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Chapter 13: Problem 22

A \(30.00 \%\) -by-mass solution of nitric acid, \(\mathrm{HNO}_{3},\) in water has a density of \(1.18 \mathrm{g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). What is the molarity of \(\mathrm{HNO}_{3}\) in this solution?

Short Answer

Expert verified
The molarity of the \(HNO_3\) solution is approximately \(5.61 M\).

Step by step solution

01

Convert percentage concentration into grams

A \(30.00\%\) -by-mass solution of nitric acid means that there are \(30.00 g\) of \(HNO_3\) in \(100 g\) of solution.
02

Calculate moles of \(HNO_3\)

The molar mass of nitric acid (\(HNO_3\)) is approximately \(63.01 g/mol\). To find the number of moles of \(HNO_3\), divide the mass of the \(HNO_3\) by the molar mass. So, \(\frac{30.00 g}{63.01 g/mol} \approx 0.476 mol\) of \(HNO_3\) are in the solution.
03

Use the density to get the volume of the solution

The density of the solution is given as \(1.18 g/cm^3\), which can be converted to \(1.18 g/mL\) since \(1 cm^3\) is equivalent to \(1 mL\). It's known that the solution includes \(100 g\), so to find the volume, divide the mass of the solution by its density. \(\frac{100 g}{1.18 g/mL} \approx 84.75 mL\)
04

Convert the volume from mL to L

To use in the molarity formula, the volume must be in liters. So convert the volume from \( mL\) to \( L\) by dividing the volume in \( mL\) by \(1000 mL/L\). So, \( \frac{84.75 mL}{1,000 mL/L} = 0.08475 L\)
05

Calculate the molarity

Finally, the molarity can be calculated by dividing the number of moles of \(HNO_3\) by the volume of the solution in liters. So, the molarity of the \(HNO_3\) solution is \(\frac{0.476 mol}{0.08475 L} \approx 5.61 M\)

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Most popular questions from this chapter

Which of the following do you expect to be most water soluble, and why? \(\mathrm{C}_{10} \mathrm{H}_{8}(\mathrm{s}), \mathrm{NH}_{2} \mathrm{OH}(\mathrm{s})\) \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{l}), \mathrm{CaCO}_{3}(\mathrm{s})\).

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