Problem 78 - Chemistry Matter and Change

Question

Use Le Chátelier's principle to explain what happens to the equilibrium \(\mathrm{H}_{2} \mathrm{O}(1) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-(\mathrm{aq})}\) when a few drops of HCl are added to pure wate.

Step-by-Step Solution

Answer

When a few drops of HCl are added to pure water, the concentration of H+ ions increases due to the complete ionization of HCl. According to Le Chátelier's principle, the system will shift its equilibrium position to counteract this increase in H+ ions. The equilibrium reaction \( \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-(\mathrm{aq})} \) shifts towards the left, decreasing the concentrations of H+ and OH- ions by combining them to form water molecules. This process increases the acidity of the water.

Step 1: Understanding the Equilibrium Reaction

The given equilibrium reaction is: \[ \mathrm{H}_{2} \mathrm{O}(1) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-(\mathrm{aq})} \] This represents that in water, a small number of water molecules undergo self-ionization, producing hydronium ions (H+) and hydroxide ions (OH-).

Step 2: Understanding Le Chátelier's Principle

Le Chátelier's principle states that when an externally induced stress like the change in temperature, pressure, or concentration is applied to a system at equilibrium, the system will shift its equilibrium position to counteract that stress and reestablish equilibrium.

Step 3: Identifying the Effect of Adding HCl to Water

Hydrochloric acid (HCl) is a strong acid, which means it fully ionizes in water and does not reach an equilibrium. When HCl is added to water, it dissociates into H+ and Cl- ions as follows: \[ \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}^{+}(\mathrm{aq}) + \mathrm{Cl}^{-}(\mathrm{aq}) \] This addition increases the concentration of H+ ions in the solution.

Step 4: Applying Le Chátelier's Principle

Now we can apply Le Chátelier's principle to predict how the equilibrium system will respond to an increase in H+ ion concentration. According to Le Chátelier's principle, when the concentration of a reactant or product increases, the system will shift towards the side that reduces the concentration. In this case, the increase in H+ ions will cause the equilibrium to shift to the left: \[ \mathrm{H}_{2} \mathrm{O}(l) \leftarrow \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-(\mathrm{aq})} \] As the equilibrium shifts to the left, more H+ ions and OH- ions will combine to form water molecules, thus decreasing the concentrations of H+ and OH-. In other words, the addition of HCl to pure water will increase the acidity by increasing the concentration of H+ ions (and decreasing that of OH- ions).

Key Concepts

Chemical Equilibrium

Imagine a dance floor where dancers represent molecules in a reaction. Just like dancers moving back and forth to balance the floor space, molecules in a chemical equilibrium react back and forth at equal rates. This dynamic state doesn't mean the dancers (molecules) stop moving; they simply change directions at a rate that maintains a steady composition.

In our watery dance hall, water molecules are constantly 'dancing' by breaking into H+ and OH- ions and then coming back together to form H2O. This equilibrium is a delicate balance, almost like a see-saw that barely tilts either way. The solution, in this case, is neither becoming more acidic nor more basic - maintaining that 'just right' neutral pH of 7, because the concentration of H+ and OH- ions remains unchanged over time.

When a change is introduced, such as the addition of HCl, it's akin to adding more dancers to one side of the floor. The dance of equilibrium changes to accommodate this, shifting to reduce the crowding by encouraging some dancers to leave. In chemical terms, the equilibrium will shift to decrease the concentration of H+ ions, trying to get back to the 'just right' scenario by converting H+ and OH- ions back into H2O.

Acid-Base Reaction

Think of acid-base reactions as a game of hot potato. Acids are like players eager to give away their 'hot potato' H+ ions, while bases are more than happy to accept them. When acids and bases are mixed, they play by swapping H+ ions until neither side wants to exchange anymore.

Under this analogy, HCl is a player that can't wait to pass on its hot potato, meaning it's eager to donate its H+ ion to water - it's a very good player in the acid league. When we add HCl to water, it's like introducing a new player who immediately throws in an extra hot potato. This disrupts our ongoing game (or chemical equilibrium) because now there are too many H+ ions ('hot potatoes') in play, and the water has to adapt by getting rid of the excess to go back to playing comfortably.

The result is a solution that's more acidic - which means it has a higher concentration of H+ ions, as HCl has effectively made the water accept its hot potato. The water must adjust by shifting the equilibrium to reduce this surplus, reflecting the basic rule of acid-base reactions: acids donate H+ ions to bases, which accept them.

Self-Ionization of Water

Water is the mediator that never rests. On its own, it undergoes self-ionization, meaning that it can act both as an acid and a base - it's perfectly impartial. During this process, a water molecule (H2O) splits into an H+ ion and an OH- ion, and then various H+ and OH- ions can rejoin to form water again. This is done in tiny amounts, so you don't notice it - there's no large-scale transformation, just a microscopic shuffling between the molecules.

This delicate dance keeps the number of H+ ions and OH- ions in pure water perfectly balanced, which is why pure water has a neutral pH. When equilibrium is disturbed by adding an acid like HCl, there's a brief flurry of activity as the system adjusts. The self-ionization of water is essential to understand because it sets the stage for how water interacts with other substances. Whenever we add an acid or a base, we're essentially inviting more players to the water's ongoing microscopic dance, and the system must respond to maintain its equilibrium.