How many gold atoms are in an 0.408 ounce, 18 gold bracelet? (18 gold is 75% gold by mass.)

Steps are

0.408 oz x 0.75 give masss of gold

convert the mass in oz to mass in g (say =X)

Look up molar mass for gold (say =M)

number of moles of gold is then

X/M

If Avogadro's Number =N (number of atoms per mole)

then the number of atoms is

XN/M

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.