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: Set up the proportion

Since \(ppb=\frac{\text{mass of solute}}{\text{mass of solution}}\), and we have \(ppb = 7\) and mass of solute \(m_{solute}=7\space g\). Let the mass of solution be \(m_{solution}\). Then \(7=\frac{7}{m_{solution}}\times10^{9}\) (because \(ppb=\frac{\text{mass of solute}}{\text{mass of solution}}\times10^{9}\)).
Solving for \(m_{solution}\), we get \(m_{solution}=\frac{7\times10^{9}}{7}= 10^{9}\space g\).

Step2: Find the mass of water

The mass of solution \(m_{solution}=m_{solute}+m_{water}\). We know \(m_{solute} = 7\space g\) and \(m_{solution}=10^{9}\space g\). Then \(m_{water}=m_{solution}-m_{solute}\).
\(m_{water}=10^{9}- 7\approx10^{9}\space g\) (since \(7\ll10^{9}\)).

Step3: Convert mass of water to volume

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

Answer:

\(10^{9}\space mL\)