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The solubility of calcium carbonate is $14 \frac{\text { milligrams }}{\text { liter }}$. This rate means that 14 milligrams of calcium carbonate can dissolve in 1 liter of water.
How much water would be required to fully dissolve 11 grams of calcium carbonate? Express your answer to the correct number of significant figures. One milligram is equal to 0.001 grams.
It would take $\square$ liters of water to fully dissolve 11 grams of calcium carbonate.
Answer (2)
Convert 11 grams to milligrams: 11 e wl in e g = 11000 e wl in e m g .
Divide the total milligrams by the solubility to find the required liters of water: 14 e wl in e m g / L 11000 e wl in e m g ≈ 785.714 e wl in e L .
Round the result to two significant figures, as both initial values (11 grams and 14 mg/L) have two significant figures.
The final answer is 790 liters.
Explanation
Problem Analysis and Conversion We are given that the solubility of calcium carbonate is 14 milligrams per liter. This means that 14 mg of calcium carbonate can dissolve in 1 liter of water. We need to find out how much water is required to dissolve 11 grams of calcium carbonate. First, we need to convert grams to milligrams, since the solubility is given in milligrams per liter.
Converting Grams to Milligrams We know that 1 milligram (mg) is equal to 0.001 grams (g). Therefore, to convert 11 grams to milligrams, we can use the following conversion: 11 e wl in e g × 0.001 e wl in e g 1 e wl in e m g = 11000 e wl in e m g
Calculating the Required Water Now that we know we have 11000 mg of calcium carbonate, and we know that 14 mg of calcium carbonate can dissolve in 1 liter of water, we can calculate the amount of water needed by dividing the total amount of calcium carbonate by the solubility: 14 e wl in e m g / L 11000 e wl in e m g = 14 11000 e wl in e L ≈ 785.714 e wl in e L
Significant Figures and Final Answer Since we need to express the answer to the correct number of significant figures, we look at the initial value, 11 grams, which has two significant figures, and the solubility, 14 mg/L, which also has two significant figures. Therefore, our answer should have two significant figures. Rounding 785.714 L to two significant figures gives us 790 L.
Final Answer Therefore, it would take approximately 790 liters of water to fully dissolve 11 grams of calcium carbonate.
Examples
Understanding solubility is crucial in many real-world applications. For instance, in environmental science, knowing the solubility of pollutants helps predict their spread in water bodies. In medicine, the solubility of a drug affects its absorption and effectiveness in the body. In cooking, the solubility of sugar and salt determines how well they dissolve in recipes, affecting the taste and texture of the final dish. This concept is fundamental in various scientific and practical fields.
To dissolve 11 grams of calcium carbonate, you need to convert grams to milligrams, resulting in 11000 mg. Using the solubility of 14 mg/L, we find that about 785.71 liters of water is needed, which rounds to 790 liters when expressed to two significant figures. Thus, it would take approximately 790 liters of water to fully dissolve 11 grams of calcium carbonate.
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