Question

A solution is made containing 20.8 \(\mathrm{g}\) of phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) in 425 \(\mathrm{g}\) of ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right) .\) Calculate (a) the mole fraction of phenol, ( b) the mass percent of phenol, (c) the molality of phenol.

Short answer

The short answer is: a) Mole fraction of phenol = 0.0234 b) Mass percent of phenol = 4.67% c) Molality of phenol = 0.519 mol/kg

Step-by-step solution

Calculate the moles of phenol and ethanol

First, we need to find the moles of phenol and ethanol in the solution. We can do this using the given masses and the molar masses of the two compounds. Molar mass of phenol (C6H5OH) = 6(12.01) + 5(1.01) + 16.00 + 1.01 = 94.11 g/mol Moles of phenol = mass of phenol / molar mass of phenol Moles of phenol = 20.8 g / 94.11 g/mol = 0.221 mol Molar mass of ethanol (CH3CH2OH) = 12.01 + 3(1.01) + 12.01 + 2(1.01) + 16.00 + 1.01 = 46.07 g/mol Moles of ethanol = mass of ethanol / molar mass of ethanol Moles of ethanol = 425 g / 46.07 g/mol = 9.22 mol

Calculate the mole fraction of phenol

Mole fraction of phenol (X_phenol) = moles of phenol / (moles of phenol + moles of ethanol) X_phenol = 0.221 mol / (0.221 mol + 9.22 mol) = 0.0234

Calculate the mass percent of phenol

Mass percent of phenol = (mass of phenol / total mass of solution) * 100 Total mass of solution = mass of phenol + mass of ethanol = 20.8 g + 425 g = 445.8 g Mass percent of phenol = (20.8 g / 445.8 g) * 100 = 4.67%

Calculate the molality of phenol

Molality of phenol = moles of phenol / mass of ethanol (in kg) Mass of ethanol in kg = 425 g * (1 kg / 1000 g) = 0.425 kg Molality of phenol = 0.221 mol / 0.425 kg = 0.519 mol/kg The final answers are: a) Mole fraction of phenol = 0.0234 b) Mass percent of phenol = 4.67% c) Molality of phenol = 0.519 mol/kg

Key concepts

Understanding Mole Fraction

When you hear the term "mole fraction," think of it as a way to express the composition of a solution in terms of the amount of a particular substance relative to the total number of moles present. Imagine you have a basket of apples and oranges. The mole fraction of apples would be the number of apples divided by the total number of fruits in the basket.
For any component in a solution, you can use this formula:

• Mole fraction of component (X) \( = \frac{\text{moles of component}}{\text{total moles of all components}} \)

To calculate the mole fraction for phenol in the given solution:

• We found that phenol has 0.221 moles, and ethanol has 9.22 moles.
• The total moles are 0.221 + 9.22 = 9.441 moles.
• The mole fraction of phenol is \( \frac{0.221}{9.441} = 0.0234 \).

This low number indicates that phenol is present in a small proportion compared to ethanol in the solution. Understanding this concept helps you determine the relative quantities of different substances in mixtures.

Exploring Mass Percent

Mass percent is another method to express the concentration of a component in a solution. It tells you how much of the mass of the solution comes from that component. Think of it like a pie chart, where you see the percentage slice that belongs to phenol.
The formula for calculating mass percent is:

• Mass percent of a component = \( \left(\frac{\text{mass of component}}{\text{total mass of solution}}\right) \times 100 \)

Here's how we apply this to phenol:

• The mass of phenol is 20.8 g, and the total mass of the solution (phenol + ethanol) is 445.8 g.
• The mass percent of phenol is \( \left(\frac{20.8}{445.8}\right) \times 100 = 4.67\% \).

Mass percent is vital, especially in industries where the proportion of components by weight is crucial for quality control and formulation of products like medicines and cosmetics.

Introducing Molality

Molality is a concentration unit that measures how many moles of solute are present per kilogram of solvent. It's a bit different from molarity, which uses the volume of solution. This property is useful because it doesn't change with temperature or pressure.
To find the molality of phenol in this exercise:

• We calculate using the formula: Molality (\(m\)) = \( \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \)
• Phenol here acts as the solute, so it has 0.221 moles. Ethanol, the solvent, weighs 0.425 kg.
• The molality of the solution is \( \frac{0.221\, \text{mol}}{0.425\, \text{kg}} = 0.519\, \text{mol/kg} \).

Remember, molality is a particularly convenient measure in scenarios where temperature variations might occur, such as in lab settings or certain chemical processes. It gives a clear representation of solute concentration, unaffected by the expansion or contraction of the solvent.