The solubility of calcium carbonate is [tex]$14 \frac{\text { milliene }}{\text { film }}$[/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.
I would take [$\square$] liters of water to fully dissolve [tex]$11$[/tex] grams of calcium carbonate
Answer (1)
Convert the solubility from milligrams per liter to grams per liter: 14 liter milligrams × 0.001 milligram grams = 0.014 liter grams .
Divide the total amount of calcium carbonate (11 grams) by the solubility in grams per liter to find the required volume of water: 0.014 liter grams 11 grams = 785.7142857142857 liters .
Round the result to two significant figures: 790 liters .
Therefore, it would take 790 liters of water to fully dissolve 11 grams of calcium carbonate.
Explanation
Convert solubility to grams per liter First, we need to convert the solubility of calcium carbonate from milligrams per liter to grams per liter. We know that 1 milligram is equal to 0.001 grams. Therefore, the solubility in grams per liter is calculated as follows:
Calculate solubility in grams per liter Solubility in grams per liter = 14 liter milligrams × 0.001 milligram grams = 0.014 liter grams
Calculate the required volume of water Next, we need to determine how much water is required to dissolve 11 grams of calcium carbonate. We can find this by dividing the total amount of calcium carbonate by the solubility in grams per liter:
Perform the division Volume of water = 0.014 liter grams 11 grams = 785.7142857142857 liters
Round to correct significant figures Finally, we need to express the answer to the correct number of significant figures. Since the given value 11 grams has two significant figures and 14 milligrams has two significant figures, we should round our answer to two significant figures:
State the final answer Volume of water ≈ 790 liters
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. If the solubility of your salt is, say, 360 grams per liter, you can calculate that to dissolve 720 grams of salt, you'd need 2 liters of water. This concept is crucial in many real-world applications, from chemistry experiments to industrial processes where precise solutions are required.
