How many gold atoms are in a 0.495 ounce, 18 k gold bracelet?

How can we calculate the number of gold atoms in a 0.495 ounce, 18-karat gold bracelet?

We need to determine the number of gold atoms in a 0.495 ounce, 18-karat gold bracelet. How do we calculate it?

Calculation of Gold Atoms in a 0.495 Ounce, 18 K Gold Bracelet

To determine the number of gold atoms in a 0.495 ounce, 18-karat gold bracelet, we need to consider the mass of gold in the bracelet and the molar mass of gold. First, we calculate the mass of pure gold in the bracelet. Since 18-karat gold is 75% gold by mass, we can calculate the mass of gold using the following formula:

Mass of Gold = Total Mass of Bracelet * Percentage of Gold

Given that the total mass of the bracelet is 0.495 ounces and the gold content is 75%, we can calculate:

Mass of Gold = 0.495 ounces * 0.75 = 0.37125 ounces

Next, we need to convert the mass of gold from ounces to grams because the molar mass of gold is typically expressed in grams. Since 1 ounce is approximately equal to 28.3495 grams, we can convert the mass of gold:

Mass of Gold = 0.37125 ounces * 28.3495 grams/ounce = 10.51054625 grams

The molar mass of gold (Au) is 196.97 grams/mol. Using this molar mass, we can calculate the number of moles of gold in the bracelet:

Number of moles of Gold = Mass of Gold / Molar mass of Gold

Number of moles of Gold = 10.51054625 grams / 196.97 grams/mol = 0.053359 moles

To calculate the number of gold atoms, we use Avogadro's number (6.022 x 10^23 atoms/mol), which represents the number of particles (atoms, molecules) in one mole:

Number of Gold Atoms = Number of moles of Gold * Avogadro's Number

Number of Gold Atoms = 0.053359 moles * 6.022 x 10^23 atoms/mol ≈ 3.209 x 10^22 atoms