Problem: 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 5.1×10−2 % sodium by mass, have to be consumed to exceed the FDA recommendation? (Assume a water density of 1.0 g/mL.)

FREE Expert Solution

We are asked to determine the volume of softened water containing a sodium concentration of 5.1×10−2 % sodium by mass that would exceed the FDA recommendation

We shall rely on the mass percent formula below:


mass percent=mass componenttotal mass×100


Since we are dealing with a solution (i.e. the softened water), we can rewrite the equation as:


mass percent=mass solutemass solution×100


We don’t have the mass of the solution but we can calculate it using the mass of the solute and the mass of solvent.

▪ solute → sodium
▪ solvent → where KNO3 is dissolved → Water (H2O)


The equation now becomes:

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Problem Details

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 5.1×10−2 % sodium by mass, have to be consumed to exceed the FDA recommendation? (Assume a water density of 1.0 g/mL.)

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