To determine how much water is needed to dissolve 11 grams of calcium carbonate, we'll follow these steps:
1. Convert grams to milligrams:
- 1 gram is equal to 1000 milligrams.
- Therefore, 11 grams is equal to [tex]\( 11 \times 1000 = 11000 \)[/tex] milligrams of calcium carbonate.
2. Use the solubility information:
- The solubility of calcium carbonate is [tex]\( 14 \frac{\text { milligrams }}{\text { liter }} \)[/tex]. This means that 14 milligrams of calcium carbonate can dissolve in 1 liter of water.
- To find out how much water is required to dissolve 11000 milligrams of calcium carbonate, we can set up a proportion:
[tex]\[
\frac{14 \ \text{mg}}{1 \ \text{L}} = \frac{11000 \ \text{mg}}{x \ \text{L}}
\][/tex]
3. Solve for the amount of water (x):
- Cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
14 \cdot x = 11000
\][/tex]
- Divide both sides by 14 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{11000}{14} = 785.7142857142857
\][/tex]
4. Express the answer to the correct number of significant figures:
- Since the given values have two significant figures (14 and 11), the answer should also be expressed with two significant figures:
[tex]\[
x \approx 790 \ \text{liters}
\][/tex]
Therefore, it would take [tex]\( \mathbf{790} \text{ liters} \)[/tex] of water to fully dissolve 11 grams of calcium carbonate.
