Question

Predict whether the equilibrium lies to the right or to the left in the following reactions: (a) \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{PO}_{4}{ }^{3-}(a q) \rightleftharpoons\) \(\mathrm{NH}_{3}(a q)+\mathrm{HPO}_{4}^{2-}(a q)\) (The ammonium ion is a stronger acid than the hydrogen phosphate ion.) (b) \(\mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{CN}^{-}(a q) \rightleftharpoons\) \(\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{HCN}(a q)\) (The cyanide ion is a stronger base than the acetate ion.)

Short answer

(a) In the reaction \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{PO}_{4}{ }^{3-}(a q) \rightleftharpoons\mathrm{NH}_{3}(a q)+\mathrm{HPO}_{4}^{2-}(a q)\), the equilibrium lies to the left because the stronger acid (\(\mathrm{NH}_{4}^{+}\)) reacts with the stronger base (\(\mathrm{PO}_{4}^{3-}\)) to produce weaker species (\(\mathrm{NH}_{3}\) and \(\mathrm{HPO}_{4}^{2-}\)). (b) In the reaction \(\mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{CN}^{-}(a q)\rightleftharpoons\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{HCN}(a q)\), the equilibrium lies to the right because the stronger base (\(\mathrm{CN}^{-}\)) reacts with the stronger acid (\(\mathrm{CH}_{3} \mathrm{COOH}\)) to produce weaker species (\(\mathrm{CH}_{3} \mathrm{COO}^{-}\) and \(\mathrm{HCN}\)).

Step-by-step solution

Compare Acid Strengths

Compare the ammonium ion (\(\mathrm{NH}_{4}^{+}\)) and the hydrogen phosphate ion (\(\mathrm{HPO}_{4}^{2-}\)). According to the exercise, the ammonium ion is a stronger acid.

Determine Equilibrium Direction

The stronger acid will react with the stronger base to produce the weaker acid and the weaker base. In this case, the stronger acid is \(\mathrm{NH}_{4}^{+}\) and the stronger base is \(\mathrm{PO}_{4}^{3-}\). The reaction between them will produce \(\mathrm{NH}_{3}\) (weaker acid) and \(\mathrm{HPO}_{4}^{2-}\) (weaker base). So, the equilibrium will favor the reactants. Therefore, the equilibrium lies to the left. (b) \(\mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{CN}^{-}(a q)\rightleftharpoons\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{HCN}(a q)\) (The cyanide ion is a stronger base than the acetate ion.)

Compare Base Strengths

Compare the cyanide ion (\(\mathrm{CN}^{-}\)) and the acetate ion (\(\mathrm{CH}_{3} \mathrm{COO}^{-}\)). According to the exercise, the cyanide ion is a stronger base.

Determine Equilibrium Direction

The stronger base will react with the stronger acid to produce the weaker acid and the weaker base. In this case, the stronger base is \(\mathrm{CN}^{-}\) and the stronger acid is \(\mathrm{CH}_{3} \mathrm{COOH}\). The reaction between them will produce \(\mathrm{CH}_{3} \mathrm{COO}^{-}\) (weaker base) and \(\mathrm{HCN}\) (weaker acid). So, the equilibrium will favor the products. Therefore, the equilibrium lies to the right.

Key concepts

Acid-Base Reactions

In chemistry, acid-base reactions are an essential concept that helps us understand how substances interact at the molecular level. An acid is a substance that can donate a proton ( H^+ ), while a base can accept a proton. During a typical acid-base reaction, an acid and a base react to form their conjugate base and conjugate acid, respectively. This interplay determines the direction and extent of chemical reactions.

In the exercise given, the ammonium ion ( NH_4^+ ) is described as a stronger acid than the hydrogen phosphate ion ( HPO_4^{2-} ). This information allows us to predict how the equilibrium will adjust. When we compare the relative strengths of acids and bases in a reaction, we can determine which direction the equilibrium will lie. A stronger acid will react with a base to produce a weaker acid and base, as such, the equilibrium of this system tends to favor the direction that forms weaker entities.

Hence, in the reaction involving the ammonium ion and hydrogen phosphate ion, the equilibrium leans towards the formation of products that are weaker in comparison to their reactants. This is crucial in determining the position of equilibrium in such systems.

Le Chatelier's Principle

Le Chatelier's Principle offers insight into how a system at equilibrium responds to external changes. It essentially states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change and re-establish equilibrium. Changes can include alterations in concentration, temperature, pressure, or volume.

In the context of acid-base reactions, Le Chatelier's Principle can explain equilibrium shifts when either reactant or product concentrations are altered. If an acid is added to an equilibrium mixture, the system will adjust to consume the added acid by shifting towards the side that neutralizes it, hence restoring balance. Likewise, removing products will cause the equilibrium to shift towards the products to replace the lost substances.

Understanding this principle helps illustrate why healthy balance in reactions is crucial. It underscores the inherent stability of chemical systems and their natural tendency to adjust to disturbances, maintaining equilibrium.

Reaction Favorability

Reaction favorability involves determining which direction a reaction will proceed when it reaches equilibrium. In acid-base reactions, this primarily depends on the strengths of the acids and bases involved. Reactions favor the formation of the weaker acid and base because they are less reactive and more stable.

In the exercise example, comparing the relative strengths of acids like ammonium ion ( NH_4^+ ) and acetic acid ( CH_3COOH ) with bases like phosphate ( PO_4^{3-} ) and cyanide ( CN^- ) allows us to determine direction. The stronger acid and base react to shift the equilibrium towards the side that produces weaker acids and bases.

Thus, understanding which species are stronger provides essential insight into the expected position of equilibrium in a reaction. The reaction to the right is considered favorable if stronger acid-base pairs react to form weaker counterparts. Conversely, it is less favorable or drifts to the left if weaker agents try to react in the opposite direction.