# Possibility of determining the mass of the water without a scale?

Possibility of determining the mass of the water by knowing water volume, water temperature and atmospheric pressure.

I want to know if I can determine the mass of $V=0.01\,m^3$ of water in $T=298\,k$ and $P=1\,atm$.

So what formula should I use?

• What's the density of water? – Kyle Kanos Jul 22 '13 at 17:55
• Hint: A cubic meter is $10^6$ cubic centimeters, which, if it's full of water, is $10^6$ grams. – Mike Dunlavey Jul 22 '13 at 18:00
• wolframalpha.com/input/… – Ali Jul 22 '13 at 18:06

The density of water is, nominally, 1g/ml, but varies depending on several factors

• Impurities (dissolved ions, salts, other solutes will change the density)

Salts and ions are typically higher mass atoms/molecules than the 18atm H$_2$O molecule, as such any dissolved ions increase the mass of the liquid in the same volume and therefore increase the density, Ocean Salt water can be 3-5% more dense than freshwater at the same temperature, for instance. Salt water also depresses the freezing point and this affects the temperature dependence of the density.

• Temperature

Water density varies greatly with temperature, fresh water near boiling can be as low as 950 g/l (.95g/ml or 950kg/m$^3$) increasing as temperature decreases to a maximum at 4$^\circ$C (1g/ml) before decreasing slightly to freezing. For water room temperature and below the variation is less than $.5$% . This is by far the largest contribution to variation in density for fresh water at normal earth conditions.

• External Pressure

Liquids are relatively poorly compressible, so at atmospheric levels the atmospheric pressure will contribute negligibly to the density of water, however freezing temperatures get depressed with changes in atmospheric pressure and can affect the density vs temperature. At higher pressures the effects are more pronounced

For all of these conditions, there are really no equations to determine the density, and those that exist are typically quantitatively based on experimental measurement and apply to a certain set of conditions. THe answer is that you have to look it up based on your conditions. (Most tables for density vs temperature online are given for fresh water at 1 ATM)

Depending on the accuracy you desire you can analyze all these properties without measuring its mass to determine the density with greater precision. However for most daily uses, an estimate of 1g/ml is close enough

$$9971 \text{grams}$$