To find the number of gold atoms in the bracelet, we need to follow a series of steps.
Step 1: Convert the weight of the bracelet from ounces to grams.
Since the atomic weight of gold is expressed in grams, we need to convert the weight from ounces to grams. To do this, we'll use the conversion factor: 1 ounce = 28.35 grams.
Weight of the bracelet in grams = 0.408 ounce × 28.35 grams/ounce
Step 2: Determine the mass of the gold in the bracelet.
The bracelet is made of 18 karat gold, which means it is 75% gold by mass. Therefore, we can calculate the mass of the gold in the bracelet by multiplying the total mass of the bracelet by the gold percentage (75%).
Mass of gold in the bracelet = Total mass of the bracelet × Gold percentage
Step 3: Convert the mass of the gold to moles.
To find the number of gold atoms, we need to convert the mass of the gold to moles. This can be done by dividing the mass of gold by the molar mass of gold, which is 196.967 grams/mole.
Number of moles of gold = Mass of gold in grams / Molar mass of gold
Step 4: Calculate the number of gold atoms.
Once we have the number of moles, we can calculate the number of gold atoms using Avogadro's number, which is 6.022 × 10^23 atoms/mole.
Number of gold atoms = Number of moles of gold × Avogadro's number
By following these steps, we can determine the number of gold atoms in the bracelet.