finding grams in chemistry

Question

How many grams of water are in a puddle that contains 9.1 x1025 molecules of water (H2O)?

Answer 1

This question is asking about mole to gram conversions. The key is Avogadro's number (roughly 6.022 x 10²³)!

The definition of 1 mole of any substance (ever!) is that it contains Avogadro's number of particles. In this question we are told that we have 9.1 x 10²⁵ molecules of H₂O and we are asked to find how many grams of water are present.

We can pull the conversion factors right off the periodic table in the form of the molecular weights. These are the numbers usually found below the chemical symbols in each tile of the periodic table. For this problem we know that the substance in question is water, with two hydrogen atoms for every one oxygen atom. In order to find our molar conversion, we need to add the mass of two hydrogen atoms to the mass of one oxygen atom. Reading off the periodic table (and paying attention to significant figures!), we find

mass_H = 1.0 g/mol

mass_O = 16 g/mol

mass_H2O = 2 * (mass_H) + (mass_O)

= 18 g/mol

Now we can use dimensional analysis to work our way from our given to our unknown as follows:

(9.1 x 10²⁵ molecules H₂O) * (1 mole H₂O) / (6.0 x 10²³ molecules H₂O) * (18 g H₂O) / (1 mole H₂O)

All of the units cancel until we are left with our desired dimensionality, namely g H₂O, with the numerical part evaluating to:

2.7 x 10³ g H₂O.