A Fascinating Calculation of Gold Atoms in a Bracelet

Calculating Gold Atoms in the Bracelet

In order to determine the number of particles of gold atoms in the bracelet, we first need to calculate the mass of gold present in the bracelet.

Given that the bracelet contains 0.364 mol of metal atoms and that 66% of the bracelet is gold, we can calculate the mass of gold in the bracelet as follows:

0.364 mol x 66% = 0.364 mol x 0.66 = 0.24024 mol

Next, we need to convert the moles of gold into grams. The molar mass of gold is 196.966569 g/mol, so:

0.24024 mol x 196.966569 g/mol = 47.32 g

Therefore, the mass of gold in the bracelet is 47.32 grams.

Finally, we need to convert the mass of gold into the number of particles of gold atoms. Since the question asks for particles rather than mass, we need to convert the mass into particles using the molar mass of gold:

47.32 g x (1 mol / 196.966569 g) = 0.24024 mol

There are 0.24024 moles of gold atoms in the bracelet.

Now, we know that 1 mole of any substance contains Avogadro's number of particles, which is 6.022 x 10^23. Therefore:

0.24024 mol x 6.022 x 10^23 atoms/mol = 1.448 x 10^23 atoms

Thus, there are approximately 1.448 x 10^23 particles of gold atoms in the bracelet.