Problem 98 - Chemistry Matter and Change

Question

Jewelry A bracelet containing 0.200 mol metal atoms is 75\(\%\) gold. How many particles of gold atoms are in the bracelet?

Step-by-Step Solution

Answer

There are \(9.033 \times 10^{22}\) gold atoms in the bracelet.

Step 1: Find the Number of Moles of Gold

Since the bracelet is 75% gold, you start by calculating the number of moles of gold in the bracelet. You have 0.200 moles of metal atoms in total, so the number of moles of gold is given by \(0.200 \times 0.75 = 0.150\) moles.

Step 2: Calculate the Number of Gold Atoms

Use Avogadro's Number, which is \(6.022 \times 10^{23}\), to convert moles of gold to the number of atoms. Since you have 0.150 moles of gold, multiply this by Avogadro's Number: \(0.150 \times 6.022 \times 10^{23} = 9.033 \times 10^{22}\) gold atoms.

Key Concepts

Moles and Molar Mass

When dealing with chemical compositions, understanding moles and molar mass is essential. A mole is a fundamental unit in chemistry that represents a specific number of particles, such as atoms, molecules, or ions. The number of particles in one mole is equal to Avogadro's Number, which we’ll discuss later.

The molar mass, on the other hand, refers to the mass of one mole of a given substance and is usually measured in grams per mole (g/mol). For example, the molar mass of gold (Au) is approximately 197 g/mol. This means when you have one mole of gold atoms, they collectively weigh 197 grams. Connecting moles and molar mass is crucial as it allows scientists to calculate how many atoms are present in a sample by using its mass or vice-versa. This conversion is key in understanding chemical quantities and reactions.

Avogadro's Number

Avogadro's Number is a cornerstone concept in chemistry, helping bridge the microscopic world of atoms and the macroscopic world we can observe. It is defined as the number of constituents (such as atoms or molecules) in one mole of any substance, which is approximately \[6.022 \times 10^{23}\] per mole.

This massive number implies that even a tiny amount of a substance contains an incredibly large collection of atoms. For example, if we have 0.150 moles of gold, as indicated in the original problem, utilizing Avogadro's Number allows us to precisely calculate just how many gold atoms are present. Multiplying 0.150 moles by Avogadro's Number gives us \[9.033 \times 10^{22}\] gold atoms, emphasizing the vast number of particles even in small quantities of matter. Avogadro's Number is fundamental in understanding and visualizing chemical quantities and is used across various calculations in chemistry.

Gold Atoms

Gold, symbolized as Au, is a precious metal known for its luster, malleability, and conductivity. At the atomic level, gold atoms have a distinct set of properties that differentiate them from other metals.

Gold atoms are characterized by their atomic number 79, which means they have 79 protons in their nucleus. The existence and quantity of gold atoms in a given sample can be quantified using the concept of moles. For instance, in the exercise provided, the bracelet contains 75% gold, which translates to 0.150 moles of gold atoms.

This understanding allows one to apply Avogadro's Number to derive the total number of atoms within the bracelet. The computation confirms that \[9.033 \times 10^{22}\] gold atoms are present, underlining the enormous number of atoms constituting even a fractional mole of a material. Such calculations are central to the practical applications of chemistry, be it in crafting jewelry or sophisticated scientific explorations.