Answer
11.7
Work Step by Step
Let's take,
The volume of material is filled = V
Number of cubes = N
Length of an edge of a cube = L
So, we can write,
$V=NL^{3}=>L=\sqrt[3] {\frac{V}{N}}-(1)$
We know that,
Volume = (mass)/(Density), Therefore (1)=>
$L=\sqrt[3] {\frac{m}{\rho N}}$
We know that,
m/N = Molecular mass (M), Therefore,
$L=\sqrt[3] {\frac{M}{\rho}}$
Let's apply this equation to both the vapor and the liquid phase and we get,
$\frac{L_{vapor}}{L_{liquid}}=\frac{\sqrt[3] {\frac{M}{\rho_{vapor}}}}{\sqrt[3] {\frac{M}{\rho_{liquid}}}}=\sqrt[3] {\frac{\rho_{liquid}}{\rho_{vapor}}}$
Let's plug known values into this equation.
$\frac{L_{vapor}}{L_{liquid}}=\sqrt[3] {\frac{958\space kg/m^{3}}{0.598\space kg/m^{3}}}=11.7$
