Problem 20 - Chemistry The Central Science

Question

(a) Write an equation for the reaction in which \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-}(a q)\) acts as a base in \(\mathrm{H}_{2} \mathrm{O}(l)\) (b) Write an equation for the reaction in which \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-}(a q)\) acts as an acid in \(\mathrm{H}_{2} \mathrm{O}(l) .(\mathrm{c})\) What is the conjugate acid of \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-}(a q) ?\) What is its conjugate base?

Step-by-Step Solution

Answer

As a base in water, the reaction is: \[\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{H}_{3}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}(aq) + \mathrm{OH}^{-}(aq)\] As an acid in water, the reaction is: \[\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{HC}_{6}\mathrm{H}_{6}\mathrm{O}_{5}^{2-}(aq) + \mathrm{H}_{3}\mathrm{O}^{+}(aq)\] The conjugate acid is \(\mathrm{H}_{3}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}(aq)\) and the conjugate base is \(\mathrm{HC}_{6}\mathrm{H}_{6}\mathrm{O}_{5}^{2-}(aq)\).

Step 1: Reaction as a Base

When \(\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}^{-}(aq)\) acts as a base, it will accept a proton from the solvent, water. The equation of this reaction will look like this: \[\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{H}_{3}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}(aq) + \mathrm{OH}^{-}(aq)\]

Step 2: Reaction as an Acid

When \(\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}^{-}(aq)\) acts as an acid, it will donate a proton to the solvent, water. The equation of this reaction will look like this: \[\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{HC}_{6}\mathrm{H}_{6}\mathrm{O}_{5}^{2-}(aq) + \mathrm{H}_{3}\mathrm{O}^{+}(aq)\]

Step 3: Conjugate Acid

The conjugate acid of \(\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}^{-}(aq)\) is formed when the base gains a proton. In the first reaction, we saw that the product after gaining a proton is \(\mathrm{H}_{3}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}(aq)\). Hence, the conjugate acid is \(\mathrm{H}_{3}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}(aq)\).

Step 4: Conjugate Base

The conjugate base of \(\mathrm{H}_{2}\mathrm{C}_{6}\mathrm{H}_{7}\mathrm{O}_{5}^{-}(aq)\) is formed when the acid loses a proton. In the second reaction, we saw that the product after losing a proton is \(\mathrm{HC}_{6}\mathrm{H}_{6}\mathrm{O}_{5}^{2-}(aq)\). Hence, the conjugate base is \(\mathrm{HC}_{6}\mathrm{H}_{6}\mathrm{O}_{5}^{2-}(aq)\).

Key Concepts

Chemical Equilibrium

Understanding chemical equilibrium is crucial for grasping many concepts in chemistry, including acid-base reactions. At its core, chemical equilibrium pertains to a state where the rates of the forward and reverse reactions are equal, leading to no net change in the concentration of reactants and products over time.

For an acid-base reaction, such as when \(\mathrm{H}_2\mathrm{C}_6\mathrm{H}_7\mathrm{O}_5^-\) acts either as a base or an acid, equilibrium would entail a balance between the amounts of the species involved. This means that the concentrations of the acid, base, and their respective conjugate pairs remain constant at equilibrium. However, it's essential to note that equilibrium does not imply equal concentrations; rather, the proportion of the concentrations adheres to the equilibrium constant \(K_{eq}\) for the specific reaction at a given temperature.

In both reactions provided in the exercise solutions, an equilibrium can be established where the forward and reverse rates become equal. In the classroom, we often use Le Chatelier’s Principle to predict how changes in conditions (like concentration, temperature, or pressure) will affect the equilibrium position.

Conjugate Acid-Base Pairs

When discussing acid-base chemistry, we always encounter conjugate acid-base pairs. These pairs are related by the loss or gain of a single proton (H+). The concept is pivotal as it helps us understand how substances can act as acids or bases depending on the context.

In the given exercise, \(\mathrm{H}_2\mathrm{C}_6\mathrm{H}_7\mathrm{O}_5^-\) transforms into its conjugate acid by accepting a proton, becoming \(\mathrm{H}_3\mathrm{C}_6\mathrm{H}_7\mathrm{O}_5\). Conversely, it forms its conjugate base, \(\mathrm{HC}_6\mathrm{H}_6\mathrm{O}_5^{2-}\), when it donates a proton. Each conjugate pair contains two species that easily convert into each other by exchanging a proton.

Understanding Conjugate Pairs

With any acid-base reaction, identifying the conjugate acid-base pairs is a valuable skill. In the acid reaction example, water acts as the base and forms its conjugate acid, \(\mathrm{H}_3\mathrm{O}^+\). On the other hand, in the base reaction, water is the acid which transforms into its conjugate base, \(\mathrm{OH}^-\). Thus, every acid-base reaction involves two conjugate acid-base pairs that help maintain the balance of the system.

Proton Transfer Reactions

Now, let us delve into the realm of proton transfer reactions, often the heart of acid-base chemistry. These reactions involve the transfer of a proton from an acid to a base. It's a beautiful dance between the donor and the acceptor, and it's how we classify substances as acids or bases in the Brønsted-Lowry definition.

In the solutions provided for the exercise, we observe two proton transfer reactions. \(\mathrm{H}_2\mathrm{C}_6\mathrm{H}_7\mathrm{O}_5^-\) receives a proton in one scenario, exhibiting its basic nature, and donates a proton in another, showing its acidic side. Through these reactions, we can see the dynamic nature of proton transfer and how it ties back to the concept of conjugate acid-base pairs.

The Essential Role of Water

Moreover, water's role as both a proton donor and acceptor in these reactions exemplifies its amphoteric behavior, meaning it can act as both an acid and a base. This versatility of water is what makes it a critical player in the acid-base reactions occurring in biological and environmental systems.