Question

Question #82dbf

Answer 1

`"% m/m" = 0.00732%`

Explanation:

Parts per million, or ppm, is simply another way of expression the concentration of a solution.

More specifically, parts per million can be used for solutions that contain very, very small amounts, often called trace amounts, of solutes.

By definition, ppm concentration is expressed as

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

In essence, a concentration of `"1 ppm"` tells you that you get `"1 g"` of solute for every `10^6"g"` of solvent.

`"1 ppm" = (1color(red)(cancel(color(black)("g"))) "solute")/(color(brown)(cancel(color(black)(10^6)))color(red)(cancel(color(black)("g")))"solvent") xx color(brown)(cancel(color(black)(10^6)))`

In your case, the solution is said to have a concentration of `"73.,2 ppm"`. This means that you have `"73.2 g"` of solute for every `10^6"g"` of solvent.

Notice that if you were to pick a sample of `10^6"g"` of solvent and add `"73.2 g"` of solute, you can approximate the mass of the resulting solution as

`"73.2 g solute " + color(white)(a)10^6"g solvent" ~~ 10^6"g solution"`

Now, to get the solution's percent concentration by mass (or weight percent), `"% m/m"`, you need to determine how many grams of solute you get for every `"100 g"` of solution.

`color(blue)(|bar(ul(color(white)(a/a)"% m/m" = "grams of solute"/"grams of solution" xx 10^2color(white)(a/a)|)))`

Since we've picked a sample that contains `"73.2 g"` of solute per `10^6"g"` of solvent, and since we can approximate the mass of the solution as being equal to that of the solvent, you can say that the solution's percent concentration by mass will be

`"% m/m" = (73.2 color(red)(cancel(color(black)("g"))))/(10^6color(red)(cancel(color(black)("g")))) xx 10^2 = color(green)(|bar(ul(color(white)(a/a)"0.00732%"color(white)(a/a)|)))`

So, instead of saying that your solution is `"0.00732%"` by mass, you would say that it's `"73.2 ppm"`.

Answer 2

Ppm stands for "parts per million".

Explanation:

In other words, "How many grams are in one million grams of the sample?"

In the same way, mass percent is the number of grams in 100 g of the sample.

For example, `"73.2 ppm" = "73.2 g"/(10^6 "g")` of sample.

We want to know the mass of the component in `100color(white)(l) "g"`, so we divide both numerator and denominator by `10^4`.

`"% by mass" = ("73.2 g" -: 10^4)/(10^6 "g" -: 10^4) = "0.007 32 g"/(100color(white)(l) "g") = "0.007 32 %"` (m/m)