The maximum allowable concentration of lead in drinking water is 9.0 ppb. If 2.0
X 10 grams of lead is present in 250
mL of water, is it safe to drink the water?
Support your answer with mathematical
proof.

We are given:

Maximum concentration of Lead in water = 9 ppb

Mass of Lead in the given solution = 20 grams

Volume of water in the given solution = 250 mL

What is 1 ppb?

1 ppb, short for parts-per-billion. As from its name itself, ppb is used to find how many molecules of solute are present per 1 Billion molecules of the solvent

you can also use it in grams to get the formula:

1 ppb = 1 gram of solute / 1 Billion grams of Solvent

Finding the Ideal ppb concentration:

We are given that the maximum allowed concentration is 9 ppb

which means that we need 9 grams of the solute per 1 Billion grams of Solvent:  9 grams of Solute / 10⁹ grams of Solvent

ppb Concentration of the given solution:

We have 20 grams of Solute in 250 mL of water

Since the density of water is 1 gram/mL

20 grams of Solute / 250 grams of Solvent

As we can see, this fraction is FAR more large that the maximum ppb concentration

This means that the concentration of Lead in the Given solution is higher than the maximum amount and Hence, is unfit to drink