Problem 94 - Chemistry and Chemical Reactivity

Question

A 100 -gram sample of sodium chloride (NaCl) is added to \(100 .\) mL of water at \(0^{\circ} \mathrm{C} .\) After equilibrium is reached, about \(64 \mathrm{g}\) of solid remains undissolved. Describe the equilibrium that exists in this system at the particulate level.A 100 -gram sample of sodium chloride (NaCl) is added to \(100 .\) mL of water at \(0^{\circ} \mathrm{C} .\) After equilibrium is reached, about \(64 \mathrm{g}\) of solid remains undissolved. Describe the equilibrium that exists in this system at the particulate level.

Step-by-Step Solution

Answer

At equilibrium, NaCl is both dissolved as ions and undissolved as a solid, in a dynamic exchange at a 35.7 g/100 mL solubility limit.

Step 1: Determine Total Amount of Sodium Chloride

You start with a 100-gram sample of sodium chloride (NaCl). This is the total amount available to dissolve in water.

Step 2: Establish Available Solubility Information

At 0°C, the solubility of sodium chloride in water is approximately 35.7 grams per 100 mL. Compare this with the total amount of NaCl you have.

Step 3: Calculate Saturation Amount

Since the solubility is 35.7 grams per 100 mL, this means that only 35.7 grams can dissolve in the given volume of water at 0°C. This is the maximum amount that the water can hold.

Step 4: Identify Undissolved Sodium Chloride

After maximum solubility is reached, the rest of the sodium chloride remains as solid. Starting with 100 grams, and knowing only 35.7 grams can dissolve, 64.3 grams should remain undissolved (which is closely aligned with the given 64 grams).

Step 5: Describe Particle Dynamics at Equilibrium

At equilibrium, the system contains both dissolved ions and solid NaCl. Dissolved NaCl is present as separated Na⁺ and Cl⁻ ions in the water. The solid NaCl constitutes the ions in the crystal lattice that remains undissolved. These two forms are in dynamic balance, where the rate of NaCl dissolving is equal to the rate of dissolved ions precipitating back.

Key Concepts

Solubility

When we talk about solubility, we are referring to the maximum amount of a substance that can dissolve in a solvent at a specific temperature. In this case, sodium chloride (NaCl) is the solute and water is the solvent. At 0°C, the solubility of sodium chloride in water is 35.7 grams per 100 mL of water.
This means that in our situation, with 100 mL of water, only 35.7 grams of NaCl can completely dissolve. Solubility depends on temperature, and different substances have different solubilities. When a solution reaches its maximum solubility point, it is said to be saturated.

• The solubility can change with temperature.
• Substances with high solubility dissolve more readily.
• A saturated solution has dissolved the maximum amount of solute possible.

This concept of solubility helps us understand why only part of the total NaCl added will dissolve while the rest remains as a solid.

Sodium Chloride

Sodium chloride, commonly known as table salt, is an ionic compound made up of sodium (Na⁺) and chloride (Cl⁻) ions. These ions are held together in a regular crystal lattice structure.
In water, if it is below its solubility limit, sodium chloride dissolves completely. It separates into individual Na⁺ and Cl⁻ ions. These ions are then distributed evenly throughout the water.
However, if there is more NaCl than the water can dissolve, excess remains as solid crystals. This leftover amount is what stays undissolved due to reaching the solubility limit.

• NaCl is essential for life, used universally in food and industrial applications.
• When dissolved in water, NaCl breaks down into its constituent ions.
• The undissolved portion forms a saturated solution along with dissolved ions.

Understanding the nature of sodium chloride helps explain why only some of it dissolves completely in water under given conditions.

Dynamic Equilibrium

The concept of dynamic equilibrium in chemistry is crucial when understanding dissolved salts like sodium chloride. Dynamic equilibrium occurs in a saturated solution where the process of dissolution and crystallization occur at the same rate.
In our system containing undissolved sodium chloride, once equilibrium is achieved, ions continue to dissolve into the water while simultaneously others form back into a solid.
This creates a constant, yet balanced, state where the concentration of dissolved ions remains stable over time.

• Dynamic equilibrium maintains the balance between the dissolved and undissolved states.
• The rates of dissolution and precipitation are equal.
• Even though changes occur, the system appears static at a macroscopic level.

This balance ensures that the dissolved Na⁺ and Cl⁻ions are present in constant amounts, making the solution saturated but stable.

Ionic Compounds

Ionic compounds, like sodium chloride, are composed of metals and non-metals. Sodium, a metal, donates electrons to chlorine, a non-metal. This creates positively charged sodium ions (Na⁺) and negatively charged chloride ions (Cl⁻).
The strong electrostatic attraction between these opposite charges holds the ions together in a rigid lattice structure. This gives ionic compounds like NaCl distinct properties, such as high melting points and solubility in water.
When added to water, the ionic bonds in NaCl are overcome by the attraction of water molecules, spreading the ions throughout the solvent.

• Ionic compounds consist of ions bonded by electrostatic forces.
• They dissolve in polar solvents, like water, due to attraction forces.
• The lattice structure lends them high stability and characteristic behaviors.

Understanding ionic compounds clarifies why they can dissolve in water and form dynamic equilibria efficiently.