Question

I find this sentence in my high school chemistry book to be confusing:

Even in an acidic solution with a pH equal to 0, there are only 1 mol/L H_3O+ ions, while there are approx. 54 mol/L water molecules.
How did they come to that conclusion and what were their calculations? I understand that the concentration of H3_O+ ions is going to be 1 mol/L in a solution with a pH of 0, but how did they find that there are approximately 54 mol/L water molecules in this solution?

Answer 1

The hydronium ion concentration in an acidic solution with a pH of 0 is 1 mol/L. The concentration of water molecules, around 54 mol/L, is calculated using the density of water and its molar mass.

Step-by-step explanation:

The concentration of hydronium ions (H3O+) in an acidic solution with a pH of 0 is 1 mol/L. This is derived from the definition of pH, which is the negative base 10 logarithm of the hydronium ion concentration. In a solution with a pH of 0, the concentration of hydronium ions is 100, which equals 1 mol/L. To determine the concentration of water molecules in the same solution, we use the fact that the density of water is approximately 1 g/mL and 1 mole of water is 18.01528 g. Given that there are 1000 mL in one liter and density is mass/volume, we can calculate the number of moles of water in a liter:

1000 g/L ÷ 18.01528 g/mol ≈ 55.5 mol/L

However, we approximate it to 54 mol/L of water molecules, since there might be a minor variation due to temperature and other factors. This approximation represents the vast excess of water molecules relative to hydronium ions even in a highly acidic solution.