Potassium chloride is widely used in the manufacture of fertilizers. Its solubility is 37.0 g/100 g water at 30°C. At 70°C its solubility is 48.3 g/100 g water. (a) Calculate the m... Potassium chloride is widely used in the manufacture of fertilizers. Its solubility is 37.0 g/100 g water at 30°C. At 70°C its solubility is 48.3 g/100 g water. (a) Calculate the mass of potassium chloride that dissolves in 44.5 g of water at 30°C. (b) Calculate the mass of water required to dissolve 39.6 g of potassium chloride at 70°C. (c) If 40.0 g of potassium chloride are added to 75.0 g of water at 30°C, will it all dissolve? If the temperature is increased to 70°C, will it all dissolve? How many grams (if any) are undissolved at 30°C? at 70°C? Read more

Steps to Solve

1. Calculate mass of potassium chloride at 30°C

To find the mass of potassium chloride that dissolves in 44.5 g of water at 30°C, we use the solubility information. At 30°C, the solubility of potassium chloride is 37.0 g per 100 g of water.

Using the proportion: [ \text{Mass of KCl} = \left( \frac{37.0 , \text{g KCl}}{100 , \text{g water}} \right) \times 44.5 , \text{g water} ]

Calculating this gives: [ \text{Mass of KCl} = \frac{37.0 \times 44.5}{100} = 16.465 , \text{g} ]

2. Calculate mass of water required at 70°C

Now, we need to find the mass of water required to dissolve 39.6 g of potassium chloride at 70°C. The solubility at this temperature is 48.3 g per 100 g of water.

Using the proportion: [ \text{Mass of water} = \left( \frac{100 , \text{g water}}{48.3 , \text{g KCl}} \right) \times 39.6 , \text{g KCl} ]

Calculating this gives: [ \text{Mass of water} = \frac{100 \times 39.6}{48.3} \approx 81.92 , \text{g} ]

3. Determine if all KCl dissolves at different temperatures

For part (c), we need to check if 40.0 g of KCl will dissolve in 75.0 g of water at 30°C. From earlier, we know that:

• The maximum amount of KCl that can dissolve in 75.0 g of water is: [ \text{Maximum KCl} = \left( \frac{37.0 , \text{g KCl}}{100 , \text{g water}} \right) \times 75.0 , \text{g water = 27.75 , g KCl} ]

Since 40.0 g > 27.75 g, it will not dissolve completely at 30°C.

Next, we check if the remaining KCl dissolves at 70°C. The maximum KCl that can dissolve in 75.0 g of water at 70°C is: [ \text{Maximum KCl at 70°C} = \left( \frac{48.3 , \text{g KCl}}{100 , \text{g water}} \right) \times 75.0 , \text{g water \approx 36.225 , g KCl} ]

Since 40.0 g > 36.225 g, some KCl will remain undissolved at 70°C as well.

4. Determine undissolved KCl at both temperatures

Total KCl added = 40.0 g

At 30°C:

• Dissolved KCl = 27.75 g
• Undissolved KCl = (40.0 , \text{g} - 27.75 , \text{g} = 12.25 , \text{g})

At 70°C:

• Dissolved KCl = 36.225 g
• Undissolved KCl = (40.0 , \text{g} - 36.225 , \text{g} = 3.775 , \text{g})