Question

How many atoms are there in a 5.2-g copper

Answer 1

Answer:

There are $4.93\times 10^{22}$ copper atoms in 5.2 gram of metallic copper.

Step-by-step 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?

$\displaystyle n = \frac{m}{M} =\rm \frac{5.2\; g}{63.546\; g\cdot mol^{-1}} = 0.0818305\; mol$.

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

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

$N_A \approx \rm 6.022\times 10^{23}\;mol^{-1}$. (Encyclopedia Britannica)

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

$N = n\cdot N_A \approx \rm 0.0818305\; mol\times 6.023\times 10^{23}\;mol^{-1} \approx 4.93\times 10^{22}$

copper atoms.