Answer :
To determine how many grams of potassium chloride (KCl) must be dissolved in 200 grams of water to make a saturated solution at 60°C, we use the given solubility data for potassium chloride. According to the data, the solubility of potassium chloride in water at 60°C is approximately 45 grams of KCl per 100 grams of water.
Let's break it down step-by-step:
1. Understand the solubility information: At 60°C, 45 grams of KCl can be dissolved in 100 grams of water to form a saturated solution.
2. Identify the amount of water available: We have 200 grams of water.
3. Set up the proportion: If 100 grams of water can dissolve 45 grams of KCl, then we need to find out how much KCl 200 grams of water can dissolve.
4. Calculate the amount of KCl:
- Since 100 grams of water can dissolve 45 grams of KCl, doubling the water to 200 grams will also double the amount of KCl that can be dissolved.
- 200 grams of water can therefore dissolve [tex]\( 45 \times 2 = 90 \)[/tex] grams of KCl.
5. Verify the answer: By setting up a proportion, we get:
[tex]\[ \frac{45 \text{ grams of KCl}}{100 \text{ grams of water}} = \frac{x \text{ grams of KCl}}{200 \text{ grams of water}} \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \left( \frac{45 \text{ grams}}{100 \text{ grams}} \right) \times 200 \text{ grams} = 90 \text{ grams} \][/tex]
Based on this step-by-step calculation, the correct answer is (4) 90 grams.
Let's break it down step-by-step:
1. Understand the solubility information: At 60°C, 45 grams of KCl can be dissolved in 100 grams of water to form a saturated solution.
2. Identify the amount of water available: We have 200 grams of water.
3. Set up the proportion: If 100 grams of water can dissolve 45 grams of KCl, then we need to find out how much KCl 200 grams of water can dissolve.
4. Calculate the amount of KCl:
- Since 100 grams of water can dissolve 45 grams of KCl, doubling the water to 200 grams will also double the amount of KCl that can be dissolved.
- 200 grams of water can therefore dissolve [tex]\( 45 \times 2 = 90 \)[/tex] grams of KCl.
5. Verify the answer: By setting up a proportion, we get:
[tex]\[ \frac{45 \text{ grams of KCl}}{100 \text{ grams of water}} = \frac{x \text{ grams of KCl}}{200 \text{ grams of water}} \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \left( \frac{45 \text{ grams}}{100 \text{ grams}} \right) \times 200 \text{ grams} = 90 \text{ grams} \][/tex]
Based on this step-by-step calculation, the correct answer is (4) 90 grams.
