Question

Question #b81e1

Answer 1

You use the density and percent concentration by mass of the stock solution.

Explanation:

You know that you're dealing with a `"1-mol/L"` nitric acid, `"HNO"""_3`, solution.

To get the solution's percent concentration 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 diluting 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 solutions 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.