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The solubility of calcium carbonate is [tex]$14 \frac{\text { milligrams }}{\text { liter }}$[/tex]. 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 ÷ 0.001 = 11000 mg.
Divide the total milligrams by the solubility rate: 11000 ÷ 14 ≈ 785.714 liters.
Round the result to two significant figures: 785.714 ≈ 790 liters.
It would take 790 liters of water to fully dissolve 11 grams of calcium carbonate.
Explanation
Understanding the Problem We are given that the solubility of calcium carbonate is 14 milligrams per liter. This means that 14 milligrams 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.
Converting Grams to Milligrams First, we need to convert the mass of calcium carbonate from grams to milligrams, since the solubility is given in milligrams per liter. We know that 1 milligram is equal to 0.001 grams. Therefore, to convert grams to milligrams, we divide the mass in grams by 0.001. So, 11 grams is equal to 0.001 11 = 11000 milligrams.
Calculating the Amount of Water Needed Now that we know we have 11000 milligrams of calcium carbonate, and we know that 14 milligrams of calcium carbonate can dissolve in 1 liter of water, we can find the amount of water needed by dividing the total milligrams of calcium carbonate by the solubility rate: 14 11000 ≈ 785.714 liters.
Rounding to Significant Figures Finally, we need to round the answer to the correct number of significant figures. The given solubility (14 mg/L) has two significant figures, and the mass to dissolve (11 g) also has two significant figures. Therefore, the final answer should have two significant figures. Rounding 785.714 to two significant figures gives us 790.
Final Answer Therefore, it would take 790 liters of water to fully dissolve 11 grams of calcium carbonate.
Examples
Imagine you're making a saltwater solution for a science experiment. Knowing the solubility of salt (like calcium carbonate in our problem) helps you determine how much water you need to dissolve a specific amount of salt. This is crucial in many real-world applications, such as preparing solutions in chemistry labs, creating cleaning solutions, or even understanding how minerals dissolve in natural water sources. By understanding solubility, you can accurately prepare solutions and predict how substances will behave in different environments.
To fully dissolve 11 grams of calcium carbonate, 790 liters of water are required after converting grams to milligrams, calculating the necessary liters based on solubility, and rounding to the correct significant figures.
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