Question

27. The density of nickel is 8.91 g/cm3. How large a cube, in cm3, would contain 2.00 x 10^24 atoms of nickel? Use dimensional analysis to solve and show all work including units on every number! (5 points)

Answer 1

Answer : The volume of the cube is, $21.88cm^3$

Solution : Given,

Density of nickel = $8.91g/cm^3$

Number of nickel atoms = $2\times 10^{24}$

Molar mass of nickel = 58.7 g/mole

First we have to calculate the moles of nickel.

As, $6.022\times 10^{23}$ atoms form 1 mole of nickel

So, $2\times 10^{24}$ atoms form $\frac{2\times 10^{24}}{6.022\times 10^{23}}=3.321$ moles of nickel

The moles of nickel = 3.321 moles

Now we have to calculate the mass of nickel.

$\text{ Mass of Ni}=\text{ Moles of Ni}\times \text{ Molar mass of Ni}$

$\text{ Mass of Ni}=(3.321moles)\times (58.7g/mole)=194.94g$

The mass of nickel = 194.94 g

Now we have to calculate the volume of nickel.

$Density=\frac{Mass}{Volume}$

$8.91g/cm^3=\frac{194.94g}{Volume}$

$Volume=21.88cm^3$

Therefore, the volume of the cube is, $21.88cm^3$