# What is the percentage concentration by mass of a #16*mol*L^-1# solution of nitric acid, for which density is #1.42*g*mL^-1#?

##### 2 Answers

Around 70% concentration, mass of acid/mass of solution.

#### Explanation:

A *solution* . We can work out percentages (

So now we calculate the quotient, 1008.2 g

Your stock solution is

#### Explanation:

What you need to do here is pick a sample of this stock nitric acid solution and use its molarity to find out how much nitric acid it would contain.

Then use its density to determine athe sample's mass.

So, to make calculations easier, pick a

#C = n/V implies n = C * V#

#n_(HNO_3) = "16 M" * "1.00 L" = "16 moles"#

Use nitric acid's molar mass to help you find how many grams of acid would contain this many moles

#16color(red)(cancel(color(black)("moles HNO"""_3))) * "63.013 g"/(1color(red)(cancel(color(black)("mole HNO"""_3)))) = "1008.2 g HNO"""_3#

What would be the mass of the sample? Use its known density!

#1.00color(red)(cancel(color(black)("L"))) * (1000color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L")))) * "1.42 g"/(1color(red)(cancel(color(black)("mL")))) = "1420 g"#

The solution's percent concentration by mass, or

#"%w/w" = "mass of solute"/"mass of solution" xx 100#

In your case, you would have

#"%w/w" = (1008.2color(red)(cancel(color(black)("g"))))/(1420color(red)(cancel(color(black)("g")))) xx 100 = color(green)(71%)#

**SIDE NOTE** *You can redo the calculations using any sample of the stock solution, the result will always come out the same.*