Question

How many atoms are there in a 5.2-g copper

Answer 1

There are
`4.93* 10^(22)` copper atoms in 5.2 gram of metallic copper.

Explanation:

Start by finding the number of moles of copper atoms in that 5.2 gram of metallic copper. Look up the relative atomic mass of copper on a modern periodic table.

• Cu: 63.546.

In other words, the mass of one mole of copper atoms is 63.546 gram.

`M(\mathrm{Cu}) = \rm 63.546\; g\cdot mol^(-1)`.

How many moles of copper atoms in that 5.2 gram sample?

`\displaystyle n = (m)/(M) =\rm (5.2\; g)/(63.546\; g\cdot mol^(-1)) = 0.0818305\; mol`.

Now, how many atoms is
`\rm 0.0818305\; mol`?

The Avogadro's Number gives the number of particles in one mole:

`N_A \approx \rm 6.022* 10^(23)\;mol^(-1)`. (Encyclopedia Britannica)

There are
`6.022* 10^(23)` particles (a very large number) in one mole.
`\rm 0.0818305\; mol` of copper atoms will thus contain

`N = n\cdot N_A \approx \rm 0.0818305\; mol* 6.023* 10^(23)\;mol^(-1) \approx 4.93* 10^(22)`

copper atoms.