Question

Potassium fluoride has a solubility of \(92 \mathrm{~g}\) of \(\mathrm{KF}\) in \(100 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) at \(18^{\circ} \mathrm{C}\). State if each of the following mixtures forms an unsaturated or saturated solution at \(18^{\circ} \mathrm{C}\) : a. \(35 \mathrm{~g}\) of \(\mathrm{KF}\) and \(25 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) b. \(42 \mathrm{~g}\) of \(\mathrm{KF}\) and \(50 . \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) c. \(145 \mathrm{~g}\) of \(\mathrm{KF}\) and \(150 . \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\)

Short answer

a: Saturated, b: Unsaturated, c: Saturated

Step-by-step solution

Determine the solubility ratio

The solubility of potassium fluoride (KF) in water is given as 92 g of KF in 100 g of H₂O at 18°C. First, establish this ratio for use in the calculations: Solubility ratio: \[ \frac{92 \text{ g KF}}{100 \text{ g H}_{2}\text{O}} = 0.92 \text{ g KF per g H}_{2}\text{O} \]

Calculate amount of KF that can dissolve in the given amount of water

For each part (a, b, c), calculate how much KF can dissolve in the specified grams of water by multiplying the amount of water by the solubility ratio.

Step 3a: Calculate solubility for mixture a

Given: 25 g of H₂O. Using the solubility ratio, the amount of KF that can dissolve is: \[ 25 \text{ g H}_{2}\text{O} \times 0.92 \frac{\text{g KF}}{\text{g H}_{2}\text{O}} = 23 \text{ g KF} \] Compared to the given 35 g of KF, since 35 g > 23 g, it is a saturated solution.

Step 3b: Calculate solubility for mixture b

Given: 50 g of H₂O. Using the solubility ratio, the amount of KF that can dissolve is: \[ 50 \text{ g H}_{2}\text{O} \times 0.92 \frac{\text{g KF}}{\text{g H}_{2}\text{O}} = 46 \text{ g KF} \] Compared to the given 42 g of KF, since 42 g < 46 g, it is an unsaturated solution.

Step 3c: Calculate solubility for mixture c

Given: 150 g of H₂O. Using the solubility ratio, the amount of KF that can dissolve is: \[ 150 \text{ g H}_{2}\text{O} \times 0.92 \frac{\text{g KF}}{\text{g H}_{2}\text{O}} = 138 \text{ g KF} \] Compared to the given 145 g of KF, since 145 g > 138 g, it is a saturated solution.

Key concepts

saturation point

The saturation point is a vital concept in chemistry. It refers to the maximum amount of solute that can dissolve in a solvent at a specific temperature. At this point, any additional solute will not dissolve. This can help us determine if a given solution is saturated or unsaturated.

In the exercise, we know that the saturation point for potassium fluoride (KF) in water at 18°C is 92 g of KF in 100 g of H₂O. This means that adding more than 92 g of KF to 100 g of water will result in some KF not dissolving. This creates a saturated solution.

Understanding the saturation point is essential. It tells us the maximum solubility of a substance. Once the saturation point is reached, the solution cannot hold any more solute.

solubility ratio

The solubility ratio helps us understand how much a solute can dissolve in a solvent. It is given as a simple ratio or fraction. For potassium fluoride (KF), the solubility is 92 g of KF in 100 g of H₂O at 18°C.

This can be written as: \ \[ \frac{92 \text{ g KF}}{100 \text{ g H}_{2} \text{O}} = 0.92 \text{ g KF per g H}_{2} \text{O} \].

Using the solubility ratio makes it easier to calculate how much solute can dissolve in different amounts of solvent. For example: \ \[ 25 \text{ g H}_{2} \text{O} \times 0.92 \frac{\text{g KF}}{\text{g H}_{2} \text{O}} = 23 \text{ g KF} \]

This calculation shows that 25 g of H₂O can dissolve 23 g of KF.

solubility calculations

Solubility calculations help determine if a solution is unsaturated or saturated. By using the solubility ratio, we can find out how much solute can dissolve in a given amount of solvent.

Let's go through the calculations for the given mixtures in the exercise:

• Mixture a: 35 g of KF in 25 g of H₂O. Using the solubility ratio: 25 g H₂O × 0.92 g KF/g H₂O = 23 g KF. Since 35 g > 23 g, it is a saturated solution.
• Mixture b: 42 g of KF in 50 g of H₂O. Using the solubility ratio: 50 g H₂O × 0.92 g KF/g H₂O = 46 g KF. Since 42 g < 46 g, it is an unsaturated solution.
• Mixture c: 145 g of KF in 150 g of H₂O. Using the solubility ratio: 150 g H₂O × 0.92 g KF/g H₂O = 138 g KF. Since 145 g > 138 g, it is a saturated solution.


By knowing the amount of solvent and using the solubility ratio, we can easily determine if the given solution is saturated or not.