Converting Units to Find Density of Unit Cell

[i_love_science]

I don't understand the ratio [ 1 g / 6.02*10^23 amu] in the following conversion factor:

[228.2 amu / 4.75*10^(-23) cm3] * [ 1 g / 6.02*10^23 amu] = 7.98 g/cm3

(This calculation is in a problem where you're finding the density of a unit cell in g/cm3 - though it has nothing to do with the conversion factor itself)

Thanks.

 

[etotheipi]

The atomic mass unit $m_u$ is defined as $1/12$ the mass of an atom of $^{12}C$. Also, a mole is the number $^{12}C$ atoms in $12\text{g}$ of $^{12}C$ $\implies$ the mass of an individual $^{12}C$ atom is $\mathrm{12g}/N_A$ and the atomic mass unit is $m_u = \mathrm{1g}/N_A$. It follows that$$\frac{1\text{g}}{6.02 \times 10^{23} m_u} = 1$$