Question

Complete and balance the following reaction for the weak base pyridine: $$ \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons $$ Write the equilibrium expression for the \(K_{\mathrm{b}}\) of \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\).

Short answer

The balanced chemical equation for the reaction of pyridine with water is \(\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{N}(aq) + \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{5}\mathrm{H}_{5}\mathrm{NH}^{+}(aq) + \mathrm{OH}^{-}(aq)\). The equilibrium expression for the \(K_b\) is \(K_b = \frac{ [\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{NH}^{+}][\mathrm{OH}^{-}] }{ [\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{N}] }\).

Step-by-step solution

Balance the Chemical Equation

The chemical reaction of a base with water involves the base accepting a hydrogen ion. So, in this case, a hydrogen ion from water is taken up by pyridine (\(\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{N}(aq)\)) to form its conjugate acid, and leaving hydroxide ion in the process. The balanced chemical reaction is:\[\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{N}(aq) + \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{5}\mathrm{H}_{5}\mathrm{NH}^{+}(aq) + \mathrm{OH}^{-}(aq)\]

Write the Equilibrium Expression

Next, the equilibrium expression or the base dissociation constant expression (\(K_b\)) for the weak base, pyridine, can be written according to the law of mass action. The concentrations of water are not included in the \(K_b\) expression as it is a constant. The \(K_b\) expression for the reaction is:\[K_b = \frac{ [\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{NH}^{+}][\mathrm{OH}^{-}] }{ [\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{N}] }\]

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, leading to no net change in the concentration of the reactants and products. This state can be achieved in both physical processes, such as evaporation and condensation, and chemical processes, like the one involving weak bases like pyridine in water.

Imagine a busy intersection with cars equally leaving and arriving at a parking lot. At chemical equilibrium, the number of cars (representative of molecules) leaving equals the number arriving, so the total number of cars in the lot (analagous to concentration of reactants and products) remains constant over time. It's vital to understand that at equilibrium, the reaction hasn't stopped; it is dynamically ongoing, maintaining a steady state where forward and reverse reactions balance each other out.

Acid-Base Reaction

Acid-base reactions are essential in chemistry and involve the exchange of protons (H+) between substances. When an acid and a base react, they can form water and a salt in a process called neutralization. In the context of weak bases like pyridine reacting in water, the base doesn't fully dissociate in solution. Instead, it partially accepts protons from water to form a weakly ionized conjugate acid, substantially less than a strong base would.

Considering our analogy, a weak base is like a small-time investor in the stock market. It doesn’t buy (or, in chemical terms, bind to protons) as aggressively as the big players (strong bases) do, and so has a modest impact on the market's (solution's) overall activity.

Equilibrium Constant Expression

The equilibrium constant expression relates to the concentrations of the reactants and products in a balanced chemical reaction when the reaction has reached equilibrium. For any given reaction at a constant temperature, the equilibrium constant (K) is indeed a constant, unique to that specific reaction. The expression is derived from the Law of Mass Action which states that the rate of a reaction is proportional to the product of the concentrations of the reactants, each raised to the power of their respective coefficients in the balanced equation.

In simpler terms, the equilibrium constant is like a recipe that measures the 'flavor' of equilibrium. For the weak base reaction of pyridine, you can think of its Kb value as an indicator of how 'tasty' pyridine finds the protons in water—its willingness to form the conjugate acid and release hydroxide ions.

Base Dissociation Constant

The base dissociation constant (Kb) is a specific type of equilibrium constant that quantifies a base's strength by showing the extent to which the base dissociates into its conjugate acid and hydroxide ion in water. For weak bases like pyridine, Kb is relatively small, indicating limited dissociation as compared to strong bases which nearly completely dissociate in water.

To understand Kb, imagine a social gathering where a certain person (the weak base) is hesitant to mingle (dissociate). They might chat with a few people (accept a few protons to form a small number of conjugate acid molecules), but mostly they keep to themselves (stay undissociated). A strong base, however, would be the life of the party, interacting (dissociating) far more freely.