Problem 71 - Chemistry and Chemical Reactivity

Question

Hexachlorophene has been used in germicidal soap. What is its molar mass if \(0.640 \mathrm{g}\) of the compound, dissolved in \(25.0 \mathrm{g}\) of chloroform, produces a solution whose boiling point is \(61.93^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

The molar mass of hexachlorophene is approximately 403.8 g/mol.

Step 1: Identify known data

Given the problem, identify the known data: the mass of hexachlorophene is \(0.640\, \mathrm{g}\), the mass of chloroform is \(25.0\, \mathrm{g}\), and the boiling point of the solution is \(61.93^{\circ}\, \mathrm{C}\). The normal boiling point of chloroform is \(61.7^{\circ}\, \mathrm{C}\), and the ebullioscopic constant \(K_b\) for chloroform is \(3.63^{\circ} \mathrm{C} \cdot \mathrm{kg/mol}\).

Step 2: Calculate boiling point elevation

Use the formula for boiling point elevation: \[\Delta T_b = T_b - T_b^0\]where \(T_b\) is the boiling point of the solution and \(T_b^0\) is the boiling point of pure solvent. Thus, \[\Delta T_b = 61.93^{\circ}\, \mathrm{C} - 61.7^{\circ}\, \mathrm{C} = 0.23^{\circ}\, \mathrm{C}\].

Step 3: Determine molality

The boiling point elevation formula is: \[\Delta T_b = K_b \cdot m\],where \(m\) is the molality of the solution. Rearranging for molality,\[\m = \frac{\Delta T_b}{K_b} = \frac{0.23^{\circ}\, \mathrm{C}}{3.63^{\circ}\, \mathrm{C} \cdot \mathrm{kg/mol}} = 0.0634 \, \mathrm{mol/kg}.\]

Step 4: Calculate moles of solute

Using the definition of molality:\[m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}\]Convert the mass of chloroform to kg:\[\text{mass} = 25.0\, \mathrm{g} = 0.025\, \mathrm{kg}\]Thus, the moles of hexachlorophene is \[\text{moles} = m \times \text{mass of solvent in kg} = 0.0634 \, \text{mol/kg} \times 0.025 \, \mathrm{kg} = 0.001585 \, \text{mol}.\]

Step 5: Find molar mass of hexachlorophene

Determine the molar mass (MM) using the formula: \[\text{MM} = \frac{\text{mass of solute}}{\text{moles of solute}} = \frac{0.640\, \mathrm{g}}{0.001585\, \mathrm{mol}} = 403.8\, \mathrm{g/mol}.\]

Step 6: Conclusion

Thus, the molar mass of hexachlorophene is approximately \(403.8\, \mathrm{g/mol}\).

Key Concepts

Boiling Point Elevation

When a solute is added to a solvent, like chloroform, the boiling point of the solution differs from that of the pure solvent. This phenomenon is known as boiling point elevation. It occurs due to the solute particles disrupting the solvent molecules, which makes it harder for the solvent to vaporize, hence increasing the boiling point. In the given exercise, chloroform's normal boiling point is 61.7°C. However, with hexachlorophene dissolved in it, the boiling point increased to 61.93°C. The difference, 0.23°C, is the boiling point elevation.

Molality

Molality is a measure of the concentration of a solute in a solution. It is expressed as the number of moles of solute per kilogram of solvent. Unlike molarity, which uses volume, molality is advantageous for temperature-dependent studies, such as boiling point elevation, because mass doesn't change with temperature. In our exercise, we calculate molality by dividing the boiling point elevation by the ebullioscopic constant of chloroform, giving us a molality of 0.0634 mol/kg.

Ebullioscopic Constant

The ebullioscopic constant (\( K_b \)) is a property specific to each solvent that quantifies how much the boiling point of the solvent increases per molal concentration of a non-volatile solute. It serves as a key factor in calculating the boiling point elevation. Chloroform has a higher ebullioscopic constant (\( 3.63^{\circ} \mathrm{C} \cdot \mathrm{kg/mol} \)) compared to many other solvents, meaning even a small amount of solute can cause a noticeable increase in the boiling point.

Chloroform as Solvent

Chloroform is a commonly used solvent in experimental and lab settings due to its ability to dissolve a wide range of organic compounds. Its boiling point at 61.7°C makes it suitable for moderate temperature conditions. Additionally, chloroform's significant ebullioscopic constant means it can effectively showcase boiling point elevation in experiments, such as with our hexachlorophene example, where we determine the solute's molar mass through this property.