Problem 4 - Introductory Chemistry Atoms First

Question

Suppose you have \(0.5\) mole of gold, Au, atoms. (a) How many gold atoms do you have? (b) What is the mass in grams of this much gold?

Step-by-Step Solution

Answer

(a) The number of gold atoms in 0.5 moles of gold is \(3.011\times 10^{23}\) atoms. (b) The mass of 0.5 moles of gold is \(98.5\) grams.

Step 1: Determine moles of gold atoms

Given, we have 0.5 moles of gold atoms.

Step 2: Calculate the number of gold atoms

To calculate the number of gold atoms, use the moles and Avogadro's constant: Number of atoms = Moles x Avogadro's constant The number of gold atoms can be calculated as: Number of atoms = 0.5 moles x (6.022 x 10^23 atoms/mole) #a) Answer:# The number of gold atoms in 0.5 moles of gold is \(0.5 * 6.022 \times 10^{23}\) atoms, or \(3.011\times 10^{23}\) atoms. #b) Mass in grams of this much gold#

Step 1: Determine moles of gold

We already have 0.5 moles of gold (given).

Step 2: Calculate the mass in grams

To calculate the mass in grams, use moles and the atomic weight of gold: Mass (g) = Moles x Atomic weight The mass in grams of 0.5 mole of gold can be calculated as: Mass (g) = 0.5 moles x 197 g/mole #b) Answer:# The mass of 0.5 moles of gold is \(0.5\ * 197\) grams, or \(98.5\) grams.

Key Concepts

Avogadro's Constant

Understanding Avogadro's constant is crucial for grasping the basics of chemistry. Simply put, it's the number of particles, like atoms or molecules, that you'll find in one mole of substance. With Avogadro's constant valued at approximately \(6.022 \times 10^{23}\) entities per mole, it becomes a key player in converting between microscopic scale entities and macroscopic scale quantities, which is particularly useful in chemical equations and reactions.

For instance, if we have 0.5 moles of a substance, as in the gold atom example, we multiply this amount by Avogadro's constant \(0.5 moles \times 6.022 \times 10^{23} atoms/mole\) to determine the exact number of atoms. This calculation is pivotal in both theoretical and practical chemistry since it bridges the atomic scale and amounts we can actually measure.

Atomic Weight of Gold

The atomic weight of gold, which is \(197g/mole\), represents the average mass of one mole of gold atoms. This concept is akin to a 'chemical-scale' unit of mass, establishing a link between the mole concept and the actual physical weight of a substance. It allows us to calculate the mass of gold in grams when dealing with moles.

When confronted with the need to calculate the mass of 0.5 moles of gold, one can employ this atomic weight. The calculation would be \(0.5 moles \times 197 g/mole\), yielding a result of \(98.5 grams\) of gold. Subsequently, this method is essential in many fields, ranging from jewelry making to chemistry labs, as it empowers us to precisely translate the quantity of matter from the atomic level to tangible weights that are applicable in the real world.

The Mole Concept

The mole concept serves as an indispensable bridge in chemistry, by providing a link between the micro world of atoms and the macro world we can observe. A mole is a unit of measurement used to quantify a specific number of chemical entities, typically atoms or molecules. One mole is related to Avogadro's constant, corresponding to \(6.022 \times 10^{23}\) particles.

To comprehend this concept more deeply, consider your spice rack at home. Just as a teaspoon allows you to count out servings without counting each grain of spice, the mole lets chemists work with atoms without counting each one. The idea of the mole allows us to use everyday scales to measure out amounts of substance that correspond to very precise numbers of atoms, molecules, or ions, changing abstract numbers into practical ones. For example, 0.5 moles of a substance would have half of Avogadro's constant of particles, and we can then calculate mass or volume of the substance at hand with ease, making it an elegant simplicity that's at the heart of chemical practice and education.