Question

Concentrated nitric acid used in laboratory work is \[68\% \] nitric acid by mass in aqueous solution. What should be the molarity of such a sample of the acid if the density of the solution is \[1.504gm{L^{ - 1}}\]?

Answer 1

Hint – Start by describing the general concepts behind moles, density and molarity. - Then assume that you start off with \[100g\] of the given sample and calculate the amount of nitric acid (\[68\% \] of \[100g\]). Then use the equation \[No{\text{ }}of{\text{ }}moles = \dfrac{{Weight}}{{Molar\;mass}}\] to find the number of moles of nitric acid. Then use the equation for density to find out the volume i.e.\[Density = \dfrac{{Weight}}{{Volume}}\].
- Then use \[Molarity = \dfrac{{Number{\text{ }}of{\text{ }}moles}}{{Volume}}\] to find out the molarity.

Complete step step solution:
> Before attempting the solution, we should describe what mole, density and molarity is.
 So, 1 mole is the amount of a substance that has exactly $6.02214076 \times {10^{23}}$atoms or particles of that substance.
- Density (\[d\]) – It is the measurement of the amount (in\[kg\]) of a substance in unit volume (in\[L\]) of the solution. The SI unit of density is\[kg/L\].
- Molarity ($M$) – It is a measurement of concentration of a certain substance in a solution.
- Molarity is by definition the moles of a solute that is present in a liter of the solution.
- Molarity is called the molar concentration of a solution. The unit of molarity is $moles/L$.
 > Let the weight of the solution be\[100g\]. So given in the problem is that\[100g\] of the solution contains \[68\% \]nitric acid by mass in aqueous solution i.e. \[68g\].
> We know that
\[No{\text{ }}of{\text{ }}moles = \dfrac{{Weight}}{{Molar\;mass}}\]
No of moles of nitric acid \[ = \dfrac{{68}}{{63}}\](\[\therefore \]Molar mass of nitric acid is 63)
\[ \Rightarrow n = 1.079{\text{ }}moles{\text{ }}of{\text{ }}nitric{\text{ }}acid\]
Now, we know
\[Density = \dfrac{{Weight}}{{Volume}}\]
\[ \Rightarrow 1.504 = \dfrac{{100}}{V}\]
\[ \Rightarrow V = \dfrac{{100}}{{1.504}}\]
\[ \Rightarrow V = 66.5mL\;or0.0665L\]
We know that the equation for molarity is
\[Molarity = \dfrac{{Number{\text{ }}of{\text{ }}moles}}{{Volume}}\]
\[ \Rightarrow M = \dfrac{{1.079}}{{0.0665}}\]
\[ \Rightarrow M = 16.22moles/liter\]
Hence, the molarity of the given sample is \[16.22moles/liter\]

Note – 68% Nitric acid solution in water is an azeotropic mixture , which is a constant boiling mixture in which concentration of solute and solvent remains constant in solution as well as in vapour phase.