You use the and by mass of the stock solution.

You know that you’re dealing with a ##”1-mol/L”## nitric acid, ##”HNO”””_3##, solution.

To get the solution’s by volume, you would need to have some information about the stock solution of nitric acid used to make the ##”1-mol/L”## solution.

The idea here is that your ##”1-mol/L”## nitric acid solution was prepared by a sample taken from a stock solution of nitric acid. This means that you need to find the volume of the stock solution used to prepare the ##”1-mol/L”## solution in order to be able to find its volume by volume percent concentration.

Usually, nitric acid stock have a percent concentration by mass of nitric acid equal to ##70.2%## and a density of ##”1.41 g/mL”##.

Use nitric acid’s molar mass to determine how many grams of acid you get in your ##”1-mol/L”## solution

##1color(red)(cancel(color(black)(“mole HNO”””_3))) * “63.013 g”/(1color(red)(cancel(color(black)(“mole HNO”””_3)))) = “63.013 g”##

Now focus on finding what volume of the stock solution will contain 63.013 g of nitric acid.

To make calculations easier, assume that you have a ##”1-L”## sample of the stock solution. This sample will have a mass of

##1color(red)(cancel(color(black)(“L”))) * (1000color(red)(cancel(color(black)(“mL”))))/(1color(red)(cancel(color(black)(“L”)))) * “1.41 g”/(1color(red)(cancel(color(black)(“mL”)))) = “1410 g”##

Since nitric acid makes up 70.2% of this mass, you know that the ##”1-L”## stock sample will contain

##1410color(red)(cancel(color(black)(“g solution”))) * (“70.2 g HNO”””_3)/(100color(red)(cancel(color(black)(“g solution”)))) = “989.82 g HNO”””_3##

Now, the volume of this solution that will contain 63.013 g of nitric acid is

##63.013color(red)(cancel(color(black)(“g HNO”””_3))) * “1000 mL stock”/(989.92color(red)(cancel(color(black)(“g HNO”””_3)))) = “63.7 mL”##

So, you prepared your ##”1-mol/L”## nitric acid solution by taking a ##”63.7-mL”## sample of the stock solution and adding enough water to make the total volume of th solution equal to ##”1-L”##.

This means that the volume by volume, ##”%v/v”##, percent concentration of the ##”1-mol/L”## solution is

##”%v/v” = V_(HNO_3)/V_”sol” xx 100##

##”%v/v” = (63.7color(red)(cancel(color(black)(“mL”))))/(1000color(red)(cancel(color(black)(“mL”)))) xx 100 = 6.37 = color(green)(“6.4% v/v”)##

SIDE NOTE The answer will depend on the percent concentration by mass, and implicitly on the density, of the stock solution of nitric acid.

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