Answer:
(a) The weight percent HNO3 is 63%.
(b) Density of HNO3 = 111.2 lb/ft3
(c) Molarity = 13792 mol HNO3/m3
Explanation:
(a) Weight percent HNO3
To calculate a weight percent of a component of a solution we can express:

(b) Density of HNO3, in lb/ft3
In this calculation, we use the specific gravity of the solution (1.382). We can start with the volume balance:
![V_s=V_{HNO3}+V_w\\\\\frac{M_s}{\rho_s}=\frac{M_{HNO3}}{\rho_{HNO3}}+\frac{M_w}{\rho_w}\\\\\frac{M_{HNO3}}{\rho_{HNO3}} = \frac{M_s}{\rho_s}-\frac{M_w}{\rho_w}\\\\\rho_{HNO3}=\frac{M_{HNO3}}{\frac{M_s}{\rho_s}-\frac{M_w}{\rho_w}} \\\\ \rho_{HNO3}=\frac{1.704}{\frac{2.704}{1.382*\rho_w}+\frac{1}{\rho_w}} \\\\ \rho_{HNO3}=\frac{1.704}{2.956/ \rho_w}= 0.576*\rho_w[tex]V_s=V_{HNO3}+V_w\\\\\frac{M_s}{\rho_s}=\frac{M_{HNO3}}{\rho_{HNO3}}+\frac{M_w}{\rho_w}\\\\\frac{M_{HNO3}}{\rho_{HNO3}} = \frac{M_s}{\rho_s}-\frac{M_w}{\rho_w}\\\\\rho_{HNO3}=\frac{M_{HNO3}}{\frac{M_s}{\rho_s}-\frac{M_w}{\rho_w}} \\\\ \rho_{HNO3}=\frac{1.704}{\frac{2.704}{1.382*\rho_w}-\frac{1}{\rho_w}} \\\\ \rho_{HNO3}=\frac{1.704}{0.956/\rho_w}= 1.782*\rho_w](https://tex.z-dn.net/?f=V_s%3DV_%7BHNO3%7D%2BV_w%5C%5C%5C%5C%5Cfrac%7BM_s%7D%7B%5Crho_s%7D%3D%5Cfrac%7BM_%7BHNO3%7D%7D%7B%5Crho_%7BHNO3%7D%7D%2B%5Cfrac%7BM_w%7D%7B%5Crho_w%7D%5C%5C%5C%5C%5Cfrac%7BM_%7BHNO3%7D%7D%7B%5Crho_%7BHNO3%7D%7D%20%3D%20%5Cfrac%7BM_s%7D%7B%5Crho_s%7D-%5Cfrac%7BM_w%7D%7B%5Crho_w%7D%5C%5C%5C%5C%5Crho_%7BHNO3%7D%3D%5Cfrac%7BM_%7BHNO3%7D%7D%7B%5Cfrac%7BM_s%7D%7B%5Crho_s%7D-%5Cfrac%7BM_w%7D%7B%5Crho_w%7D%7D%20%5C%5C%5C%5C%20%5Crho_%7BHNO3%7D%3D%5Cfrac%7B1.704%7D%7B%5Cfrac%7B2.704%7D%7B1.382%2A%5Crho_w%7D%2B%5Cfrac%7B1%7D%7B%5Crho_w%7D%7D%20%5C%5C%5C%5C%20%5Crho_%7BHNO3%7D%3D%5Cfrac%7B1.704%7D%7B2.956%2F%20%5Crho_w%7D%3D%200.576%2A%5Crho_w%5Btex%5DV_s%3DV_%7BHNO3%7D%2BV_w%5C%5C%5C%5C%5Cfrac%7BM_s%7D%7B%5Crho_s%7D%3D%5Cfrac%7BM_%7BHNO3%7D%7D%7B%5Crho_%7BHNO3%7D%7D%2B%5Cfrac%7BM_w%7D%7B%5Crho_w%7D%5C%5C%5C%5C%5Cfrac%7BM_%7BHNO3%7D%7D%7B%5Crho_%7BHNO3%7D%7D%20%3D%20%5Cfrac%7BM_s%7D%7B%5Crho_s%7D-%5Cfrac%7BM_w%7D%7B%5Crho_w%7D%5C%5C%5C%5C%5Crho_%7BHNO3%7D%3D%5Cfrac%7BM_%7BHNO3%7D%7D%7B%5Cfrac%7BM_s%7D%7B%5Crho_s%7D-%5Cfrac%7BM_w%7D%7B%5Crho_w%7D%7D%20%5C%5C%5C%5C%20%5Crho_%7BHNO3%7D%3D%5Cfrac%7B1.704%7D%7B%5Cfrac%7B2.704%7D%7B1.382%2A%5Crho_w%7D-%5Cfrac%7B1%7D%7B%5Crho_w%7D%7D%20%5C%5C%5C%5C%20%5Crho_%7BHNO3%7D%3D%5Cfrac%7B1.704%7D%7B0.956%2F%5Crho_w%7D%3D%201.782%2A%5Crho_w)
The density of HNO3 is 1.782 times the density of water (Sp Gr of 1.782). If the density of water is 62.4 lbs/ft3,

(c) HNO3 molarity (mol HNO3/m3)
If we use the molar mass of HNO3: 63.012 g/mol, we can say that in 1,704 kg (or 1704 g) of HNO3 there are 1704/63.012=27.04 mol HNO3.
When there are 1.704 kg of NHO3 in solution, the total mass of the solution is (1.704+1)=2.704 kg.
If the specific gravity of the solution is 1.382 and the density of water at 20 degC is 998 kg/m3, the volume of the solution is

We can now calculate the molarity as
