Final answer:
To calculate the molality of the given sugar solution, we need to find the moles of sugar and the kilograms of water in the solution. Once we have these values, we can divide the moles of sugar by the kilograms of water to find the molality.
Step-by-step explanation:
To calculate the molality of a solution, we need to divide the moles of solute by the mass of the solvent in kilograms. In this case, the solution is sugar (C12H22O11) with a density of 1.12 g/ml. To find the molality, we first need to find the mass of sugar in the solution. We can do this by multiplying the concentration (0.840 M) by the molar mass of sugar (342.2979 g/mol). This gives us 286.938 g of sugar in 1 L of solution. If we convert this to kilograms, we get 0.286938 kg of sugar.
Next, we need to find the mass of water in the solution. We can do this by multiplying the density (1.12 g/ml) by the volume of the solution. Assuming we have 1 L of solution, this gives us 1120 g or 1.12 kg of water.
Finally, we can calculate the molality by dividing the moles of sugar by the kilograms of water:
Molality = moles of sugar / kilograms of water = 0.286938 mol / 1.12 kg = 0.257 mol/kg.