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,
have to be consumed to exceed the FDA recommendation?
(Assume a density of 1.0 g/mL for water.)
2.4 = .0005 *(grams of water)
so
grams of water = mL of water = 2.4/.0005
so
liters of water = 2.4/.5 = 4.8 liters
To determine the amount of softened water needed to exceed the FDA recommendation for sodium intake, we can follow these steps:
Step 1: Calculate the maximum amount of sodium allowed per day:
The FDA recommendation is for adults to ingest less than 2.4 g of sodium per day.
Step 2: Determine the mass of sodium allowed per mL of water:
Since the softened water has a sodium concentration of 0.050% sodium by mass, we can convert it to grams:
0.050% = 0.050 g per 100 g of water
So, 1 L of water would contain 0.050 g of sodium.
Step 3: Convert the amount of sodium to be ingested per day to the volume of water required:
Since we know that 1 mL of water has a mass of 1 g (density of water = 1.0 g/mL), we can calculate the volume of water needed to provide the maximum sodium intake allowed:
Volume of water = Mass of sodium allowed / Mass of sodium per mL of water
Volume of water = 2.4 g / 0.050 g/mL
Now, let's calculate the volume of water needed to exceed the FDA recommendation:
Volume of water = 2.4 g / 0.050 g/mL
Volume of water ≈ 48 mL
Therefore, to exceed the FDA recommendation for sodium intake, approximately 48 mL (or 0.048 L) of softened water would need to be consumed.