Question

The mass of a copper atom is 1.06 10-25 kg, and the density of copper is 8 920 kg/m3 . (a) determine the number of atoms in 1 cm3 of copper.

Answer 1

Mass of copper atom is $1.06\times 10^{-25}kg$ and density of copper atom is $8920 kg/m^{3}$.

First calculate the volume from density and mass as follows:

$V=\frac{m}{d}=\frac{1.06\times 10^{-25} kg}{8920 kg/m^{3}}=1.188\times 10^{-29}m^{3}$

Now, convert $m^{3}$ to $cm^{3}$,

$1 m^{3} = 10^{6} cm^{3}$

Thus,

$1.188\times 10^{-29}m^{3}=1.188\times 10^{-23}cm^{3}$

Now,

$1.188\times 10^{-23}cm^{3}\rightarrow 1.06\times 10^{-25}kg$

Thus,

$1cm^{3}\rightarrow \frac{1.06\times 10^{-25}kg}{1.188\times 10^{-23}kg}=0.00892 kg$

or,

m=8.92 g

The molar mass of copper is 63.54 g/mol thus, number of moles can be calculated as:

$n=\frac{m}{M}=\frac{8.92 g}{63.54 g/mol}=0.1403 mol$

Now, in 1 mol of Cu there are $6.023\times 10^{23}$ atoms, number of atoms in 0.1403 mol will be:

$N=0.1403\times 6.023\times 10^{23}=8.45\times 10^{22} atoms$