Question

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

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

Step-by-step solution

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.

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.

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. \(\frac{100 g}{1.18 g/mL} \approx 84.75 mL\)

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, \( \frac{84.75 mL}{1,000 mL/L} = 0.08475 L\)

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 \(\frac{0.476 mol}{0.08475 L} \approx 5.61 M\)

Key concepts

Density

Density is a way to express how much something weighs relative to the amount of space it occupies. Imagine comparing a balloon filled with air to a balloon filled with water. Even if both balloons are the same size (volume), the one with water is heavier (denser) because the water molecules are packed more tightly. This concept is crucial in chemistry when dealing with solutions.
The density formula is given by:

• Density = Mass / Volume

In the given exercise, the solution has a density of 1.18 g/cm³. This means every 1 cubic centimeter of this nitric acid solution weighs 1.18 grams. Understanding this helps us convert mass into volume and vice versa, which is essential when calculations need volume rather than mass, like in molarity calculations. By knowing both the mass of the solution and its density, you can easily find the volume it occupies.

Solution Concentration

Solution concentration describes how much solute is present in a given amount of solution. There are different ways to express concentration, but the exercise focuses on percent by mass, which indicates how many grams of solute are present per 100 grams of solution.
Let's break down the terms:

• 30% by mass means 30 grams of nitric acid (solute) in every 100 grams of the solution (solute plus solvent).

Expressing concentration in this way is useful because it considers both the solute and the solvent, giving you a clearer picture of how concentrated or dilute a solution is. It's a standard method that helps chemists prepare solutions accurately. Using this percentage allows us to calculate the grams of HNO₃ directly needed for further steps in finding molarity.

Molar Mass

Molar mass is like the weight of the building blocks that make up a substance. It explains how many grams one mole of a particular substance weighs and is expressed in g/mol. For nitric acid (HNO₃), its molar mass is calculated by summing the atomic masses:

• Hydrogen (H): roughly 1.01
• Nitrogen (N): roughly 14.01
• Oxygen (O, 3 atoms): roughly 16.00 x 3 = 48.00

This gives: 1.01 + 14.01 + 48.00 = 63.01 g/mol.
Knowing the molar mass is crucial when converting grams of a substance to moles, which is a necessary step in many chemical calculations, including finding the molarity. For nitric acid in the exercise, using 30 grams of HNO₃ allowed us to compute the number of moles using its molar mass. This step translates weight into a number of particles, crucial for stoichiometry and understanding chemical reactions.

Volume Conversion

When dealing with chemical solutions, consistency in units is important for accuracy. Volume is often given in milliliters (mL), but for molarity, which is moles per liter (M), you need volume in liters (L).
The conversion from mL to L is straightforward:

• Divide the number of milliliters by 1,000

This is because 1 L equals 1,000 mL.
In the problem at hand, the solution volume calculated was approximately 84.75 mL. To convert it to liters, divide by 1,000, resulting in 0.08475 L. Making this conversion ensures all parts of the molarity formula are compatible, allowing for correct calculations of solution concentration. Understanding this quick conversion is handy for any chemistry task involving liquid measurements.