Question

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

Short answer

The mass of sodium chloride (NaCl) containing \(4.59 \times 10^{24}\) formula units is approximately 445.77 grams.

Step-by-step solution

Find the number of moles of NaCl

To find the number of moles, we will use the formula: \[Moles = \frac{Formula\:Units}{Avogadro's\:Number}\] Here, Avogadro's number is \(6.022 \times 10^{23}\) formula units/mol and the given formula units are \(4.59 \times 10^{24}\). Now, let's calculate the moles. \[Moles\:of\:NaCl = \frac{4.59 \times 10^{24}\:Formula\:Units}{6.022 \times 10^{23}\:Formula\:Units/mol}\]

Calculating the moles of NaCl

Calculate the moles of NaCl by dividing the given formula units by Avogadro's number. \[Moles\:of\:NaCl = \frac{4.59 \times 10^{24}}{6.022 \times 10^{23}} = 7.62\:moles\]

Calculate the molar mass of NaCl

Find the molar mass of NaCl using the periodic table. The atomic mass of sodium (Na) is approximately 23 g/mol, and the atomic mass of chlorine (Cl) is approximately 35.5 g/mol. Add these atomic masses to find the molar mass of NaCl. \[Molar\:Mass\:of\:NaCl = 23\:\cancel{g/mol\:Na} + 35.5\:\cancel{g/mol\:Cl} = 58.5\:g/mol\:NaCl\]

Calculate the mass of NaCl

Now, we will calculate the mass of NaCl using the formula: \[Mass = Moles \times Molar\:Mass\] Insert the calculated moles and molar mass of NaCl into the formula: \[Mass\:of\:NaCl = 7.62\:moles \times 58.5\:g/mol\]

Calculate the mass of NaCl and express the result with the correct unit

Multiply the calculated moles and molar mass of NaCl to find the mass. \[Mass\:of\:NaCl = 7.62 \times 58.5 = 445.77\:g\] So, the mass of sodium chloride (NaCl) containing \(4.59 \times 10^{24}\) formula units is approximately 445.77 grams.

Key concepts

Avogadro's Number

Understanding Avogadro's number is crucial when dealing with stoichiometry problems involving chemical substances at the molecular or atomic level. Avogadro's number, designated as \(6.022 \times 10^{23}\), represents the quantity of entities (atoms, molecules, ions, or other particles) in one mole of a substance.

When we refer to Avogadro's number in a real-world scenario, we're essentially addressing how many units of a specific substance we have when we weigh out one mole of that substance. For instance, if we say we have a mole of sodium chloride (NaCl), we mean that we have \(6.022 \times 10^{23}\) formula units of NaCl.

Therefore, when the exercise asks for the mass of sodium chloride that contains \(4.59 \times 10^{24}\) formula units, we're effectively dealing with a quantity several times larger than Avogadro's number, indicating we have more than one mole of NaCl. The step-by-step solution demonstrates how this large number relates to the substantive amount of NaCl.

Molar Mass Calculation

Molar mass is a fundamental concept when solving stoichiometry problems because it connects the mass of a substance with its amount in moles. The molar mass of a chemical compound such as sodium chloride (NaCl) is the sum of the atomic masses of its constituent atoms, based on the atomic weights given in the periodic table.

To perform a molar mass calculation, simply look up the atomic mass of each element in a compound and then multiply each by the number of times that element appears in one molecule of the compound. For NaCl, the molar mass calculation uses the atomic mass of sodium (approximately 23 g/mol) and chlorine (approximately 35.5 g/mol) to yield the combined molar mass of 58.5 g/mol for NaCl.

This value is vital in converting moles of NaCl to grams, as it provides the conversion factor needed to compute the mass of a certain number of moles of NaCl, a step shown in the exercise's solution.

Mole Concept

The mole concept is the cornerstone of quantitative chemistry, providing a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and liters that we can measure and observe. A mole is defined as the amount of a substance that contains the same number of particles as there are atoms in exactly 12 grams of carbon-12, which is Avogadro's number.

In the provided example, the calculation begins with the mole concept by determining the number of moles from a given number of formula units of NaCl. Once the moles are calculated, we can use this information, along with the molar mass, to find out the corresponding mass in grams. The mole ensures that chemists have a consistent method to convert back and forth between the mass of a substance and the number of atoms or molecules it contains.

This concept clearly demonstrates the importance of moles in stoichiometry, as it's the unit that helps chemists make sense of large quantities of tiny particles in a practical and measurable way, ultimately allowing the computation of the mass of NaCl as shown in the final steps of the exercise.