How many liters of softened water, containing a sodium concentration of 0.050% sodium by mass, have to be consumed to exceed the FDA recommendation? (Assume a density of 1.0 g/mL for water.)
and waht is the FDS recommendation for salt?
To determine how many liters of softened water need to be consumed to exceed the FDA recommendation for sodium, we need to follow these steps:
Step 1: Find the mass of sodium in 1 liter of softened water.
First, convert the sodium concentration of 0.050% to a decimal by dividing it by 100:
0.050% = 0.050/100 = 0.0005
Since we know the density of water is 1.0 g/mL, we can conclude that 1 liter of water weighs 1000 grams.
To find the mass of sodium in 1 liter of softened water, we can multiply the mass of water by the sodium concentration:
Mass of sodium = Mass of water x Sodium concentration
Mass of sodium = 1000 g x 0.0005
Mass of sodium = 0.5 g
Therefore, 1 liter of softened water contains 0.5 grams of sodium.
Step 2: Determine the FDA recommendation for sodium intake.
The FDA recommends that the daily intake of sodium should not exceed 2300 mg (milligrams), which is equivalent to 2.3 grams.
Step 3: Calculate the number of liters of softened water required to exceed the FDA recommendation.
To find the volume of softened water required, we will set up a proportion based on the mass of sodium:
0.5 g is to 1 liter as 2.3 g is to x liters
Using a cross-multiplication approach, we can solve for x:
0.5 g * x liters = 2.3 g * 1 liter
0.5x = 2.3
x = 2.3 / 0.5
x = 4.6
Therefore, to exceed the FDA recommendation, one would need to consume approximately 4.6 liters of softened water with a sodium concentration of 0.050%.