What is the molality of a solution composed of 192g of acetone ((CH3)2CO) dissolved in 416g of water

To calculate the molality of a solution, we first need to know the moles of solute and the mass of the solvent.

Step 1: Calculate the moles of solute (acetone):

The molar mass of acetone ((CH3)2CO) is calculated by adding up the atomic masses of its constituent elements:
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol
Molar mass of O = 16.00 g/mol

Total molar mass of acetone = (2 × molar mass of C) + (6 × molar mass of H) + molar mass of O
= (2 × 12.01 g/mol) + (6 × 1.01 g/mol) + 16.00 g/mol
= 58.08 g/mol

Now, we can convert the mass of acetone to moles using its molar mass:
Moles of acetone = Mass of acetone / Molar mass of acetone
= 192 g / 58.08 g/mol
≈ 3.31 mol

Step 2: Calculate the mass of solvent (water):

The mass of solvent is given as 416g of water.

Step 3: Calculate the molality:

Molality (m) is defined as the moles of solute per kilogram of solvent.

First, we need to convert the mass of water from grams to kilograms:
Mass of water in kg = 416 g / 1000
= 0.416 kg

Now, we can calculate the molality:
Molality (m) = Moles of solute / Mass of solvent in kg
= 3.31 mol / 0.416 kg
≈ 7.96 mol/kg

Therefore, the molality of the solution is approximately 7.96 mol/kg.