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 shows evidence of a dynamic equilibrium between the saturated sucrose solution and the undissolved solute, as the transformation from many small crystals to a single large crystal occurs. This change results from sucrose molecules dissolving in the solution and crystallizing at the same time, with no net change in the mass of undissolved solute. The constant overall rate of these two processes indicates the presence of a dynamic equilibrium in the system.

Step-by-step solution

Recap: Dynamic Equilibrium

A dynamic equilibrium occurs when the rate of the forward process equals the rate of the reverse process. In the context of dissolution, when a solute dissolves in a solvent, it forms a saturated solution. A solute is in dynamic equilibrium with its solution when the rate of dissolution (solute dissolving in the solvent) is equal to the rate of crystallization (solvent releasing solute in the form of solid crystals).

Observation of the Saturated Sucrose Solution

In this experiment, a saturated solution of sucrose is formed by dissolving excess table sugar in water. There is 50 g of undissolved sucrose crystals at the beginning, and after a year, a single large crystal of mass 50 g is at the bottom of the flask. This means that over time, the multiple small crystals transformed into a single large crystal.

Dynamic Equilibrium in the Experiment

The change from many small crystals to one large crystal supports the existence of a dynamic equilibrium between the saturated sucrose solution and the undissolved solute. Sucrose molecules from small crystals dissolved in the solution, and at the same time, sucrose molecules from the solution crystallized onto the single large crystal. Since these two processes occur at a constant overall rate, there is no net change in the mass of undissolved solute present in the solution.

Conclusion

The experiment provides evidence for a dynamic equilibrium between the saturated solution and the undissolved solute. The transformation from many small crystals to a single large crystal is a result of sucrose molecules dissolving in the solution and crystallizing at the same time, with no net change in the mass of undissolved solute.