Question #37461

1 Answer
Dec 27, 2017

Answer:

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"#.