To solve this problem, we need to determine how much water is required to fully dissolve 11 grams of calcium carbonate, given that the solubility of calcium carbonate is 14 milligrams per liter. Here’s the step-by-step solution:
1. Convert the amount of calcium carbonate from grams to milligrams:
- Given: 11 grams of calcium carbonate
- Since 1 gram = 1000 milligrams, we convert grams to milligrams:
[tex]\[ 11 \text{ grams} \times 1000 = 11000 \text{ milligrams} \][/tex]
2. Determine how much water is needed based on the solubility:
- Given: Solubility is 14 milligrams per liter, meaning 14 milligrams of calcium carbonate can dissolve in 1 liter of water.
- To find out how many liters are needed to dissolve 11000 milligrams, we use the following proportion:
[tex]\[ \text{Amount of water needed} = \frac{\text{total milligrams of calcium carbonate}}{\text{solubility}} \][/tex]
Substituting the given values:
[tex]\[ \text{Amount of water needed} = \frac{11000 \text{ milligrams}}{14 \text{ milligrams per liter}} = 785.7142857142857 \text{ liters} \][/tex]
3. Express the answer to the correct number of significant figures:
- The values given in the problem (14 mg/L and 11 grams) both have two significant figures. Therefore, the final answer should be reported to two significant figures:
[tex]\[ 785.7142857142857 \approx 790 \text{ liters} \][/tex]
Thus, it would take approximately [tex]\( \boxed{790} \)[/tex] liters of water to fully dissolve 11 grams of calcium carbonate.
