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.

Question

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 5.6×10^−2% sodium by mass, have to be consumed to exceed the FDA recommendation? (Assume a water density of 1.0 g/mL)

Answer 1

Please don't listen to the one above me.

it is 4.28571 L

Answer 2

To solve this problem, we need to determine the amount of sodium in the water and compare it to the FDA recommendation of 2.4 grams per day.

First, let's convert the given sodium concentration from a percentage to a decimal:

5.6×10^−2% = 5.6×10^−2/100 = 5.6×10^−4

Next, we need to determine the mass of sodium in the water. We can do this by multiplying the concentration by the mass of the water consumed.

Since we are given the concentration as a percentage by mass, we can assume that 1 gram of water will contain 5.6×10^−4 grams of sodium.

Now, we need to convert the mass of sodium to liters of water. We are given the water density of 1.0 g/mL, which means that 1 liter of water has a mass of 1000 grams.

Therefore, the number of grams of sodium in 1 liter of water is 5.6×10^−4 grams.

To determine how many liters of water need to be consumed to exceed the FDA recommendation of 2.4 grams of sodium, we can set up the following equation:

(5.6×10^−4 grams of sodium) x (x liters of water) = 2.4 grams

Solving for x:

x = 2.4 grams / (5.6×10^−4 grams of sodium)
x ≈ 4285.7 liters

Therefore, approximately 4285.7 liters of softened water need to be consumed to exceed the FDA recommendation of 2.4 grams of sodium per day.

Answer 3

it is worth noting that 5.6x10^-2% w/w is the same as w/v as the density=1.0 g/ml

so 5.6x10^-2 g/100g is the same as

5.6 x 10^-4 g/g or

5.6 x 10^-4 g/ml

so to injest 2.4 g then

2.4 g / (5.6 x 10^-4 g/ml)

needed

then convert to litres.

5L

Please don't listen to the one above me.

To solve this problem, we need to determine the amount of sodium in the water and compare it to the FDA recommendation of 2.4 grams per day.

it is worth noting that 5.6x10^-2% w/w is the same as w/v as the density=1.0 g/ml