Question

Which sample contains the greatest number of atoms? (a) 10.0 g He (b) 25.0 g Ne (c) 115 g Xe

Short answer

Using Avogadro's number, He has \(1.505 \times 10^{24}\) atoms, Ne has \(7.525 \times 10^{23}\) atoms, and Xe has \(5.297 \times 10^{23}\) atoms. Therefore, the helium (He) sample contains the greatest number of atoms.

Step-by-step solution

Determine Moles of Each Gas

Use the molar mass to convert grams to moles for each gas using the formula: number of moles = mass / molar mass. Molar masses (in g/mol) are approximately 4 for Helium (He), 20 for Neon (Ne), and 131 for Xenon (Xe). So the moles for each sample are: for He: 10.0 g / 4 g/mol, for Ne: 25.0 g / 20 g/mol, for Xe: 115 g / 131 g/mol.

Calculate the Number of Atoms

Use Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol) to convert moles to atoms. Multiply the moles calculated in Step 1 by Avogadro's number to get the number of atoms for each gas.

Compare the Number of Atoms

Compare the calculated number of atoms for each gas to determine which sample contains the greatest number of atoms.

Key concepts

Avogadro's Number

In the wondrous world of chemistry, Avogadro's number represents a foundational cornerstone that helps us understand the link between macroscopic measurements and the world of atoms and molecules. Named after the scientist Amedeo Avogadro, this constant is approximately equal to \(6.022 \times 10^{23}\) and is used to define the number of constituent particles, typically atoms or molecules, in one mole of a substance.

Whenever you weigh out a substance and measure its mass in grams, Avogadro's number offers a bridge to the atomic scale. For example, if you have a mole of helium atoms, this means you have \(6.022 \times 10^{23}\) helium atoms at your disposal. Understanding the magnitude of Avogadro's number can be tough—it's incredibly large. Imagine this: if each atom were the size of a pea, a mole of atoms would create a mountain much larger than Earth!

Molar Mass Calculation

To unravel the mystery of how much one mole of a substance weighs, we turn to molar mass calculation. Molar mass, essentially the mass of one mole of a substance, is an intrinsic property of each element and compound, typically measured in grams per mole (g/mol).

You can find the molar mass listed on the periodic table as the atomic weight for elements. For compounds, you would calculate it by adding up the atomic weights of all the atoms present in the formula. Here's a simple rule to follow: The molar mass of an element in grams per mole is numerically equivalent to its atomic mass in atomic mass units (amu).

For exercises like the one above, to convert grams to moles, the formula takes the form: \[ \text{number of moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}}. \] So when it comes to deciding how many moles are in a given mass of an element, remember that the molar mass acts as your chemistry currency exchange rate.

Mol-to-Atom Conversion

Cracking the code from moles to atoms is a cinch once you get the hang of it. The process, known famously as mol-to-atom conversion, employs Avogadro's number as a conversion factor. When you determine the amount of moles in a sample using its mass and molar mass, you're only halfway through the journey.

To proceed to the realm of atoms, just multiply the number of moles by Avogadro's number:\[ \text{number of atoms} = \text{number of moles} \times \text{Avogadro's number}. \]

Each mole of any substance contains the same number of particles as there are atoms in exactly 12 grams of carbon-12. This allows chemists to relatively count atoms by weighing. So, in the textbook problem, after calculating moles, one simply multiplies by Avogadro's number to find the greatest number of atoms—in absolute terms, not the size of atoms or their molecular makeup. The universality of Avogadro's number across all elements makes this conversion simple and uniformly applicable.