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:
![wt = \frac{mass \, of \, solute}{mass \, of \, solution}=\frac{mass\,HNO_3}{mass \, HNO_3+mass \, H_2O}\\ \\wt=\frac{1.704}{1.704+1} =\frac{1.704}{2.704}= 0.63](https://tex.z-dn.net/?f=wt%20%3D%20%5Cfrac%7Bmass%20%5C%2C%20of%20%5C%2C%20solute%7D%7Bmass%20%5C%2C%20of%20%5C%2C%20solution%7D%3D%5Cfrac%7Bmass%5C%2CHNO_3%7D%7Bmass%20%5C%2C%20HNO_3%2Bmass%20%5C%2C%20H_2O%7D%5C%5C%20%20%5C%5Cwt%3D%5Cfrac%7B1.704%7D%7B1.704%2B1%7D%20%3D%5Cfrac%7B1.704%7D%7B2.704%7D%3D%200.63)
(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,
![\rho_{HNO3}= 1.782*\rho_w=1.782*62.4 \, lbs/ft3=111.2\, lbs/ft3](https://tex.z-dn.net/?f=%5Crho_%7BHNO3%7D%3D%201.782%2A%5Crho_w%3D1.782%2A62.4%20%5C%2C%20lbs%2Fft3%3D111.2%5C%2C%20lbs%2Fft3)
(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
![Vol=\frac{M_{sol}}{\rho_{sol}}=\frac{2.704\, kg}{1.382*998 \, kg/m3} = 0.00196m3](https://tex.z-dn.net/?f=Vol%3D%5Cfrac%7BM_%7Bsol%7D%7D%7B%5Crho_%7Bsol%7D%7D%3D%5Cfrac%7B2.704%5C%2C%20kg%7D%7B1.382%2A998%20%5C%2C%20kg%2Fm3%7D%20%3D%200.00196m3)
We can now calculate the molarity as
![Molarity HNO_3=\frac{MolHNO3}{Vol}=\frac{27.04mol}{0.00196m3} =13792 \frac{molHNO3}{m3}](https://tex.z-dn.net/?f=Molarity%20HNO_3%3D%5Cfrac%7BMolHNO3%7D%7BVol%7D%3D%5Cfrac%7B27.04mol%7D%7B0.00196m3%7D%20%20%3D13792%20%5Cfrac%7BmolHNO3%7D%7Bm3%7D)