Question

it turns out that molarity isnt the only unit of concentration. in fact, as youve already noticed, the epa sometimes reports the concentration of substances in ppb or parts per billion.
so what is parts per billion? parts per billion, or ppb, is a unit of measurement that compares the mass of the solute to the mass of the solution.
for example, a 5 ppb solution is one that contains 5 grams of the solute in 1,000,000,000 grams of solution.
how much water (in ml) would need to be added to a 7 gram sample of iron to create a 7 ppb solution?

• remember that 1 gram of water is equal to 1 ml.

Explanation:

Step1: Use the ppb formula

The formula for ppb is \(ppb=\frac{\text{mass of solute}}{\text{mass of solution}}\times10^{9}\). We know \(ppb = 7\) and mass of solute \(m_{solute}=7\space g\). Let the mass of the solution be \(m_{solution}\). Then \(7=\frac{7}{m_{solution}}\times10^{9}\).

Step2: Solve for the mass of the solution

From \(7=\frac{7}{m_{solution}}\times10^{9}\), we can cross - multiply: \(7\times m_{solution}=7\times10^{9}\). Divide both sides by 7: \(m_{solution}=10^{9}\space g\).

Step3: Find the mass of water

The mass of the solution \(m_{solution}=m_{solute}+m_{water}\). We know \(m_{solute} = 7\space g\) and \(m_{solution}=10^{9}\space g\). So \(m_{water}=m_{solution}-m_{solute}\). Substitute the values: \(m_{water}=10^{9}-7\approx10^{9}\space g\).

Step4: Convert mass of water to volume

Since \(1\space g\) of water is equal to \(1\space mL\), the volume of water \(V = m_{water}\space mL\). So \(V = 10^{9}\space mL\).

Answer:

\(1000000000\space mL\)