Problem 45 - Chemistry Matter and Change

Question

What mass of sodium chloride (NaCl) contains \(4.59 \times 10^{24}\) formula units?

Step-by-Step Solution

Answer

The mass of sodium chloride is approximately 445.62 g.

Step 1: Review Molar Mass of NaCl

Find the molar mass of sodium chloride by adding the atomic masses of sodium (Na) and chlorine (Cl). Sodium has an atomic mass of approximately 22.99 g/mol, and chlorine has an atomic mass of approximately 35.45 g/mol. The molar mass of NaCl is therefore 22.99 + 35.45 = 58.44 g/mol.

Step 2: Calculate Number of Moles

To calculate the number of moles, we use Avogadro's number, which states there are approximately \(6.022 \times 10^{23}\) formula units per mole. Divide the number of formula units given by Avogadro's number. This is \(\frac{4.59 \times 10^{24}}{6.022 \times 10^{23}} \approx 7.625\) moles of NaCl.

Step 3: Convert Moles to Mass

To find the mass, multiply the number of moles by the molar mass of NaCl. Therefore, the mass is \(7.625 \text{ moles} \times 58.44 \text{ g/mol} \approx 445.62 \text{ g}\).

Key Concepts

Understanding Sodium Chloride (NaCl)

Sodium chloride, commonly known as table salt, is one of the most well-known compounds. This compound is made up of two elements: sodium (Na) and chlorine (Cl). When sodium, a highly reactive metal, combines with chlorine, a greenish-yellow gas, they form a stable compound called sodium chloride. The chemical formula for sodium chloride is NaCl, meaning each unit of sodium chloride consists of one sodium atom and one chlorine atom. It is this simple 1:1 ratio that defines the structure of sodium chloride and allows it to form the well-known crystalline solid that you sprinkle on your food.

Exploring Avogadro's Number

Avogadro's number is a fundamental concept in chemistry and is essential for converting between atoms, molecules, and moles. Avogadro's number is approximately \(6.022 \times 10^{23}\). It defines the quantity of particles (such as atoms, molecules, or formula units) in one mole of a substance. By using Avogadro's number, chemists can relate the microscopic world of atoms to the macroscopic world of grams and moles. This significant number is based on the number of atoms in exactly 12 grams of carbon-12 isotope, but it applies universally across different elements and compounds. When using Avogadro's number, it is crucial to remember that it considers particles at the atomic or molecular level, making it invaluable for converting formula units of a chemical substance into moles.

Performing Moles to Mass Conversion

Converting moles to mass is a common task in chemistry which involves using the molar mass of the substance. The molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). For sodium chloride (NaCl), the molar mass is approximately 58.44 g/mol, as calculated from the atomic masses of sodium and chlorine. To convert moles to mass, you will multiply the number of moles by the molar mass. For example, if you have 7.625 moles of NaCl, you can calculate the mass by multiplying: \(7.625 \text{ moles} \times 58.44 \text{ g/mol} \approx 445.62 \text{ grams}\). This method is essential for practical applications in the lab, where precise measurements are vital for experiments and reactions.