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Answer :
To solve this problem, we need to determine the solubility of the salt in grams per 100 grams of solvent. Here’s a step-by-step breakdown:
1. Understand the Problem:
- We start with a 25-gram saturated solution of salt at [tex]\( 60^{\circ}C \)[/tex].
- Upon heating and drying this solution, 4 grams of anhydrous salt is recovered.
- Solubility is defined as the amount of salt that can dissolve in 100 grams of solvent.
2. Calculate the Weight of the Solvent:
- The weight of the solution is the total weight (25 grams).
- The weight of the anhydrous salt recovered from the solution is 4 grams.
- Therefore, the weight of the solvent (water) in the original solution can be calculated as:
[tex]\[
\text{Weight of solvent} = \text{Weight of solution} - \text{Weight of anhydrous salt} = 25\, \text{g} - 4\, \text{g} = 21\, \text{g}
\][/tex]
3. Calculate Solubility:
- Solubility is the amount of salt that can dissolve in 100 grams of solvent. Therefore, to find the solubility, we use the proportion:
[tex]\[
\frac{\text{4 g of salt}}{\text{21 g of solvent}} \times 100 = x \, \text{g of salt per 100 g of solvent}
\][/tex]
- Calculating this gives:
[tex]\[
x = \left( \frac{4}{21} \right) \times 100 \approx 19.05\, \text{g}
\][/tex]
4. Conclusion:
- The solubility of the salt at [tex]\( 60^{\circ}C \)[/tex] is approximately 19.05 grams per 100 grams of solvent.
Therefore, the correct answer is [tex]\( \boxed{19.05 \, \text{g/100 g}} \)[/tex].
1. Understand the Problem:
- We start with a 25-gram saturated solution of salt at [tex]\( 60^{\circ}C \)[/tex].
- Upon heating and drying this solution, 4 grams of anhydrous salt is recovered.
- Solubility is defined as the amount of salt that can dissolve in 100 grams of solvent.
2. Calculate the Weight of the Solvent:
- The weight of the solution is the total weight (25 grams).
- The weight of the anhydrous salt recovered from the solution is 4 grams.
- Therefore, the weight of the solvent (water) in the original solution can be calculated as:
[tex]\[
\text{Weight of solvent} = \text{Weight of solution} - \text{Weight of anhydrous salt} = 25\, \text{g} - 4\, \text{g} = 21\, \text{g}
\][/tex]
3. Calculate Solubility:
- Solubility is the amount of salt that can dissolve in 100 grams of solvent. Therefore, to find the solubility, we use the proportion:
[tex]\[
\frac{\text{4 g of salt}}{\text{21 g of solvent}} \times 100 = x \, \text{g of salt per 100 g of solvent}
\][/tex]
- Calculating this gives:
[tex]\[
x = \left( \frac{4}{21} \right) \times 100 \approx 19.05\, \text{g}
\][/tex]
4. Conclusion:
- The solubility of the salt at [tex]\( 60^{\circ}C \)[/tex] is approximately 19.05 grams per 100 grams of solvent.
Therefore, the correct answer is [tex]\( \boxed{19.05 \, \text{g/100 g}} \)[/tex].
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