Question

Given the chemical equation for the ionization of water $$ \mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ Predict the direction of equilibrium shift for each of the following stresses: (a) increase \(\left[\mathrm{H}^{+}\right]\) (b) decrease \(\left[\mathrm{OH}^{-}\right]\) (c) increase \(\mathrm{pH}\) (d) decrease \(\mathrm{pH}\)

Short answer

(a) Left, (b) Right, (c) Right, (d) Left.

Step-by-step solution

Understanding Equilibrium

The chemical equation \(\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q)\) represents an equilibrium between water and its ions. According to Le Chatelier's Principle, if a stress is applied to a system at equilibrium, the system will shift in the direction that reduces the stress.

Analyzing Increase in \(\left[\mathrm{H}^{+}\right]\)

When \(\left[\mathrm{H}^{+}\right]\) is increased, the equilibrium will shift to the left to reduce the concentration of \(\mathrm{H}^{+}\). This produces more \(\mathrm{H}_{2} \mathrm{O}\) and reduces \(\left[\mathrm{OH}^{-}\right]\).

Analyzing Decrease in \(\left[\mathrm{OH}^{-}\right]\)

If \(\left[\mathrm{OH}^{-}\right]\) is decreased, the equilibrium will shift to the right to produce more \(\mathrm{OH}^{-}\). This will also result in an increase in \(\left[\mathrm{H}^{+}\right]\).

Analyzing Increase in \(\mathrm{pH}\)

An increase in \(\mathrm{pH}\) implies a decrease in \(\left[\mathrm{H}^{+}\right]\). According to Le Chatelier's Principle, the equilibrium will shift to the right to increase \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\).

Analyzing Decrease in \(\mathrm{pH}\)

A decrease in \(\mathrm{pH}\) means an increase in \(\left[\mathrm{H}^{+}\right]\). The equilibrium will consequently shift to the left to reduce \(\left[\mathrm{H}^{+}\right]\) and increase the concentration of \(\mathrm{H}_{2} \mathrm{O}\).

Key concepts

Chemical Equilibrium

Chemical equilibrium is a concept that describes the state of a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant over time. This is not to say that the reactions stop completely. Instead, they occur simultaneously at the same rate, creating a balance.
Le Chatelier's Principle helps us understand how an equilibrium system responds to changes in conditions. When a system at equilibrium experiences a change in concentration, temperature, or pressure, it will adjust to counteract the effect and re-establish equilibrium. For example, if you add more of a product or reactant, the system will shift to reduce that addition, achieving a new balance.
In the context of the ionization of water, if something disrupts the equilibrium, such as changing concentrations of \(\mathrm{H}^+\) or \(\mathrm{OH}^-\), the reaction will shift to either the left or the right to accommodate that change according to Le Chatelier's principle.

Ionization of Water

The ionization of water is a fundamental concept in chemistry. It describes water's ability to dissociate into hydrogen ions \(\mathrm{H}^+\) and hydroxide ions \(\mathrm{OH}^-\).
The reaction can be represented as:

• \(\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q)\)

Water naturally undergoes a tiny degree of self-ionization. This means that in pure water, the concentrations of \(\mathrm{H}^+\) and \(\mathrm{OH}^-\) are equal. This balance represents the neutral pH of 7. However, when an external factor alters the concentration of either ion, equilibrium shifts to restore balance.
For example, adding an acid increases \(\mathrm{H}^+\) concentrations, causing the equilibrium to shift left, reforming water and decreasing \(\mathrm{OH}^-\). Conversely, adding a base increases \(\mathrm{OH}^-\) concentration, prompting a right shift to increase \(\mathrm{H}^+\), maintaining equilibrium.

pH and Concentration Changes

pH is a measure of the acidity or basicity of a solution. It depends on the concentration of hydrogen ions \(\mathrm{H}^+\). A low pH (below 7) means high \(\mathrm{H}^+\) concentration, while a high pH (above 7) means low \(\mathrm{H}^+\) concentration.
Changes in \(\mathrm{H}^+\) concentrations directly affect equilibrium shifts. For instance, raising the pH implies decreasing \(\mathrm{H}^+\), prompting the system to shift right, producing more \(\mathrm{H}^+\) and \(\mathrm{OH}^-\) to counteract the change.
Similarly, decreasing the pH increases \(\mathrm{H}^+\), causing a left shift where \(\mathrm{OH}^-\) decreases and \(\mathrm{H}_{2}\mathrm{O}\) forms more readily.

• An increase in \(\mathrm{pH}\) suggests a decreased \(\mathrm{H}^+\).
• A decrease in \(\mathrm{pH}\) suggests an increased \(\mathrm{H}^+\).

Linking concentration changes to pH aids in predicting how chemical systems alter to cope with disturbances. This allows for precise manipulation of reactions in laboratory and industrial settings.