Question

Question #f9956

Answer 1

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 `"500 ppm"` will contain `"500 g"` of solute for every `10^6` `"g"` of solution. By comparison, a solution that has a concentration of `"500 ppb"` will contain `"500 g"` of solute for every `10^9` `"g"` of solution.

So in order to convert the `"500-ppm"` solution to `"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 `"100 g"` of this `"500-ppm"` solution, you need to add enough water to get the mass of the solution to

`color(blue)(1000) * "100 g" = 10^5color(white)(.)"g"`

So, to sum this up, you can convert a `"500-ppm"` solution to `"500-ppb"` by diluting your sample to a total mass that is `color(blue)(1000)` times higher than the mass of the initial sample.