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QUESTION

# How do you convert 1 mol/L HNO3 to % v/v HNO3?

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.