Question

Potassium permanganate \(\left(\mathrm{KMnO}_{4}\right)\) has a solubility of \(6.4 \mathrm{~g} / 100 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) at \(20^{\circ} \mathrm{C}\) and a curve of solubility vs. temperature that slopes upward to the right. How would you prepare a supersaturated solution of \(\mathrm{KMnO}_{4} ?\)

Short answer

Dissolve \(\text{KMnO}_4\) in hot water; then cool slowly to 20°C.

Step-by-step solution

Understand Supersaturation

A supersaturated solution contains more solute than can be dissolved under normal circumstances. This can be achieved by increasing the solubility temporarily and then cooling the solution down.

Determine the Solubility at Higher Temperature

Since the solubility curve of \(\text{KMnO}_4\) slopes upward to the right, solubility increases with temperature. Choose a higher temperature (e.g., 50°C) where the solubility will be higher than at 20°C.

Dissolve \(\text{KMnO}_4\) in Water

Measure out a certain amount of water, say 100 g. Gradually heat the water to the chosen higher temperature (e.g., 50°C). Add \(\text{KMnO}_4\) into the water and stir until no more \(\text{KMnO}_4\) can dissolve.

Cool the Solution Slowly

Once all the \(\text{KMnO}_4\) has dissolved at the higher temperature, slowly cool the solution back down to 20°C. Do this gradually to avoid premature crystallization.

Obtain Supersaturated Solution

As the solution cools, it will be supersaturated because it contains more \(\text{KMnO}_4\) than it can normally hold at 20°C. Handle the solution carefully to avoid disturbing the formation of crystals.

Key concepts

Solubility

Solubility refers to the maximum amount of a solute that can dissolve in a solvent at a given temperature and pressure. For example, at 20°C, potassium permanganate (KMnO₄) has a solubility of 6.4 g per 100 g of water. Solubility varies depending on the nature of the solute and solvent, as well as environmental conditions. Factors such as temperature, pressure, and the presence of other chemicals can significantly influence solubility. Understanding solubility is crucial for preparing solutions in chemistry, as this determines how much solute can be added before the solution becomes saturated.

Temperature Dependence

Temperature dependence means that the solubility of many substances changes with temperature. For KMnO₄, the solubility curve slopes upward to the right, which means its solubility increases as the temperature rises. When you heat the solution, more KMnO₄ can be dissolved in water. This property is harnessed when creating a supersaturated solution. By heating the water, you can dissolve more solute than would be possible at room temperature. This later allows for temporary supersaturation when the solution is cooled back down to a lower temperature.

Crystal Formation

Crystal formation occurs when the dissolved solute in a solution comes out of the solution and forms solid particles. In a supersaturated solution, any disturbance can trigger this process. For example, a tiny seed crystal or slight agitation can cause the excess solute to form crystals. This is because the solution holds more solute than it can normally at that temperature. The molecules of the solute start to come together and form a structured, repeating pattern, which grows into visible crystals. Handling supersaturated solutions with care is essential to prevent premature crystallization.

Supersaturation Process

The supersaturation process involves creating a solution that contains more dissolved solute than it can normally hold at a given temperature. To prepare a supersaturated solution of KMnO₄, follow these steps:

• Step 1: Heat the solvent (water) to a higher temperature such as 50°C.
• Step 2: Add KMnO₄ to the hot solvent and stir until no more can dissolve.
• Step 3: Slowly cool the solution back down to 20°C.

As the solution cools, it will become supersaturated because it retains more dissolved KMnO₄ than it would typically hold at 20°C. This creates a delicate state that can easily revert to a stable, saturated solution through crystallization if disturbed. Supersaturated solutions are valuable in various scientific and industrial processes because they facilitate the study and use of crystallization.