Question

The water molecules now in your body were once part of a molecular cloud. Only about onemillionth of the mass of a molecular cloud is in the form of water molecules, and the mass density of such a cloud is roughly 4.0×10−21 g/cm3 Estimate the volume of a piece of molecular cloud that has the same amount of water as your body.

Answer 1

To solve the problem we first need to define the nomenclature by which there is an X amount of water in our body. Let's call this a variable m, corresponding to the total mass in us and whose units are Kilograms.

$Amount_{water} = m (Kg)$

We understand that one millionth of this mass, a small fraction of it, is the equivalent of that of a Water Molecule.

Assuming this to have the same body of water in our body that amount should be approximately

$m_{water}=10^6$

Density of water molecule

$\rho = 10^{-18}kg/m^3$

$V = \frac{m*10^6}{10^{-18}}$

$V = m*10^{24}m^3$