How many moles of HNO_3HNO3 are needed to prepare 5.0 liters of a 2.0 M solution of HNO_3HNO3?

1 Answer
May 22, 2017

"10. moles"10. moles

Explanation:

All you have to do here is to use the molarity of the solution as a conversion factor to determine the number of moles of solute that must be dissolved in "5.0 L"5.0 L of solution in order to have a concentration of "2.0 M"2.0 M.

As you know, molarity tells you the number of moles of solute present in "1 L"1 L of solution. In your case, a "2.0 M"2.0 M solution will contain 2.02.0 moles of solute for every "1 L"1 L of solution.

Now, because solutions are homogeneous mixtures, i.e. they have the same composition throughout, you can use the molarity of the solution as a conversion factor to get the moles of solute needed for your solution

5.0 color(red)(cancel(color(black)("L solution"))) * overbrace("2.0 moles HNO"_3/(1color(red)(cancel(color(black)("L solution")))))^(color(blue)("= 2.0 M")) = color(darkgreen)(ul(color(black)("10. moles HNO"_3)))

The answer is rounded to two sig figs.

This tells you that dissolving 10. moles of nitric acid in enough water to get the total volume of the solution to "5.0 L" will give you the same molarity as dissolving 2.0 moles of nitric acid in enough water to get the total volume of the solution to "1.0 L".