Water softeners often replace calcium ions in hard water with sodium ions. Since sodium compounds are soluble, the presence of sodium ions in water does not cause the white, scaly residues caused by calcium ions. However, calcium is more beneficial to human health than sodium because calcium is a necessary part of the human diet, while high levels of sodium intake are linked to increases in blood pressure. The U.S. Food and Drug Administration (FDA) recommends that adults ingest less than 2.4 g of sodium per day. How many liters of softened water, containing a sodium concentration of 0.050% sodium by mass, would a person have to consume to exceed the FDA recommendation? (Assume a water density of 1.0 g/mL.)

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Hey everyone today, we're dealing with a pretty cool question. So the problem is telling us that there are calcium ions that are found in hard water and that the US FDA has recommended minimum ingestion of calcium is 1.3 g per day, 1.3 g of calcium. So if we have a sample of water That is 0.03% calcium by mass. What is the minimum volume in leaders in leaders of hardened water that needs to be consumed in order to exceed the US FDA is recommended ingested amount and were given the density of hardened water. So let's just write that down as well. The density Row is equal to 1. g per milliliter. So for the sake of this question, since we don't actually have a volume of water to work with that is given in the question. We can use this percent by mass. That's given to both assume how much calcium that we have and how much water that we have. So if it's 0.03%,, The easiest 1 to work with would be to assume that we have g of water 100 g of water. So if only 0.03% of 100 g is calcium. Then that means we have 0.03g of calcium. Again, this suggests an assumption to make our lives a little easier for calculations. So with all this in mind, let's go ahead and start converting our grams of calcium, the minimum amount right here and find out how many liters of water we need to drink to exceed that. Remember? Do not try this at home. So We start with 1.3 g of calcium to convert this to liters of water. We first need to convert this two g of water. Using the assumption we've made earlier g H 20. Divided by 0.03 g of calcium. So our calcium terms will cancel out and were given the density. So that means that we can calculate the milliliters the volume from the mass of water. So we multiply by the inverse of the density in order to put milliliters on top graham. So our grams will cancel out and we'll be left with millions. Finally we are asked to find the volume in leaders. Remember that for every one leader there are 1000 ml. This is a basic conversion mL. So our milliliters will finally cancel out and our answer will be in leaders. This answer is 4. leaders. Therefore the volume of water needed to be ingested to exceed the FDA regulated recommended amount of calcium Is 4.33 L. I hope this helps. And I look forward to seeing you on the next one

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Key Concepts

Hard Water and Water Softeners

Sodium Concentration and Mass Percent

Daily Sodium Intake Recommendations