# Question f9956

Sep 15, 2017

Here's how you can do that.

#### Explanation:

A solution's concentration in parts per million, or ppm, tells you the number of grams of solute you get for every

${10}^{6} = 1 , 000 , 000$

grams of solution.

Similarly, a solution's concentration in parts per billion, or ppb, tells you the number of grams of solute present for every

${10}^{9} = 1 , 000 , 000 , 000$

grams of solution.

In your case, a solution that has a concentration of $\text{500 ppm}$ will contain $\text{500 g}$ of solute for every ${10}^{6}$ $\text{g}$ of solution. By comparison, a solution that has a concentration of $\text{500 ppb}$ will contain $\text{500 g}$ of solute for every ${10}^{9}$ $\text{g}$ of solution.

So in order to convert the $\text{500-ppm}$ solution to $\text{500 ppb}$, you need to increase its volume by a factor of

"DF" = (10^9 color(red)(cancel(color(black)("g"))))/(10^6color(red)(cancel(color(black)("g")))) = color(blue)(1000) -># the dilution factor

So, for example, if you start with $\text{100 g}$ of this $\text{500-ppm}$ solution, you need to add enough water to get the mass of the solution to

$\textcolor{b l u e}{1000} \cdot \text{100 g" = 10^5color(white)(.)"g}$

So, to sum this up, you can convert a $\text{500-ppm}$ solution to $\text{500-ppb}$ by diluting your sample to a total mass that is $\textcolor{b l u e}{1000}$ times higher than the mass of the initial sample.