Question #f9956

1 Answer
Sep 15, 2017

Answer:

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.