To solve this problem, we need to determine how much water is required to dissolve 11 grams of calcium carbonate, given its solubility rate.
1. Understand the Solubility Rate:
- The given solubility is 14 milligrams of calcium carbonate per liter of water. This means 14 milligrams (mg) of calcium carbonate can dissolve in 1 liter of water.
2. Convert Grams to Milligrams:
- We are given 11 grams of calcium carbonate. We need to convert this mass into milligrams to use the solubility rate properly.
- 1 gram (g) = 1000 milligrams (mg).
- Therefore, 11 grams is equivalent to [tex]\( 11 \times 1000 = 11000 \)[/tex] milligrams.
3. Calculate the Volume of Water Needed:
- Now, we need to find out how many liters of water are needed to dissolve 11000 milligrams of calcium carbonate.
- Since the solubility rate is 14 milligrams per liter, we can set up a ratio:
[tex]\[
\text{Required water in liters} = \frac{\text{Amount of calcium carbonate in milligrams}}{\text{Solubility in milligrams per liter}}
\][/tex]
- Plugging in the values:
[tex]\[
\text{Required water in liters} = \frac{11000 \text{ mg}}{14 \text{ mg/liter}}
\][/tex]
- This gives:
[tex]\[
\text{Required water in liters} = 785.7142857142857 \text{ liters}
\][/tex]
4. Express the Answer in Significant Figures:
- The given solubility (14 milligrams) has 2 significant figures.
- The given mass (11 grams) has 2 significant figures.
- Therefore, our answer should be expressed with 2 significant figures:
[tex]\[
\text{Required water in liters} \approx 790 \text{ liters}
\][/tex]
Thus, it would take approximately 790 liters of water to fully dissolve 11 grams of calcium carbonate.
