Final answer:
The molality of phenol in water is calculated using the mass and volume of phenol and water, converting the mass of phenol to moles, and then dividing by the mass of the water in kilograms. The calculated molality of the phenol solution is approximately 8.2375 mol/kg.
Step-by-step explanation:
To calculate the molality of phenol in water, we first need to find the mass of phenol using its density and volume. The formula for density is mass over volume, so we rearrange this to calculate the mass of phenol (mass = density × volume). With the given density of phenol as 1.070 g/ml and volume of 289.8 ml, we have:
Mass of phenol = 1.070 g/ml × 289.8 ml = 310.026 g
We then convert this mass to moles using the molar mass (mw) of phenol. The number of moles (n) is the mass (m) divided by the molar mass (M):
Moles of phenol = 310.026 g / 94.11 g/mol = approximately 3.295 mol
Now, we find the mass of the solvent, water, in kilograms. Since the density of water is 1.000 g/ml, the mass of 400.0 ml of water is 400.0 g or 0.400 kg.
The molality (m) of the solution is defined as moles of solute per kilogram of solvent. Therefore, the molality of phenol in water is:
Molality = 3.295 mol / 0.400 kg = approximately 8.2375 mol/kg
This is the required molality of the phenol solution.