# Weight of water from molecular mass to grams per cubic centimeter

1. Nov 11, 2012

### engine123

I’ve been scratching my head (and working in ms excel) about the following for about 6 hours and would greatly appreciate it if somebody could help me.

Basically, I am trying to figure out WHY the density of water is approximately one gram per cubic centimeter (at 1 atm pressure and 4 degrees Celsius).

Note the following conversions:
1 atm = 101,325.01 Pa = 14.7 psi
4 C = 39.2 F = 277 K

Also:
Gas Law Constant = 8.3145

Starting at the molecular level, water has a molecular mass of 18.015 g/mol.

Using the ideal gas law:
density = (pressure) (molar mass) / ((temp) (8.3145))
g/m^3 = (Pa) (g/mol) / ((K) (8.3145))

This is what I come up with:
density = (101,325 Pa) (18.015 g/mol) / ((277 K) (8.3145))
density = 792.56 grams per cubic meter

792.56 grams per cubic cm does NOT equal 1 gram per cubic centimeter.
Why?
Where did I go wrong?

Any guidance is greatly appreciated.

2. Nov 11, 2012

Staff Emeritus
Why did you apply the ideal gas law for a liquid?

3. Nov 11, 2012

### jbriggs444

As Vanadium 50 has pointed out, liquid water is not an ideal gas. The density of liquid water is [much] higher than Boyle's law would predict. The molecules of water stick together and thus exert less pressure on their surroundings than would otherwise be the case.

You also dropped a factor of 10^6, in what appears to be a transcription error. 792.56 grams per cubic cm is incorrect. 792.56 grams per cubic meter is right for an ideal gas with a molecular weight of 18.

I sanity-checked your computation by taking 1200 grams per cubic meter (density of air, according to Google) and multiplying by 18/28 (air is mostly nitrogen with a molecular weight of 28). That comes to 771 grams per cubic meter -- close enough for back-of-the-envelope work.