Problem 114 - Chemistry Matter and Change

Question

Arrange from least to most in moles: \(3.00 \times 10^{24}\) atoms Ne, 4.25 mole \(\mathrm{Ar}, 2.69 \times 10^{24}\) atoms \(\mathrm{Xe}, 65.96 \mathrm{g} \mathrm{Kr}\) .

Step-by-Step Solution

Answer

Order: Kr, Ar, Xe, Ne.

Step 1: Identify the Units for Each Quantity

We are given quantities in moles, number of atoms, and grams. To compare them, all quantities must be converted to moles: \(3.00 \times 10^{24}\) atoms Ne, 4.25 moles \(\mathrm{Ar}\), \(2.69 \times 10^{24}\) atoms \(\mathrm{Xe}\), and 65.96 g \(\mathrm{Kr}\).

Step 2: Convert Atoms to Moles for Ne

Use Avogadro's Number, \(6.022 \times 10^{23}\) atoms per mole, to convert the number of atoms of Ne to moles: \[ \text{Moles of Ne} = \frac{3.00 \times 10^{24}}{6.022 \times 10^{23}} \approx 4.98 \text{ moles} \]

Step 3: Convert Atoms to Moles for Xe

Similarly, convert the number of atoms of Xe to moles using Avogadro's Number:\[ \text{Moles of Xe} = \frac{2.69 \times 10^{24}}{6.022 \times 10^{23}} \approx 4.47 \text{ moles} \]

Step 4: Convert Grams to Moles for Kr

First, you need the molar mass of Kr, which is approximately 83.80 g/mol. Then convert grams to moles:\[ \text{Moles of Kr} = \frac{65.96}{83.80} \approx 0.787 \text{ moles} \]

Step 5: List All Quantities in Moles

Now we have all quantities in moles: - Ne: 4.98 moles - Ar: 4.25 moles - Xe: 4.47 moles - Kr: 0.787 moles

Step 6: Order the Quantities from Least to Most

Finally, arrange the moles in ascending order: 1. Kr: 0.787 moles 2. Ar: 4.25 moles 3. Xe: 4.47 moles 4. Ne: 4.98 moles

Key Concepts

Avogadro's Number

Avogadro's Number is a fundamental constant in chemistry, symbolized as \(6.022 \times 10^{23}\). It represents the number of atoms, ions, or molecules present in one mole of a substance. This number is crucial when converting between atoms and moles, allowing chemists to work with manageable quantities of substances in reactions and conversions.
Understanding Avogadro's Number is essential for calculating the number of particles in a given mole or converting particles into moles. In our original problem, we used Avogadro's Number to convert the number of neon (Ne) and xenon (Xe) atoms into moles.

• **Neon (Ne):** When given \(3.00 \times 10^{24}\) atoms, dividing by Avogadro's Number gives approximately 4.98 moles.
• **Xenon (Xe):** Similarly, for \(2.69 \times 10^{24}\) atoms, dividing by Avogadro’s Number yields approximately 4.47 moles.

This highlights how Avogadro's Number acts as a bridge between the microscopic world of atoms and the macroscopic world we can measure.

Molar mass

Molar mass is the mass of one mole of a substance, generally expressed in grams per mole (g/mol). It corresponds to the relative atomic mass of an element or the sum of the atomic masses in a compound. Molar mass allows chemists to convert between the mass of a substance and the amount in moles, a crucial step in many chemical calculations.
In practice, determining the molar mass involves adding up the atomic masses of the constituent elements as seen in the periodic table. For instance, the molar mass of krypton (Kr) is approximately 83.80 g/mol, which means 1 mole of krypton atoms weighs 83.80 grams.
In the initial problem, we converted the given mass of Kr into moles using its molar mass:

• **Krypton (Kr):** Given 65.96 g, using the molar mass (83.80 g/mol) to convert mass into moles resulted in approximately 0.787 moles.

Understanding how to use molar mass is essential for moving between mass and moles in chemical equations and reactions.

Atomic structure

Atomic structure refers to the arrangement of subatomic particles—protons, neutrons, and electrons—within an atom. Every element's atomic structure is unique, with these particles influencing the atom’s chemical properties and behavior.
The nucleus, at the center of an atom, contains protons and neutrons, while electrons orbit this nucleus in electron shells or clouds. The atomic number of an element equals the number of protons and usually matches the number of electrons, determining the atom's identity and its position on the periodic table.
When calculating quantities for chemical reactions, it's key to understand how atoms combine via bonding to form substances. Each element’s unique atomic and electron configuration affects how it will engage in chemical reactions; this is fundamental for predictions based on mole conversions.

• **Neon and Xenon:** Both possess closed electron shells, making them noble gases with limited reactivity.
• **Krypton:** Like Ne and Xe, has a full outer electron shell, which also results in low reactivity.

A good grasp of atomic structure allows for a more intuitive understanding of chemical bonding, reactivity, and behavior across different elements and compounds.