The mass of a sample of a **particular chemical compound** is commonly determined by weighing the sample in air and then again in an underwater environment.

A difference in weight between the *two masses indicates* the mass of the chemical compound that has been dissolved into the water.

This method can be applied to water, determining the average mass of one molecule of water (H2O). The formula for this is mass H2O = 1/density H2O, where density H2O is g/cm3.

The problem with this method is that it does not take into account the presence of other compounds or molecules in the solution. It only *detects one specific chemical compound*, leaving out all other possible compounds that may be dissolved in the solution.

There is a more accurate way to determine the mass of a sample of water containing a certain number of molecules of H2o. Rather than simply measuring how much water there is and how many molecules of H2o are present, you *must first determine* how many molecules of H2o are present per molecule of water.

## Calculate the mass of one oxygen molecule

Now that we have the mass of *one hydrogen molecule*, we can calculate the mass of *one oxygen molecule*. One oxygen molecule weighs sixteen times as much as one hydrogen molecule.

So if we have one mole of hydrogen molecules, which has a mass of one gram, then we have six grams of oxygen molecules. This is because there are sixty-six grams in one mole of any substance.

We need to know the number of water molecules in a sample to determine its mass, so let’s figure that out! We will need to do some math, but don’t worry, it is easy math and you can do it!

We need to figure out how many molecules are in a sample of *water containing three point five million billions* (3.55×1022) molecules of H2O.

## Calculate the mass of one water molecule

As mentioned before, one water molecule is *one oxygen atom bonded* to two hydrogen atoms. The mass of one water molecule is, therefore, equal to the mass of *one oxygen atom plus* the masses of two hydrogen atoms.

The molecular mass of O2 is *32 grams per mole* and that of H2 is 2 grams per mole, so the molecular mass of H2O is 32+2=**34 grams per mole**. Therefore, the mass of one water molecule is 34 grams.

Calculate the total number of molecules in a sample

Now that you know the mass of one water molecule, you can calculate the number of these molecules in a given sample. You just need to know how many molecules are in a given volume of water.

You can do this by dividing the weight of a sample (in this case, 1 liter) by the mass of one water molecule (34 grams). The result is 10^6 molecules per liter.

## Calculate the mass of two hydrogen molecules

To calculate the mass of two hydrogen molecules in water, you must first know the mass of one hydrogen molecule and the mass of one molecule of water.

One hydrogen molecule weighs one atomic mass unit, which is 1.66×10−24 grams. One mole (6.02×1023) of **water weighs 18 grams**, so one molecule of water weighs 1 gram.

To find the mass of two hydrogen molecules in 2 milliliters (ml) of H2O, you would divide the volume by the number of molecules. Two hydrogen molecules would fit into 2 ml of H2O, so the total mass would be 2 grams.

This is just a basic explanation for how to find the mass of a sample of water containing a certain number of molecules or atoms of other substances dissolved in it.

## Calculate the mass of two oxygen molecules

The formula for the mass of one oxygen molecule is , where m is the mass, 12 is the mass of a single atom of oxygen, and 2 is the number of atoms.

Therefore, the mass of two oxygen molecules is . As there are 3.55×1022 hydrogen molecules in two grams of water, there are 6.1×1023 hydrogen atoms in that volume.

By calculating the average distance between each hydrogen atom and the neighboring oxygen atom, you can find the volume of each oxygen molecule that surrounds a hydrogen molecule. There are eight such *volumes per molecule* of water, making a total volume of .

Therefore, the mass of **water per 2 grams** is . Due to water’s low density, this value is not very significant and may be overlooked.

## Calculate the mass of two water molecules

To calculate the mass of two water molecules, you must first know the mass of one water molecule. You can find this value in a variety of ways, but one of the most reliable is by using isotopic distribution.

Isotopic distribution uses the relative masses of isotopes to determine an element’s average mass. In this case, we use H2O’s average mass as determined by isotopic distribution and *subtract one hydrogen atom* and *one oxygen atom* to find the average mass of one water molecule.

An easier way to find the mass of one water molecule is to use its molar weight, which is 18 g/mol. This means that every molecule of H2O weighs 18 grams, on average. By multiplying the number of molecules in a given sample (3.55×1022) by the sample’s molecular weight (18 grams), you can find the sample’s total molecular weight.

## Sum all masses together to determine total sample mass

Now let’s get back to our sample of water containing 3.55×1022 (3.55 billion) molecules of H2O. We know the mass of one molecule of H2O is 1 Da, so we can add up the masses of all the molecules in the sample to get the total mass of the sample.

We already calculated that the mass of one molecule of H2O is 1 Da, so we can just sum up the number of molecules in the sample and multiply by 1 Da to get the total mass of the sample.

There are 3.55×1022 molecules in our sample, so multiplying this number by 1 Da gives us a total sample mass of 3.55×10−8 kg, or 3.

## Convert to grams by dividing by 1000||3.55×1022 mol H2O0.03475 Molar H2O0.003475 Molar (18 g/mol)*(18 L/mol)*(1000 mL/L)/(18000 g/kg)*(1 kg/1000 g)*(1 mol/NA g*NA mols/(NA L*NA kg))= 0.003475 Molar (18 g/mol)*(18 L/mol)*(1000 mL/L)/(36000 g/kg)*(1 kg/(1000g)))*((1 mol/(36000 L*36000 kg)))= 0.003475 Molar (18 gr

This answer is very specific, and it takes a lot of steps to get there. It is important to know that this answer is very precise, and that your measurement will not be too large or too small.

At this point you can check your work by comparing your answer to the known value for the mass of ** one mole** of water. One mole of water has a mass of

*18 grams*, so your answer of

**18 grams per liter must**be correct!

You can also check your work by comparing your answer to the known value for the molar mass of water.