Respuesta :
Answer : The volume of the cube is, [tex]21.88cm^3[/tex]
Solution : Given,
Density of nickel = [tex]8.91g/cm^3[/tex]
Number of nickel atoms = [tex]2\times 10^{24}[/tex]
Molar mass of nickel = 58.7 g/mole
First we have to calculate the moles of nickel.
As, [tex]6.022\times 10^{23}[/tex] atoms form 1 mole of nickel
So, [tex]2\times 10^{24}[/tex] atoms form [tex]\frac{2\times 10^{24}}{6.022\times 10^{23}}=3.321[/tex] moles of nickel
The moles of nickel = 3.321 moles
Now we have to calculate the mass of nickel.
[tex]\text{ Mass of Ni}=\text{ Moles of Ni}\times \text{ Molar mass of Ni}[/tex]
[tex]\text{ Mass of Ni}=(3.321moles)\times (58.7g/mole)=194.94g[/tex]
The mass of nickel = 194.94 g
Now we have to calculate the volume of nickel.
[tex]Density=\frac{Mass}{Volume}[/tex]
[tex]8.91g/cm^3=\frac{194.94g}{Volume}[/tex]
[tex]Volume=21.88cm^3[/tex]
Therefore, the volume of the cube is, [tex]21.88cm^3[/tex]
