Question

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

Short answer

In equilibrium, 36 g of NaCl dissolves, balancing dissolution and crystallization rates.

Step-by-step solution

Identify Given Information

We have a 100-gram sample of sodium chloride (NaCl) added to 100 mL of water at 0°C. At equilibrium, 64 g of NaCl remains undissolved.

Determine the Mass of NaCl Dissolved

The amount of NaCl dissolved can be found by subtracting the mass of the undissolved NaCl from the total mass added. Thus, mass dissolved = 100 g - 64 g = 36 g.

Understand the Particulate Level Equilibrium

At the particulate level, in a saturated solution at equilibrium, the rate of dissolution of NaCl solid is equal to the rate of crystallization back into solid. This means NaCl ionic particles ( ext{Na}^+ and ext{Cl}^-) are continuously moving between the solid phase and aqueous solution.

Describe Ions in Solution

In the aqueous solution, dissolved NaCl dissociates into its ions: \(\text{Na}^+\) and \(\text{Cl}^-\). These ions are solvated by water molecules and are in dynamic equilibrium with the solid NaCl, indicating no net change in the concentration of dissolved ions over time.

Key concepts

Sodium Chloride Dissolution

When sodium chloride is added to water, it begins a process known as dissolution. This process involves breaking down the structure of solid NaCl and dispersing its particles in the liquid, creating a solution. During dissolution, water molecules surround the individual sodium (Na\(^+\)) and chloride (Cl\(^-\)) ions, pulling them away from the crystal lattice structure of the solid salt.
This separation of ions is necessary for the salt to dissolve, and many interactions between the ions and the water molecules facilitate this separation. It's a competition between the attractive forces between the Na\(^+\) and Cl\(^-\) ions and the water molecules' ability to detach and encase these ions. This encapsulation by water molecules helps stabilize the ions in the solution.
Dissolution is not always 100% efficient. In scenarios like with our initial 100-gram sodium chloride sample, only 36 grams proceed to break down into free ions until the solution reaches a point where no additional salt can dissolve under those conditions, signifying it has become saturated.

Dynamic Equilibrium

Dynamic equilibrium occurs during the dissolution process when the solution reaches saturation. At this point, the dissolution of NaCl into its ions and the crystallization of ions back into solid salt occur at equal rates. For every molecule of NaCl that dissolves, one crystallizes out of solution.
This state is what we call dynamic because the processes are continuous and ongoing, yet appear static from a macroscopic standpoint. The amounts of solid NaCl and dissolved ions remain constant over time, despite the continuous exchange between the two phases.
In our example, 64 grams of undissolved sodium chloride indicate that the saturation point has been reached. At 0°C, the rate at which NaCl dissolves matches the rate at which it returns to a solid state, maintaining a steady state of equilibrium.

Ion Solvation

Ion solvation specifically describes how ions interact with and are stabilized by solvent molecules, usually water, in a solution. When NaCl dissolves, its ions are solvated by water molecules. Here's how that works:

• Each Na\(^+\) ion is surrounded by a certain number of water molecules, which aligns their negative oxygen ends toward the positive sodium ions, providing stabilization.
• Similarly, Cl\(^-\) ions are also surrounded, but here the positive hydrogen ends of water target the negatively charged chloride ions.

The stabilizing interactions between water and these ions facilitate their dispersion in the solution. It's this ability to solvate ions that makes water such an excellent solvent, particularly for ionic compounds like NaCl.
In the dynamic equilibrium of our sodium chloride solution, solvation ensures that the dissolved ions remain fairly distributed within the water, maintaining the solution as saturated where it can no longer dissolve additional salt.