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.

Respuesta :

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

First calculate the volume from density and mass as follows:

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

Now, convert [tex]m^{3}[/tex] to [tex]cm^{3}[/tex],

[tex]1 m^{3} = 10^{6} cm^{3}[/tex]

Thus,

[tex]1.188\times 10^{-29}m^{3}=1.188\times 10^{-23}cm^{3}[/tex]

Now,

[tex]1.188\times 10^{-23}cm^{3}\rightarrow 1.06\times 10^{-25}kg[/tex]

Thus,

[tex]1cm^{3}\rightarrow \frac{1.06\times 10^{-25}kg}{1.188\times 10^{-23}kg}=0.00892 kg[/tex]

or,

m=8.92 g

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

[tex]n=\frac{m}{M}=\frac{8.92 g}{63.54 g/mol}=0.1403 mol[/tex]

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

[tex]N=0.1403\times 6.023\times 10^{23}=8.45\times 10^{22} atoms[/tex]

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