Problem 88 - Chemistry: The Central Science

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.

Step-by-Step Solution

Answer

The experiment demonstrates evidence for a dynamic equilibrium between the saturated sucrose solution and the undissolved solute. Although the individual sucrose crystals changed, the total mass of undissolved sucrose remained constant at \(50 \mathrm{~g}\), indicating that the dissolving and crystallizing processes occurred at equal rates. The formation of a single large crystal, instead of multiple small ones, also indicates a continuous exchange of sucrose particles between the solution and the crystal over time, confirming the presence of a dynamic equilibrium.

Step 1: Understand Dynamic Equilibrium

A dynamic equilibrium is a state where the rate of a forward process is equal to the rate of its reverse process, and the concentrations of the reactants and products remain constant. In a saturated solution, the solute particles dissolve into the solvent to form a homogeneous solution, and at the same time, some solute particles re-precipitate or crystallize out of the solution. When these two processes occur at the same rate, the saturated solution is in a dynamic equilibrium state with the undissolved solute.

Step 2: Analyze the Experiment

In this experiment, we have a flask containing a saturated solution of sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)) with \(50 \mathrm{~g}\) of undissolved sucrose crystals at the bottom. The flask is sealed and left undisturbed for a year. After this time, a single large crystal of mass \(50 \mathrm{~g}\) is found at the bottom of the flask.

Step 3: Changes Observed

The changes observed in the experiment are as follows: 1. There was a transformation of small sucrose crystals into a single large crystal over one year. 2. The mass of the undissolved sucrose crystal remained constant at \(50 \mathrm{~g}\).

Step 4: Evidence for Dynamic Equilibrium

The experiment supports the dynamic equilibrium concept through the following observations: 1. Although the individual sucrose crystals changed, the total mass of the undissolved sucrose remained constant at \(50 \mathrm{~g}\). This suggests that, throughout the year, the rate at which sucrose dissolved in the solution was equal to the rate at which sucrose crystallized out of the solution. 2. The formation of a single large crystal instead of multiple small crystals indicates a continuous exchange of sucrose particles between the solution and the undissolved crystal. This is due to the dynamic nature of the equilibrium that allows solute particles to move in and out of the solution over time, eventually leading to the formation of a single, larger crystal. In conclusion, this experiment provides evidence for a dynamic equilibrium between the saturated solution and the undissolved solute by demonstrating that, even though the system appears to be static, there is a constant exchange of sucrose particles between the solution and the crystal. The overall mass of the undissolved crystal remaining constant supports the notion that the dissolving and crystallizing processes are occurring at equal rates.