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Chapter 22: Problem 58

Concentrated \(\mathrm{HNO}_{3}(\text { aq })\) used in laboratories is usually \(15 \mathrm{M} \mathrm{HNO}_{3}\) and has a density of \(1.41 \mathrm{g} \mathrm{mL}^{-1}\) What is the percent by mass of \(\mathrm{HNO}_{3}\) in this concentrated acid?

Short Answer

Expert verified
The percent by mass of \(HNO_3\) in the concentrated acid is 67.0%.

Step by step solution

01

Calculate the molar mass of \(HNO_3\)

First, we need to calculate the molar mass of \(HNO_3\). Using the periodic table, we add up the atomic masses of hydrogen (H, 1.01 g/mol), nitrogen (N, 14.01 g/mol), and oxygen (O, 16.00 g/mol) multiplied by three since there are three oxygen atoms. So, \(1.01g/mol+14.01g/mol+(3*16.00g/mol) = 63.02g/mol\). This is the mass of one mole of \(HNO_3\).
02

Calculate the mass of \(HNO_3\) in one liter of solution

Knowing that molarity is the number of moles of a solute in one liter of solution and using the given molarity of \(HNO_3\), we obtain the mass of \(HNO_3\) by multiplying the molarity \(15 M\) by the molar mass \(63.02 g/mol\). This gives \(15M * 63.02g/mol = 945.3g\). This is the mass of \(HNO_3\) in one liter of solution.
03

Calculate the mass of the solution

Next, we calculate the mass of the solution. The density is defined as mass per unit volume. Using the given density \(1.41 g/mL\) and knowing that one liter equals to \(1000 mL\), we multiply the volume \(1000 mL\) by the density \(1.41 g/mL\) giving \(1000mL * 1.41g/mL = 1410g\). This is the total mass of the solution.
04

Calculate the percent by mass of \(HNO_3\)

The percent by mass is obtained by dividing the mass of the solute \(HNO_3\), by the mass of the solution and then multiplied by 100. So, \((945.3g/1410g) * 100 = 67.0%\). This is the percent by mass of \(HNO_3\) in the concentrated acid.

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