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If cost per gram were not a concern, which of the following substances would be the most efficient per unit mass for melting snow from sidewalks and roads: glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right), \mathrm{LiCl}, \mathrm{NaCl}\), or \(\mathrm{CaCl}_{2}\) ? Explain.

Short Answer

Expert verified
CaCl鈧 is the most efficient because it produces the most ions, enhancing its snow-melting capacity.

Step by step solution

01

Understanding the concept

To determine which substance is the most efficient per unit mass for melting snow, we need to understand that this involves examining the colligative properties, specifically the freezing point depression. Substances that dissociate into more ions in solution cause a greater decrease in the freezing point, making them more efficient in melting snow.
02

Counting ions

Assess the number of ions each substance dissociates into in solution. Glucose does not dissociate into ions (it remains as one molecule in solution), LiCl dissociates into 2 ions (Li鈦 and Cl鈦), NaCl also dissociates into 2 ions (Na鈦 and Cl鈦), and CaCl鈧 dissociates into 3 ions (Ca虏鈦 and 2Cl鈦).
03

Calculating effective units per mass

Since CaCl鈧 dissociates into 3 ions, it has a higher ion production than NaCl and LiCl, which dissociate into only 2 ions per formula unit. More ions mean greater freezing point depression per unit mass, making CaCl鈧 the more efficient choice since we aren鈥檛 considering cost per gram.

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Key Concepts

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

Freezing Point Depression
Freezing point depression is a colligative property, meaning it is a property of solutions that depend on the number of solute particles in the solvent, not the identity of the solute. This effect occurs when a solute is added to a solvent, such as when salt is mixed with water. The presence of solute particles interferes with the formation of the solid structure of ice, thus lowering the temperature at which the liquid becomes solid. This is why we add substances like salt to roads and sidewalks during winter. The freezing point of water is depressed, melting existing snow and preventing new snow from forming ice. An important point about freezing point depression is that it is directly related to the number of particles that the solute dissociates into when dissolved. More particles lead to a greater depression of the freezing point. This efficiency in lowering the freezing point makes certain compounds more effective for applications like de-icing than others. Choosing the right compound involves looking at how many ions it can produce in solution.
Dissociation of Compounds
When certain compounds are dissolved in water, they break apart into ions, a process known as dissociation. This is significant in determining how well a compound can depress the freezing point of a solution. The number of ions produced is indicative of how effective the compound will be for applications like de-icing, where maximum freezing point depression is desirable. Let's consider some examples:
  • Glucose (C6H12O6): Glucose does not dissociate in water; it stays as whole molecules, meaning it will have minimal impact on freezing point depression.
  • LiCl and NaCl: These ionic compounds dissociate into two ions in water (Li鈦/Na鈦 and Cl鈦), providing a moderate impact on the lowering of the freezing point per mole of compound.
  • CaCl2: This compound dissociates into three ions (Ca虏鈦 and two Cl鈦 ions), making it particularly effective at lowering the freezing point compared to solutes that produce fewer ions. As a result, CaCl2 is more efficient for melting snow for the same amount of mass compared to the others.
Understanding the dissociation of compounds helps us choose the most efficient substances to use based on their ability to produce ions.
Ionic Compounds Efficiency
The efficiency of ionic compounds in colligative properties like freezing point depression is primarily determined by the number of ions generated in solution. The more ions a solute provides, the more effective it is at disrupting the solvent's ability to freeze, hence being more efficient at processes like de-icing. In a practical sense, this is why we compare different compounds to see how many ions they can produce:
  • Glucose: No ions produced, thus very inefficient for freezing point depression.
  • LiCl and NaCl: They both generate two ions per formula unit, meaning their efficiency is similar but moderate.
  • CaCl2: Produces three ions per unit, making it the most efficient ionic compound in this context since more ions result in greater freezing point depression.
This understanding is crucial when selecting materials for real-world applications like de-icing. Without considering cost, a compound like CaCl2 is superior because it provides the greatest efficiency at a molecular level due to its higher dissociation into ions.

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Most popular questions from this chapter

What is the vapor pressure in \(\mathrm{mm} \mathrm{Hg}\) of the following solutions, each of which contains a nonvolatile solute? The vapor pressure of water at \(45.0^{\circ} \mathrm{C}\) is \(71.93 \mathrm{~mm} \mathrm{Hg}\). (a) A solution of \(10.0 \mathrm{~g}\) of urea, \(\mathrm{CH}_{4} \mathrm{~N}_{2} \mathrm{O}\), in \(150.0 \mathrm{~g}\) of water at \(45.0^{\circ} \mathrm{C}\) (b) A solution of \(10.0 \mathrm{~g}\) of LiCl in \(150.0 \mathrm{~g}\) of water at \(45.0^{\circ} \mathrm{C}\), assuming complete dissociation

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An aqueous solution of a certain organic compound has a density of \(1.063 \mathrm{~g} / \mathrm{mL}\), an osmotic pressure of \(12.16\) atm at \(25.0^{\circ} \mathrm{C}\), and a freezing point of \(-1.03^{\circ} \mathrm{C}\). The compound is known not to dissociate in water. What is the molar mass of the compound?

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A \(0.944\) M solution of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), in water has a density of \(1.0624 \mathrm{~g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\). What is the concentration of this solution in the following units? (a) Mole fraction (b) Mass percent (c) Molality

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