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Ch.13 - Solutions & Their Properties
Chapter 13, Problem 117

What is the normal boiling point in °C of ethyl alcohol if a solution prepared by dissolving 26.0 g of glucose (C6H12O6) in 285 g of ethyl alcohol has a boiling point of 79.1 °C? See Table 13.4 to find Kb for ethyl alcohol.

Verified step by step guidance
1
Step 1: Identify the known values from the problem. The boiling point of the solution is 79.1 °C, the mass of glucose is 26.0 g, and the mass of ethyl alcohol is 285 g. We need to find the normal boiling point of ethyl alcohol and the ebullioscopic constant (K_b) from Table 13.4.
Step 2: Calculate the molality of the solution. First, find the molar mass of glucose (C_6H_{12}O_6) by adding the atomic masses of its constituent atoms: 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. Then, convert the mass of glucose to moles by dividing by its molar mass. Finally, calculate the molality by dividing the moles of glucose by the mass of ethyl alcohol in kilograms.
Step 3: Use the boiling point elevation formula: \( \Delta T_b = K_b \times m \), where \( \Delta T_b \) is the boiling point elevation, \( K_b \) is the ebullioscopic constant, and \( m \) is the molality. Rearrange the formula to solve for \( \Delta T_b \).
Step 4: Determine the normal boiling point of ethyl alcohol. Subtract the boiling point elevation (\( \Delta T_b \)) from the boiling point of the solution (79.1 °C) to find the normal boiling point of ethyl alcohol.
Step 5: Verify the calculation by checking the units and ensuring that the steps logically follow the principles of colligative properties, specifically boiling point elevation.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a solute is dissolved in it. This phenomenon occurs because the presence of solute particles disrupts the formation of vapor above the liquid, requiring a higher temperature to reach the boiling point. The change in boiling point can be calculated using the formula ΔT_b = i * K_b * m, where ΔT_b is the boiling point elevation, i is the van 't Hoff factor, K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution.
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Boiling Point Elevation

Molality

Molality (m) is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. It is an important concept in colligative properties because it directly influences the extent of boiling point elevation. To calculate molality, one must first determine the number of moles of solute and then divide by the mass of the solvent in kilograms, providing a way to quantify the effect of solute on the solvent's properties.
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Ebullioscopic Constant (K_b)

The ebullioscopic constant (K_b) is a property of a solvent that indicates how much the boiling point of the solvent will increase per mole of solute added. Each solvent has a unique K_b value, which is used in the boiling point elevation formula. For ethyl alcohol, this constant is essential for calculating the normal boiling point when given the boiling point of a solution, allowing for the determination of the pure solvent's boiling point by reversing the elevation effect.
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Equilibrium Constant K