The Double Life of Water

If you thought water was a simple, innocent molecule, think again. By day, water is a refreshing drink. You might be surprised to learn that water also moonlights as both an acid and a base. Perhaps water should consider an acting role along side Bruce Willis.

When water meets up with a base (like NH₃), it acts as an acid by transferring a proton to the base. Alternatively, when water meets up with an acid (like HCl), it acts as a base by accepting a proton from the acid. What if, by some strange twist of fate, water meets itself? Suddenly, the curtain of water's double-life deception is pulled and water-as-an-acid must face water-as-a-base. Dun-dun-dahhh. Here's what happens:



This equation shows the dissociation of water to form a hydronium (H₃O⁺) ion and a hydroxide (OH^-). The hydronium ion is also known as hydrated H⁺. This is because sometimes, rather than drawing H⁺ on water, as in H₃O⁺, the proton is drawn by itself (H⁺) as in the Arrhenius definition of an acid. While we typically use H₃O⁺ in acid-base reactions to balance equations, the symbols H⁺ and H₃O⁺ have the same meaning and can sometimes be used interchangeably.

There are two important aspects of the dissociation of water equilibrium (fancy name for when water meets water in the previous paragraph):

1. The proton transfers really fast so the products and reactants are rapidly converting.
     
2. Water doesn't like fighting with itself over a proton. Because of this, the equilibrium of the dissociation of water lies far to the left side where the two waters are at peace and don't usually transfer a proton.

To precisely quantify this water dissociation equilibrium we can define a special equilibrium constant as we would for any reaction equilibrium putting the concentration of products over reactants:



This equation can be simplified because H₂O strongly disfavors dissociation. The concentration of H₂O remains virtually constant. Making this simplification (by lumping it together with the other constant K_c) and rearranging the equation gives us the definition of a special equilibrium constant called the ion-product constant for water (K_w):

K_w = K_c × [H₂O]² = [H₃O⁺][OH^-]

The equilibrium constant K_w tells us the extent to which water dissociates when only other water molecules surround it. Chemists have determined the concentration of H₃O⁺ experimentally at 25 °C to be 1 × 10^-7 M. The chemical equation for the dissociation of water tells us that for every one molecule of H₃O⁺, we also get one molecule of OH^-. Therefore the concentration of OH^- in pure water must also be 1 × 10^-7 M. These are very low concentrations, but how low are they compared to how many water molecules are around? To answer this question we'll need to know the concentration of water.

What does it even mean for water to have a concentration? Water is typically thought of as a pure liquid. This leads some people to believe that its concentration is infinite. Beware: this is not true. Water does have a concentration, and that concentration tells us how many moles of water are in 1 liter of water. Check out this mid-blowing calculation:

[H₂O] = (density of water, g/L) × ( molar mass of water, mol/g)
= (997 g/L) × (0.056 mol/g) = 55.4 mol/L

This calculation shows that the concentration of water in pure water is 55.4 M. Comparing this concentration with the concentrations of H₃O⁺ and OH^- of 1 × 10^-7 M really puts things into perspective in terms of how few water molecules actually dissociate.

Dividing the concentration of H₂O by H₃O⁺ shows that if we had a collection of a billion water molecules, only about two of those water molecules would be dissociated. In other words, the odds of finding an H₃O⁺ molecule in a sample of water are about the same as winning the lottery—twice.

The rareness of water dissociating into H₃O⁺ and OH^- is further illustrated by the very small value of the equilibrium constant, K_w:

K_w = [H₃O⁺][OH^-] = (1 × 10^-7 M) × (1 × 10^-7 M) = 1 × 10^-14 M² at 25 °C

The value of K_w is important. Commit it to memory. Recite it 10 times. This number is used to define whether a solution is acidic, neutral, or basic. K_w is constant. It's always 1 × 10^-14 M² at 25 °C (note that we'll be dropping the M² units from here on out). The product of [H₃O⁺] and [OH^-] in solution must always equal 1 × 10^-14.

So far we have been looking at pure water, where [H₃O⁺] and [OH^-] are equal and are both 1 × 10^-7 M. In fact, any solution can have H₃O⁺ and OH^- at equal concentrations, not just water. A solution that has [H₃O⁺] = [OH^-] is defined as neutral. In contrast, some solutions can have unequal proportions of H₃O⁺ and OH^- molecules. These solutions are defined as acidic when [H₃O⁺] > [OH^-] and basic when [H₃O⁺] < [OH^-]. Just remember that the product of the concentrations of these two molecules must always be 1 × 10^-14 at 25 °C in accordance with the definition of K_w.

The following must be true about solutions at 25 °C in general:

Acidic: [H₃O⁺] > 1 × 10^-7 M; [OH^-] < 1 × 10^-7 M
Neutral: [H₃O⁺] = 1 × 10^-7 M = [OH^-]
Basic: [H₃O⁺] < 1 × 10^-7 M; [OH^-] > 1 × 10^-7 M