Final answer:
To calculate the molality of the 1.21 m sugar (C₁₂H₂₂O₁₁) solution with a density of 1.12 g/ml, first, calculate the volume of the solution by multiplying the density by the molality. Then, convert the mass of the solution to kilograms. Next, calculate the moles of sugar. Finally, divide the moles of sugar by the mass of water in kilograms to get the molality.
Step-by-step explanation:
To calculate the molality of a solution, you need to divide the moles of solute by the mass of the solvent in kilograms. In this case, the solute is sugar (C₁₂H₂₂O₁₁) and the solvent is water. The given solution has a density of 1.12 g/ml, so the mass of the solution can be calculated by multiplying the density by the volume of the solution. Molality (m) is then calculated by dividing the moles of sugar by the mass of water in kilograms.
First, calculate the volume of the solution:
- Volume = Density x Mass
- Volume = 1.12 g/ml x 1.21 m = 1.3552 g
Next, convert the mass of the solution to kilograms:
- Mass = 1.3552 g / 1000 = 0.0013552 kg
Now, calculate the moles of sugar:
- Moles = Mass / Molar mass
- Molar mass of sugar (C₁₂H₂₂O₁₁) = (12 x 12.01) + (22 x 1.01) + (11 x 16.00) = 342.34 g/mol
- Moles of sugar = 1.21 m x 342.34 g/mol = 414.5014 g
Finally, divide the moles of sugar by the mass of water in kilograms to calculate the molality:
- Molality = Moles / Mass of water in kg
- Molality = 414.5014 g / 0.0013552 kg = 305,663.94 m