A sample of water is known to contain 9.5 × 1023 water molecules. What is the mass, in grams, of the sample?

Question

A sample of water is known to contain 9.5 × 1023 water molecules. What is the mass, in grams, of the sample?

A sample of water is known to contain 9.5 × 1023 water molecules. What is the mass, in grams, of the sample?

Answer 1

To convert this measurement from number of molecules to grams, we need to go through 2 steps; 1) Convert number of molecules to moles, and 2) Convert moles to grams.

 

Converting from number of molecules to moles is easy as long as you know that 1 mole = 6.02X10²³ molecules.  This is true for any substance.  If we have 9.5 x 10²³ water molecules, we divide that by 6.02 x 10²³ to get the number of moles:

9.5 x 10²³ / 6.02 x 10²³ = 1.58 moles H₂O.

 

Now that we have the number of moles of H₂O, we can use the molecular mass (the weight in g of 1 mole) to determine the weight.

To calculate the molecular mass of H₂O, we simply add up the atomic masses of the atoms in the molecule.

H=1.00794 g/mol; O=15.9994 g/mol

Since H₂O has 2 H and 1 O, the total molecular mass is 2(1.00794g/mol)+15.9994g/mol = 18.01528 g/mol

 

So../ We know from the first step that we have 1.58 moles H₂O, and we know from the second step that 1 mole of H₂O weighs = 18.01528g

 1.58 moles * 18.01528 g/mol = 28.46g.

Therefore, we have 28.46 g H₂O