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 experiment with sucrose crystals provides evidence for a dynamic equilibrium between the saturated solution and the undissolved solute. This is because the mass of the undissolved sucrose stays constant over time, even though the crystals dissolved and re-precipitated. This observation indicates that the rates of dissolution and precipitation of sucrose in the solution are happening at equal rates, maintaining a constant solute concentration in the solution, which is consistent with a dynamic equilibrium.

Step-by-step solution

Understand Dynamic Equilibrium

Dynamic equilibrium is a state where the rate of a forward process (e.g., dissolution of a solute in a solvent) exactly equals the rate of the reverse process (e.g., precipitation of the solute from the solution). In other words, the concentrations of the reacting species remain constant over time, but microscopic processes continue to happen at a molecular level.

Initial State of the Solution

Initially, the solution is saturated with undissolved sucrose crystals weighing \(50 \mathrm{~g}\). This situation indicates that the process of sucrose dissolving into water is occurring at the same rate as the process of sucrose precipitating out of the solution; this leads to a constant concentration of dissolved sucrose, and hence we have a dynamic equilibrium established right from the beginning of the experiment.

Changes Observed After a Year

After a year, it is observed that a single large crystal of mass \(50 \mathrm{~g}\) is at the bottom of the flask. This transformation suggests that the smaller undissolved sucrose crystals have dissolved and then re-precipitated over time, combining to form a single large crystal.

Relate Observed Changes to Dynamic Equilibrium

The fact that the mass of the undissolved sucrose remains constant after a year (\(50 \mathrm{~g}\)) indicates that the concentration of sucrose in the solution stayed the same throughout the entire period. This observation is consistent with the dynamic equilibrium, where the rates of dissolution and precipitation of sucrose in the solution remain constant.

Conclusion

The experiment provides evidence for a dynamic equilibrium between the saturated solution of sucrose and the undissolved solute because, although the physical state of the solute undergoes a change (small crystals to a single larger crystal), the mass of undissolved sucrose remains the same over time. This consistency supports the idea that dissolution and precipitation processes are occurring at equal rates, maintaining a constant solute concentration in the solution.

Key concepts

Saturated Solution

A saturated solution is one that contains the maximum amount of solute that can be dissolved at a given temperature and pressure. When a solution is saturated, any additional solute added will not dissolve. Instead, it remains in the solid state in the mixture. This is because the solution has reached its solubility limit.
In the original experiment with sucrose, the saturated solution contains the maximum dissolved amount of sugar. The excess sugar, unable to dissolve, stays as crystals at the bottom of the flask. The presence of these undissolved sugar crystals indicates the saturation point has been reached. As the solution is left, the saturated nature remains through the balance created by dynamic equilibrium.
This state of thorough saturation is crucial for the establishment of equilibrium. With no net change in the concentration of the dissolved substance, the system remains balanced, and this plays a pivotal role in the study of physical chemistry and solubility.

Dissolution and Precipitation

Dissolution is the process where a solute integrates into a solvent, leading to a homogeneous mixture. Precipitation is the opposite, where dissolved particles come out of the solution and form a solid.
In the sugar solution experiment, dissolution and precipitation dynamically balance each other. When sugar dissolves, sucrose molecules enter the water, but when it precipitates, they return to a crystalline form. The dynamic equilibrium is thus established not by stagnation, but via continuous movement between these states.
This experiment elegantly shows how these processes can alternate over time to maintain equilibrium. Even after a year, solute particles are moving between being dissolved in water and being part of the crystalline structure at the bottom. This evidences the ongoing nature of dissolution and precipitation in maintaining dynamic equilibrium.

Concentration of Solute

The concentration of a solute in a solution refers to how much of that solute is present compared to the solvent. It's essential in determining saturation and equilibrium.
In a dynamic equilibrium, the concentration remains stable. In our sugar experiment, despite the physical change in the crystal form, the concentration in the solution doesn't alter when equilibrium is reached and maintained. This balance shows how a dissolved substance's concentration isn’t just about how much is initially dissolved but how the processes of dissolution and precipitation sustain the concentration over time.
The constant concentration of sucrose, as evidenced by the unchanged mass of undissolved sugar, illustrates how dynamic equilibrium is closely intertwined with concentration stability. Monitoring this stability helps in understanding chemical behaviors in various solutions and reactions.