# Question #77da8

##### 1 Answer

#### Explanation:

A solution's concentration percentage by mass is defined as the mass of the solute divided by the total mass of the solution and multiplied by 100.

Nitric acid's concentration by mass is given to be

Let's assume we have a

Knowing that the solution's density is

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

we can determine the stock solution's mass

#"density" = "mass"/"volume"#

so you get

#"mass" = "density" * "volume"#

#m_"sol" = 1410"g"/color(red)(cancel(color(black)("L"))) * 1color(red)(cancel(color(black)("L"))) = "1410 g"# .

Out of this quantity,

#1410 color(red)(cancel(color(black)("g solution"))) * ("70.3 g HNO"""_3)/(100color(red)(cancel(color(black)("g solution")))) = "991.2 g HNO"""_3#

Knowing that nitric acid's molar mass is

#991.2 color(red)(cancel(color(black)("g"))) * "1 mole"/(63 color(red)(cancel(color(black)("g")))) = "15.7 moles"#

Thus, its molarity is

#C = n/V = "15.7 moles"/"1 L" = "15.7 M"#

We can now apply dilution concentration calculations to determine what the requested volume will be

#C_1V_1 = C_2V_2#

#V_1 = C_2/C_1 * V_2 = (0.5 color(red)(cancel(color(black)("M"))))/(15.7color(red)(cancel(color(black)("M")))) * 1.5 * 10^3"mL" = color(green)("47.8 mL")# .

I'll leave the answer rounded to three sig figs.