Question

A solution is made containing \(25.5 \mathrm{~g}\) phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) in \(425 \mathrm{~g}\) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\). Calculate (a) the mole fraction of phenol, (b) the mass percent of phenol, (c) the molality of phenol.

Short answer

(a) Mole fraction of phenol (χₚᵣₑ₍ₚₕₑₙₒₗ₎) = 0.263 (b) Mass percent of phenol = 5.66% (c) Molality of phenol (m) = 5.53 mol/kg

Step-by-step solution

Determine the moles of phenol and ethanol

To calculate molality and mole fraction, we will need to determine the number of moles of each component in the solution. The molecular mass of phenol (C₆H₅OH) is: C: 6 atoms × 12.01 g/mol = 72.06 g/mol H: 6 atoms × 1.008 g/mol = 6.048 g/mol O: 1 atom × 16.00 g/mol = 16.00 g/mol Total molecular mass = 94.108 g/mol The number of moles of phenol is given by: Phenol moles = \(\frac{\text{mass}}{\text{molar mass}} = \frac{25.5 \text{ g}}{94.108 \text{ g/mol}}\) The molecular mass of ethanol (C₂H₅OH) is: C: 2 atoms × 12.01 g/mol = 24.02 g/mol H: 6 atoms × 1.008 g/mol = 6.048 g/mol O: 1 atom × 16.00 g/mol = 16.00 g/mol Total molecular mass = 46.068 g/mol The number of moles of ethanol is given by: Ethanol moles = \(\frac{\text{mass}}{\text{molar mass}} = \frac{425 \text{ g}}{46.068 \text{ g/mol}}\) Calculate the number of moles of phenol and ethanol.

Calculate the mole fraction of phenol

To calculate the mole fraction of phenol (χₚᵣₑ₍ₚₕₑₙₒₗ₎), we will use the formula: Mole fraction of phenol = \(\frac{\text{moles of phenol}}{\text{total moles in the solution}}\) χₚᵣₑ₍ₚₕₑₙₒₗ₎ = \(\frac{\text{moles of phenol}}{\text{moles of phenol} + \text{moles of ethanol}}\) Calculate the mole fraction of phenol using the previously calculated values of moles of phenol and ethanol.

Calculate the mass percent of phenol

To calculate the mass percentage of phenol, we will use the following formula: Mass percent of phenol = \(\frac{\text{mass of phenol}}{\text{total mass of the solution}} × 100\%\) Total mass of the solution = 25.5 g (phenol) + 425 g (ethanol) Calculate the mass percent of phenol using the given masses and the total mass of the solution.

Calculate the molality of phenol

To calculate the molality (m) of phenol, we will use the following formula: Molality = \(\frac{\text{moles of phenol}}{\text{mass of ethanol (solvent) in kilograms}}\) Convert the mass of ethanol to kilograms: 425 g × \(\frac{1 \text{ kg}}{1000 \text{ g}}\) Calculate the molality of phenol using the previously calculated moles of phenol and the mass of ethanol in kilograms.