Question

A saturated solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) is made by dissolving excess table sugar in a flask of water. There are \(50 \mathrm{~g}\) of undissolved sucrose crystals at the bottom of the flask in contact with the saturated solution. The flask is stoppered and set aside. A year later a single large crystal of mass \(50 \mathrm{~g}\) is at the bottom of the flask. Explain how this experiment provides evidence for a dynamic equilibrium between the saturated solution and the undissolved solute.

Short answer

The formation of a single large \(50 \mathrm{~g}\) sucrose crystal over a year can be explained by a dynamic equilibrium between the saturated solution and the undissolved solute. In this equilibrium, the rate of dissolution of smaller crystals is equal to the rate of precipitation of sucrose onto the larger crystal. The constant mass of undissolved sucrose throughout the process supports the existence of this dynamic equilibrium in the system.

Step-by-step solution

Understanding dynamic equilibrium

Dynamic equilibrium is a state where the rate of the forward process is equal to the rate of the reverse process. In the context of a saturated solution, this means that the rate at which solute particles dissolve in the solvent is equal to the rate at which particles from the solution precipitate to form solids.

Analyze changes in sucrose crystals and solute over time

In the given scenario, the saturated solution initially has \(50 \mathrm{~g}\) of undissolved sucrose crystals at the bottom of the flask. After a year, there is a single large crystal of mass \(50 \mathrm{~g}\) at the bottom of the flask. This indicates that sucrose crystals have dissolved and new crystals have formed over time, but the total mass of the undissolved sucrose remains constant throughout the process.

Explain the process in terms of dynamic equilibrium

The formation of the single large crystal over the course of a year can be explained through a dynamic equilibrium between the saturated solution and the undissolved solute. As time passes, the smaller crystals dissolve in the solution, while new crystals precipitate out of the solution and attach to the larger crystal. This forward (dissolving) and reverse (precipitation) process occurs simultaneously at equal rates, which indicates a dynamic equilibrium between the saturated solution and the undissolved solute. The fact that the mass of the undissolved sucrose remains constant over the year provides evidence for the existence of the dynamic equilibrium in the system.