Question

One gram of gold costs $75. How much would one atom of gold be worth?

Answer 1

One atom of gold is worth $0.000 000 000 000 000 000 025.

Explanation:

Let's do the calculation in three steps.

1. Convert the mass of gold to moles of gold.

`1 color(red)(cancel(color(black)("g Au"))) × "1 mol Au"/(197.0 color(red)(cancel(color(black)("g Au")))) = 5.076 × 10^-3 "mol Au"`

2. Convert moles of gold to atoms of gold.

`5.076 × 10^-3 color(red)(cancel(color(black)("mol Au"))) × (6.022 × 10^23 "atoms Au")/(1 color(red)(cancel(color(black)("mol Au")))) = 3.057 × 10^21 "atoms Au"`

3. Now, find the price of 1 atom of gold.

`1 color(red)(cancel(color(black)("atom Au"))) × "$75"/(3.057 × 10^21 color(red)(cancel(color(black)("atoms Au")))) = $2.5 × 10^-20 = "$0.000 000 000 000 000 000 025"`