Question

Question #37461

Answer 1

See explanation.

Explanation:

For starters, it's worth mentioning that you won't find a volume by volume percent concentration, `"% v/v"`, solution of sodium chloride because this type of percent concentration is usually reserved for solutions that contain 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"`, which is defined as the number of grams of solute present for every `"100 mL"` of the solution.

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

For, for example, if you have a `"25% m/v"` solution of sodium chloride, you can say that this solution contains `"25 g"` of sodium chloride, the solute, for every `"100 mL"` of the solution.

By comparison, the mass by mass percent concentration, `"% m/m"`, tells you the number of grams of solute present for every `"100 g"` of the solution.

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

In this example, a `"25% m/m"` solution of sodium chloride contains `"25 g"` of sodium chloride for every `"100 g"` of the solution.

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 `rho` `"g mL"^(-1)`, which means that every `"1 mL"` of this solution has a mass of `rho` `"g"`, you can say that `"100 mL"` of the solution will have a mass 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 `> "1 g mL"^(-1)`, the mass by volume percent concentration is lower than the mass by mass percent concentration, which happens because the mass of `"100 mL"` of the solution is `>` `"100 g"`.