Problem 77 - Chemistry The Science in Context

Question

Which of the following aqueous solutions should have the highest boiling point: \(0.0200 \mathrm{m}\) ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)\) \(0.0125 \mathrm{m} \mathrm{LiClO}_{4},\) or \(0.0100 \mathrm{m} \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Step-by-Step Solution

Answer

Answer: The aqueous solution with 0.0100 molal magnesium nitrate will have the highest boiling point among the three solutions.

Step 1: Determine the van't Hoff factor for each solute

The van't Hoff factor represents the number of particles produced by each formula unit when the solute dissolves in the solvent. For the given solutes, we have: - Ethanol (CH3CH2OH): It does not dissociate in water, so i = 1 - Lithium perchlorate (LiClO4): As a 1:1 electrolyte, it dissociates into Li+ and ClO4-, so i = 2 - Magnesium nitrate (Mg(NO3)2): It dissociates into Mg2+ and 2 NO3-, so i = 3

Step 2: Calculate the boiling point elevation for each solution

We will use the boiling point elevation formula (ΔTb = i × K_b × m) to calculate the increase in boiling point for each solution. The value of K_b for water is 0.512 °C kg/mol. For ethanol (0.0200 molality): ΔTb = 1 × 0.512 °C kg/mol × 0.0200 mol/kg = 0.0102 °C For LiClO4 (0.0125 molality): ΔTb = 2 × 0.512 °C kg/mol × 0.0125 mol/kg = 0.0128 °C For Mg(NO3)2 (0.0100 molality): ΔTb = 3 × 0.512 °C kg/mol × 0.0100 mol/kg = 0.0154 °C

Step 3: Compare the boiling point elevations and identify the solution with the highest boiling point

Comparing the boiling point elevations we calculated above: Ethanol: ΔTb = 0.0102 °C LiClO4: ΔTb = 0.0128 °C Mg(NO3)2: ΔTb = 0.0154 °C We find that the aqueous solution with Mg(NO3)2 has the highest boiling point elevation, so it will have the highest boiling point among the three solutions.

Key Concepts

van't Hoff factor

Understanding the van't Hoff factor is crucial when dealing with boiling point elevation. It's a measure of the number of particles a solute forms in a solution. For instance, the more particles there are, the greater the effect on the boiling point. This is especially important in aqueous solutions where we often deal with compounds that can dissociate into ions.

The van't Hoff factor is denoted by the symbol \(i\) and can vary based on whether a solute dissociates or not:

• Non-dissociating solutes: If a compound, like ethanol (\( ext{CH}_3 ext{CH}_2 ext{OH}\)), doesn't dissociate, each molecule remains intact, so \(i=1\).
• Electrolytes: Compounds like lithium perchlorate (\( ext{LiClO}_4\)) dissociate into two ions, \(Li^+\) and \(ClO_4^-\), making \(i=2\).
• Multivalent salts: Magnesium nitrate (\( ext{Mg}( ext{NO}_3)_2\)) dissociates into three ions, one \(Mg^{2+}\) and two \( ext{NO}_3^-\), resulting in \(i=3\).

Recognizing how many particles form after dissolution helps predict changes in physical properties, such as boiling point.

aqueous solutions

In chemistry, aqueous solutions are those where water acts as the solvent. They're essential to understanding many chemical reactions and properties because water is a universal solvent.

Aqueous solutions can involve both organic molecules and salts that dissociate into ions. These ions can interact in unique ways due to water’s polar nature. This means they can influence a liquid's boiling point because the solute particles disrupt the orderly pattern of water molecules.

Here are some typical behaviors in aqueous solutions:

• Dissolution of non-electrolytes: Water surrounds and interacts with individual molecules like ethanol which doesn’t split into ions.
• Dissolution of electrolytes: Salts such as lithium perchlorate break into ions like \(Li^+\) and \(ClO_4^-\), increasing the number of dissolved particles.

Understanding these interactions helps explain why the boiling point of solutions changes, as more particles make it harder for vapor to escape, raising the boiling point.

molarity calculations

Calculating molarity is an essential skill for working with solutions, which illustrates a solute's concentration in a solution. Molarity is expressed in moles of solute per liter of solution, making it different from molality which is moles of solute per kilogram of solvent. For boiling point elevation, you often use molality since it relates directly to the solvent's weight.

To find molarity, use the formula \(M = \frac{n}{V}\), where \(n\) is the number of moles of solute, and \(V\) is the volume of the solution in liters. This isn't just a number; it's a pathway to understanding solution behavior:

• For non-dissociating solutes like ethanol, the calculations directly give you the concentration since no further particles form.
• In dissociating solutes like \( ext{Mg}( ext{NO}_3)_2\), understanding molarity helps relate the concentration in terms of \(i\) and aids in applying it to changes in boiling and freezing points.

Using this formula correctly ensures accurate predictions of how solutions behave under various conditions, particularly when assessing boiling point elevation.