in 30 ml of water, we first need to find the number of moles of sucrose.
Moles of sucrose = mass of sucrose (g) / molar mass of sucrose (g/mol) = 145g / 342.3g/mol = 0.4237 mol
Next, we convert the volume of water to kilograms since molality is defined as moles of solute per kilogram of solvent. Water has a density of 1 g/mL, so:
Mass of water = volume of water (mL) × density of water (g/mL) = 30mL × 1g/mL = 30g
To express it in kilograms, we divide by 1000:
Mass of water (kg) = 30g / 1000 = 0.030 kg
Finally, we take the moles of sucrose and divide by the kilograms of water:
Molality (m) = moles of sucrose / kg of water = 0.4237 mol / 0.030 kg = 14.12 mol/kg
However, none of the answer choices match this calculation. It appears there might be an error either in the question details or calculation; therefore, it is recommended to double-check the given values and calculations. If the details provided were supposed to be used for determining the molality, we follow:
Molality (m) = 3.1416 mol sucrose / 0.5232 kg water = 6.00 mol/kg
Again, this does not match with the provided options. It is best to review the problem to ensure accuracy before making a selection.