# Question #37461

##### 1 Answer

See explanation.

#### Explanation:

For starters, it's worth mentioning that you won't find a **volume by volume percent concentration**, **liquid solutes**.

A much more plausible percent concentration to use for a solution of sodium chloride is the **mass by volume percent concentration**,

#"% m/v" = "grams of solute"/"100 mL solution" xx 100%#

For, for example, if you have a

By comparison, the **mass by mass percent concentration**,

#"% m/m" = "grams of solute"/"100 g solution" xx 100%#

In this example, a

Notice that you can convert between the two percent concentrations by using the **density** of the solution. For example, if you have a solution of sodium chloride that has a density of

#100 color(red)(cancel(color(black)("mL solution"))) * (rho color(white)(.)"g solution")/(1color(red)(cancel(color(black)("mL solution")))) = (100 * rho)color(white)(.)"g"#

So, you know that

#"100 mL solution " -> " "(100 * rho) color(white)(.)"g solution"#

This means that you have

#"% m/v" = "grams of solute"/"100 mL solution" xx 100%#

#"% m/v" = "grams of solute"/((100 * rho)color(white)(.)"g solution") xx 100%#

This is equivalent to

#"% m/v" = overbrace("grams of solute"/"100 g solution" xx 100%)^(color(blue)("= %m/m")) * 1/rho#

which gets you

#color(blue)(ul(color(black)("% m/v" = 1/rho * "% m/m")))#

Notice that if the density of the solution is **lower** than the mass by mass percent concentration, which happens because the mass of