Answer : The volume of the cube is, ![21.88cm^3](https://tex.z-dn.net/?f=21.88cm%5E3)
Solution : Given,
Density of nickel = ![8.91g/cm^3](https://tex.z-dn.net/?f=8.91g%2Fcm%5E3)
Number of nickel atoms = ![2\times 10^{24}](https://tex.z-dn.net/?f=2%5Ctimes%2010%5E%7B24%7D)
Molar mass of nickel = 58.7 g/mole
First we have to calculate the moles of nickel.
As,
atoms form 1 mole of nickel
So,
atoms form
moles of nickel
The moles of nickel = 3.321 moles
Now we have to calculate the mass of nickel.
![\text{ Mass of Ni}=\text{ Moles of Ni}\times \text{ Molar mass of Ni}](https://tex.z-dn.net/?f=%5Ctext%7B%20Mass%20of%20Ni%7D%3D%5Ctext%7B%20Moles%20of%20Ni%7D%5Ctimes%20%5Ctext%7B%20Molar%20mass%20of%20Ni%7D)
![\text{ Mass of Ni}=(3.321moles)\times (58.7g/mole)=194.94g](https://tex.z-dn.net/?f=%5Ctext%7B%20Mass%20of%20Ni%7D%3D%283.321moles%29%5Ctimes%20%2858.7g%2Fmole%29%3D194.94g)
The mass of nickel = 194.94 g
Now we have to calculate the volume of nickel.
![Density=\frac{Mass}{Volume}](https://tex.z-dn.net/?f=Density%3D%5Cfrac%7BMass%7D%7BVolume%7D)
![8.91g/cm^3=\frac{194.94g}{Volume}](https://tex.z-dn.net/?f=8.91g%2Fcm%5E3%3D%5Cfrac%7B194.94g%7D%7BVolume%7D)
![Volume=21.88cm^3](https://tex.z-dn.net/?f=Volume%3D21.88cm%5E3)
Therefore, the volume of the cube is, ![21.88cm^3](https://tex.z-dn.net/?f=21.88cm%5E3)