Potassium nitrate has a solubility of 32 g of KNO₃ in 100. g of H₂O at 20 °C. Determine if each of the following forms an unsaturated or saturated solution at 20 °C:
a. adding 32 g of KNO₃ to 200. g of H₂O

Verified step by step guidance

1. Step 1: Understand the problem. The solubility of potassium nitrate (KNO₃) is given as 32 g in 100 g of water at 20 °C. This means that at this temperature, 32 g of KNO₃ can dissolve completely in 100 g of water to form a saturated solution. Any additional KNO₃ beyond this amount would remain undissolved, making the solution saturated.
2. Step 2: Analyze the given scenario. In this case, 32 g of KNO₃ is being added to 200 g of water. Since the amount of water is doubled (200 g instead of 100 g), the solubility limit also doubles. Therefore, calculate the new solubility limit for 200 g of water.
3. Step 3: Use proportional reasoning to determine the solubility limit. If 32 g of KNO₃ dissolves in 100 g of water, then in 200 g of water, the solubility limit is: \( 32 \text{ g} \times \frac{200 \text{ g H₂O}}{100 \text{ g H₂O}} \).
4. Step 4: Compare the amount of KNO₃ added (32 g) to the solubility limit calculated in Step 3. If the amount of KNO₃ added is less than or equal to the solubility limit, the solution is unsaturated. If it exceeds the solubility limit, the solution is saturated.
5. Step 5: Conclude whether the solution is unsaturated or saturated based on the comparison in Step 4. Remember, an unsaturated solution means all the solute dissolves, while a saturated solution means some solute remains undissolved.

Key Concepts

Solubility

Solubility is the maximum amount of a solute that can dissolve in a specific amount of solvent at a given temperature. For potassium nitrate (KNO₃), its solubility at 20 °C is 32 g per 100 g of water. This means that if you exceed this amount in a given volume of water, the solution will become saturated, and any additional solute will not dissolve.

Saturated Solution

A saturated solution is one in which the maximum amount of solute has been dissolved in the solvent at a specific temperature. In this case, if 32 g of KNO₃ is added to 100 g of water, the solution is saturated. However, if more solvent is added, such as 200 g of water, the solubility limit changes, allowing for more solute to dissolve before reaching saturation.

Unsaturated Solution

An unsaturated solution is one that contains less solute than the maximum amount that can be dissolved at a given temperature. In the scenario of adding 32 g of KNO₃ to 200 g of water, the solution is unsaturated because the increased amount of solvent allows for more solute to dissolve without reaching the saturation point, which would be 64 g of KNO₃ in this case.