Problem 58 - General Chemistry: Principles and Modern Applications

Question

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?

Step-by-Step Solution

Answer

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

Step 1: 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 \(HNO_3\).

Step 2: 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.

Step 3: 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.

Step 4: 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.

Key Concepts

Molarity

Molarity is an important concept in chemistry that describes the concentration of a solution. In simpler terms, it tells us how much of a substance, called a solute, is present in a given volume of solution. Molarity is represented by the symbol "M" and is calculated in moles per liter (mol/L). For instance, if we say an HNO3 solution has a molarity of 15 M, it means there are 15 moles of nitric acid in one liter of solution.
Calculating molarity can help in various aspects of solution chemistry such as determining the amount of reactants required in chemical reactions or analyzing the concentration changes during reactions.

• To find molarity, you divide the number of moles of solute by the volume of the solution in liters.
• Molarity provides a quantitative relationship with the chemical entities in a reaction.

Knowing the molarity of a solution is vital for precise laboratory work and efficient chemical analysis.

Molar Mass

Molar mass is the mass of one mole of a given substance. It's usually expressed in grams per mole (g/mol). To calculate it, you sum the atomic masses of all atoms in a chemical formula by consulting the periodic table. For nitric acid (HNO3), this means adding the atomic masses of hydrogen (1.01 g/mol), nitrogen (14.01 g/mol), and three oxygen atoms each weighing (16.00 g/mol).
The calculation results in a molar mass of 63.02 g/mol for HNO3. Understanding molar mass is crucial since it helps:

• Convert between grams and moles, allowing calculations of amounts necessary for chemical reactions.
• Identify how much of each element is present in a compound, critical for determining stoichiometric ratios.

Learning to compute molar mass reliably can assist in solving numerous chemical equations and plays an essential role in solution preparation.

Density

Density describes how much mass is contained in a specific volume of a substance. In simpler terms, it's the weight of an object in relation to its size. In the context of solutions, density is often expressed in grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³). This concept can tell us a lot about the concentration and make-up of a solution.
For the concentrated nitric acid solution described, the density is 1.41 g/mL. Here's why that's important:

• Density can affect how chemicals react, as solutions with higher density often indicate higher concentrations of solutes.
• It helps compute the total mass of a solution when the volume is known, which is key for further concentration calculations.

Mastering the concept of density is useful in both chemistry and everyday life, as it enables an understanding of how substances interact with each other based on mass and volume.

Solution Chemistry

Solution chemistry deals with the study of solutions, which are homogeneous mixtures of solvents and solutes. In this context, the solvent is the substance in larger quantity, while the solute is the substance that is dissolved. It's essential to understand how they work together to form a uniform mixture.
The study of solutions encompasses understanding concentrations, reaction kinetics, and thermodynamics of dissolving processes. In solution chemistry:

• Concentration concepts like molarity and percent by mass play important roles in determining the strength and properties of the solution.
• Solubility factors dictate the extent to which a solute can dissolve in a solvent, defined by temperature, pressure, and chemical nature.

By deeply understanding these processes, chemists can predict and manipulate chemical reactions in solutions, aiding in everything from industrial applications to simple laboratory tasks.