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Chapter 13: Problem 55

Commercial aqueous nitric acid has a density of $1.12 \mathrm{~g} / \mathrm{mL}\( and is 3.7 M. Calculate the percent \)\mathrm{HNO}_{3}$ by mass in the solution.

Short Answer

Expert verified
The commercial aqueous nitric acid solution has approximately 20.8% HNO3 by mass.

Step by step solution

01

Calculate the mass of 1 L of the solution

To find the mass of 1 L of the solution, we will use the given density, which is \(1.12 \,\text{g}/\text{mL}\). Since there are 1000 mL in 1 L, we can calculate the mass as follows: Mass of 1 L of solution = Density × Volume = \(1.12\, \frac{\text{g}}{\text{mL}} × 1000\, \text{mL} = 1120\, \text{g}\)
02

Calculate the number of moles of HNO3 in 1 L of the solution

We have the molarity of the solution (3.7 M), which gives us the number of moles of HNO3 per liter of the solution. So, in 1 L of the solution, there are: Number of moles of HNO3 = Molarity × Volume = \(3.7\, \text{M} × 1\, \text{L} = 3.7\, \text{moles}\)
03

Calculate the mass of HNO3 in 1 L of the solution

Now, we need to find the molar mass of HNO3. The atomic masses of hydrogen (H), nitrogen (N), and oxygen (O) can be found in the periodic table, which are approximately 1, 14, and 16, respectively. So, the molar mass of HNO3 is: Molar mass of HNO3 = 1 (for H) + 14 (for N) + 16 × 3 (for three O atoms) = 63 \(\mathrm{g/mol}\) We can now use the molar mass and the number of moles of HNO3 to find the mass of HNO3 present in 1 L of the solution: Mass of HNO3 in 1 L of the solution = Number of moles × Molar mass = \(3.7\, \text{moles} × 63\, \frac{\text{g}}{\text{mol}} = 233.1\, \text{g}\)
04

Calculate the percentage of HNO3 by mass

Finally, we can find the percentage of HNO3 by mass in the solution by dividing the mass of HNO3 by the mass of the solution and multiplying by 100: Percentage of HNO3 by mass = \(\frac{\text{Mass of HNO3}}{\text{Mass of 1 L of the solution}} × 100\% = \frac{233.1\, \text{g}}{1120\, \text{g}} × 100\% \approx 20.8\% \) Thus, the commercial aqueous nitric acid solution has approximately 20.8% HNO3 by mass.

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