To find the molality (m) of a solution, we need to determine the moles of solute (acetic acid) per kilogram of solvent (water).
First, we calculate the moles of acetic acid using its concentration (C) and volume (V):
Moles of acetic acid (n) = concentration (C) * volume (V)
Given that the acetic acid solution has a concentration of 0.218 M, we can assume a volume of 1L (since 1L of solution is approximately equal to 1kg of solution):
n = 0.218 mol/L * 1 L = 0.218 mol
Since the density of the solution is 1.00 g/mL, we can calculate the mass of the solution:
Mass of solution = density * volume
Mass of solution = 1.00 g/mL * 1000 mL = 1000 g
To calculate the mass of the solvent (water), we subtract the mass of the solute (acetic acid) from the mass of the solution:
Mass of solvent = mass of solution - mass of solute
Mass of solvent = 1000 g - 0.218 mol * 60.05 g/mol (molar mass of acetic acid)
Mass of solvent = 1000 g - 13.0699 g = 986.9301 g
Finally, we can calculate the molality (m) using the moles of acetic acid and the mass of the solvent:
Molality (m) = moles of solute / mass of solvent (in kg)
Molality (m) = 0.218 mol / 0.9869301 kg = 0.221 mol/kg
Therefore, the molality of the acetic acid solution is 0.221 mol/kg.