Question

Question #50ff0

Answer 1

`"8.3 g"`

Explanation:

You can use Parts Per Million, or ppm, to express the concentration of solutions that contain very, very small amounts, often called trace amounts, of solute.

More specifically, a concentration of `"1 ppm"` is equivalent to one part solute for every `10^6` parts of solvent. One way to express ppm concentration is to use the mass of solute in grams and the mass of solvent in grams

`color(blue)(|bar(ul(color(white)(a/a)"ppm" = "grams of solute"/"grams of solvent" xx 10^6color(white)(a/a)|)))`

This basically tells you that a concentration of `"1 ppm"` will contain `"1 g"` of solute for every `10^6"g"` of solvent.

Since you can safely assume that the mass of the solvent is equal to that of the solution, you can say that a con concentration of `"6 ppm"` will contain `"6 g"` of solute in `10^6"g"` of solution.

Now, the problem tells you this solution contains `"0.050 mg"` of solute, which is equivalent to

`0.050 color(red)(cancel(color(black)("mg solute"))) * "1 g"/(10^3color(red)(cancel(color(black)("mg solute")))) = 5.0 * 10^(-5)"g"`

Now all you have to do is use the `"6 ppm"` concentration as a conversion factor to determine how many grams of solution would contain this many grams of solvent

`5.0 * 10^(-5)color(red)(cancel(color(black)("g solute"))) * overbrace((10^6"g solution")/(6color(red)(cancel(color(black)("g solute")))))^(color(purple)("= 6 ppm")) = color(green)(|bar(ul(color(white)(a/a)"8.3 g solution"color(white)(a/a)|)))`

I'll leave the answer rounded to two sig figs.

One interesting thing to notice here is that you can write a concentration of `"1 ppm"` as

`"1 g solute"/(10^6"g solution") = (1 * color(red)(cancel(color(black)(10^(3))))"mg solute")/(1 * color(red)(cancel(color(black)(10^(6)))) * color(red)(cancel(color(black)(10^(-3))))"kg solution") = "1 mg solute"/"1 kg solution"`

So, if `"1 ppm"` is equivalent to `"1 mg"` of solute in `"1 kg"` of solution, you can say that `"6 ppm"` will be equivalent to `"6 mg"` of solute in `"1 kg"` of solution.

Therefore,

`0.050 color(red)(cancel(color(black)("mg solute"))) * overbrace("1 kg solution"/(6color(red)(cancel(color(black)("mg solute")))))^(color(purple)("= 6 ppm")) = "0.0083 kg solution"`

This will once again be

`0.0083 color(red)(cancel(color(black)("kg"))) * (10^3"g")/(1color(red)(cancel(color(black)("kg")))) = color(green)(|bar(ul(color(white)(a/a)"8.3 g solution"color(white)(a/a)|)))`