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Chapter 14: Problem 71

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 \(61.93^{\circ} \mathrm{C} ?\)

Short Answer

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

Step by step solution

01

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 \(3.63^{\circ} \mathrm{C} \cdot \mathrm{kg/mol}\).
02

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, \[\Delta T_b = 61.93^{\circ}\, \mathrm{C} - 61.7^{\circ}\, \mathrm{C} = 0.23^{\circ}\, \mathrm{C}\].
03

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,\[\m = \frac{\Delta T_b}{K_b} = \frac{0.23^{\circ}\, \mathrm{C}}{3.63^{\circ}\, \mathrm{C} \cdot \mathrm{kg/mol}} = 0.0634 \, \mathrm{mol/kg}.\]
04

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 \[\text{moles} = m \times \text{mass of solvent in kg} = 0.0634 \, \text{mol/kg} \times 0.025 \, \mathrm{kg} = 0.001585 \, \text{mol}.\]
05

Find molar mass of hexachlorophene

Determine the molar mass (MM) using the formula: \[\text{MM} = \frac{\text{mass of solute}}{\text{moles of solute}} = \frac{0.640\, \mathrm{g}}{0.001585\, \mathrm{mol}} = 403.8\, \mathrm{g/mol}.\]
06

Conclusion

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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掳C. However, with hexachlorophene dissolved in it, the boiling point increased to 61.93掳C. The difference, 0.23掳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掳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.

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Most popular questions from this chapter

Suppose you dissolve \(2.56 \mathrm{g}\) of succinic acid, \(\mathrm{C}_{2} \mathrm{H}_{4}\left(\mathrm{CO}_{2} \mathrm{H}\right)_{2},\) in \(500 .\) mL of water. Assuming that the density of water is \(1.00 \mathrm{g} / \mathrm{cm}^{3},\) calculate the molality, mole fraction, and weight percentage of acid in the solution.

When salts of \(\mathrm{Mg}^{2+}, \mathrm{Ca}^{2+},\) and \(\mathrm{Be}^{2+}\) are placed in water, the positive ion is hydrated (as is the negative ion). Which of these three cations is most strongly hydrated? Which one is least strongly hydrated?

The dispersed phase of a certain colloidal dispersion consists of spheres of diameter \(1.0 \times 10^{2} \mathrm{nm}\) (a) What is the volume \(\left(V=\frac{4}{3} \pi r^{3}\right)\) and surface area \((A=\) \(\left.4 \pi r^{2}\right)\) of each sphere? (b) How many spheres are required to give a total volume of \(1.0 \mathrm{cm}^{3} ?\) What is the total surface area of these spheres in square meters?

Silver ion has an average concentration of 28 ppb (parts per billion) in U.S. water supplies. (a) What is the molality of the silver ion? (b) If you wanted \(1.0 \times 10^{2} \mathrm{g}\) of silver and could recover it chemically from water supplies, what volume of water in liters, would you have to treat? (Assume the density of water is \(1.0 \mathrm{g} / \mathrm{cm}^{3} .\) )

Which salt, \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) or \(\mathrm{Cs}_{2} \mathrm{SO}_{4}\), is expected to have the more exothermic heat of hydration? Explain briefly.
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