# Question 82dbf

Apr 29, 2016

"% 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 $\text{1 ppm}$ tells you that you get $\text{1 g}$ of solute for every ${10}^{6} \text{g}$ 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 $\text{73.,2 ppm}$. This means that you have $\text{73.2 g}$ of solute for every ${10}^{6} \text{g}$ of solvent.

Notice that if you were to pick a sample of ${10}^{6} \text{g}$ of solvent and add $\text{73.2 g}$ of solute, you can approximate the mass of the resulting solution as

$\text{73.2 g solute " + color(white)(a)10^6"g solvent" ~~ 10^6"g solution}$

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

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{% m/m" = "grams of solute"/"grams of solution} \times {10}^{2} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Since we've picked a sample that contains $\text{73.2 g}$ of solute per ${10}^{6} \text{g}$ 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 $\text{0.00732%}$ by mass, you would say that it's $\text{73.2 ppm}$.

Apr 29, 2016

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 $100 \textcolor{w h i t e}{l} \text{g}$, so we divide both numerator and denominator by ${10}^{4}$.

$\text{% by mass" = ("73.2 g" -: 10^4)/(10^6 "g" -: 10^4) = "0.007 32 g"/(100color(white)(l) "g") = "0.007 32 %}$ (m/m)