Problem 70 - Chemistry: An Atoms-Focused Approach

Question

Determine the boiling point of an aqueous solution that is \(2.50 \mathrm{m}\) ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right) ; K_{\mathrm{b}}\) for water is \(0.52^{\circ} \mathrm{C} / \mathrm{m} .\) Assume that the boiling point of pure water is \(100.00^{\circ} \mathrm{C}\).

Step-by-Step Solution

Answer

Answer: The boiling point of the 2.50 m ethylene glycol aqueous solution is 101.30°C.

Step 1: Write down the boiling point elevation formula

The formula to calculate the boiling point of a solution is given by: \(\Delta T_b = K_b \times m\) where \(\Delta T_b\) is the change in boiling point, \(K_b\) is the boiling point elevation constant, and \(m\) is the molality of the solute.

Step 2: Input the given values

We are given the molality of the ethylene glycol solution (\(m = 2.50 \mathrm{m}\)) and the boiling point elevation constant for water (\(K_b = 0.52^{\circ} \mathrm{C} / \mathrm{m}\)). Plug these values into the formula: \(\Delta T_b = (0.52^{\circ} \mathrm{C} / \mathrm{m}) \times (2.50 \mathrm{m})\)

Step 3: Calculate the change in boiling point

Multiply the values to find the change in boiling point: \(\Delta T_b = 1.30^{\circ}\mathrm{C}\)

Step 4: Find the boiling point of the solution

To find the boiling point of the solution, add the change in boiling point to the boiling point of pure water, which is given as \(100.00^{\circ}\mathrm{C}\): Boiling point of solution = \(100.00^{\circ}\mathrm{C} + 1.30^{\circ}\mathrm{C} = 101.30^{\circ}\mathrm{C}\)

Step 5: State the final answer

The boiling point of the 2.50 m ethylene glycol aqueous solution is \(101.30^{\circ}\mathrm{C}\).

Key Concepts

Ethylene Glycol

Ethylene Glycol is a common organic compound with the formula \( ext{HOCH}_2 ext{CH}_2 ext{OH}\). It's primarily used as an antifreeze and in the manufacture of polyester fibers. Ethylene glycol is highly soluble in water, which makes it effective in lowering the freezing point and raising the boiling point of water. This property is crucial for applications where temperature extremes can be detrimental.

• Clear and odorless liquid.
• Miscible with water.
• Used in engine cooling systems.

Understanding ethylene glycol's role in boiling point elevation can help explain real-world scenarios like improving the performance of car radiators.

Molality

Molality is a measure of the concentration of a solute in a solution, expressed in moles of solute per kilogram of solvent. Unlike molarity, molality does not change with temperature since it involves mass rather than volume. This consistency becomes particularly useful in scenarios involving temperature changes, like boiling and freezing point calculations.

• Expressed as mol/kg.
• Stable across temperature changes.
• Widely used in colligative properties calculations.

For example, in this solution, the molality is 2.50 m, which directly impacts the change in boiling point.

Boiling Point of Water

The boiling point of water is a well-known reference point, standardized at 100°C at 1 atm of pressure. Understanding this baseline helps in studying how solutes affect boiling and freezing points. Adding a solute like ethylene glycol increases the boiling point due to colligative properties, where properties of solutions depend on the number of solute particles present rather than their identity.

• Standard boiling point: 100°C at 1 atm.
• Used as a reference for many scientific calculations.
• Affected by atmospheric pressure and solute presence.

Knowing this allows us to accurately calculate the new boiling points of solutions in various conditions.

Boiling Point Elevation Constant

The boiling point elevation constant, denoted \(K_b\), is a proportionality constant that relates the molality of a solution to the elevation in its boiling point. Each solvent has a unique \(K_b\), reflecting how the solvent's boiling point is affected by the addition of a solute. For water, \(K_b = 0.52^{\circ} ext{C/m}\), indicating that for every 1 molal increase in concentration, the boiling point rises by 0.52°C.

• Specific to each solvent.
• Used in calculating boiling point changes.
• Importance in colligative properties.

Applying this constant allows us to determine that a solution with 2.50 molality of ethylene glycol results in a boiling point increase of 1.30°C.