Question

Challenge The products of an acid-base reaction are \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{SO}_{4}^{2-} .\) Write a balanced equation for the reaction and identify the conjugate acid-base pairs.

Short answer

The balanced equation for the acid-base reaction is: \[\mathrm{H}_{2}\mathrm{SO}_{4} + \mathrm{OH}^{-} \rightarrow \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{SO}_{4}^{2-}\] The conjugate acid-base pairs are: 1. \(\mathrm{H}_{2}\mathrm{SO}_{4} \leftrightarrow \mathrm{HSO}_{4}^{-}\) (sulfuric acid and bisulfate ion) 2. \(\mathrm{OH}^{-} \leftrightarrow \mathrm{H}_{3}\mathrm{O}^{+}\) (hydroxide ion and hydronium ion)

Step-by-step solution

Identify the possible reactants

First, we need to identify the acid and base that, when reacted, will produce the given products. We are given that the products are \(\mathrm{H}_{3}\mathrm{O}^{+}\) and \(\mathrm{SO}_{4}^{2-}\). To determine what reactants could have produced these, we may reverse the ions' transformations. The hydronium ion \(\mathrm{H}_{3}\mathrm{O}^{+}\) could be formed from either water (\(\mathrm{H}_{2}\mathrm{O}\)) accepting a proton or a strong acid losing one. On the other hand, the sulfate ion \(\mathrm{SO}_{4}^{2-}\) could be formed from a strong base losing a proton. Considering these possibilities, let's assume that water is the base reacting with a strong acid and sulfate ion comes from a strong base releasing a proton.

Find the strong acid and base

To find the strong acid, we can add a proton back to the \(\mathrm{H}_{3}\mathrm{O}^{+}\) ion, which will give us \(\mathrm{H}_{2}\mathrm{SO}_{4}\) (sulfuric acid). This is a known strong acid. Now, to find the corresponding strong base, we should add a proton back to the \(\mathrm{SO}_{4}^{2-}\) ion, which will result in \(\mathrm{HSO}_{4}^{-}\) (bisulfate ion). The strong base should also have a proton attached to it. Thus, \(\mathrm{HSO}_{4}^{-}\) reacting with \(\mathrm{OH}^{-}\) can be considered the strong base.

Write the balanced equation

Now that we have identified the strong acid \(\mathrm{H}_{2}\mathrm{SO}_{4}\) and the strong base \(\mathrm{HSO}_{4}^{-} + \mathrm{OH}^{-}\), we can write the balanced equation for the acid-base reaction: \[\mathrm{H}_{2}\mathrm{SO}_{4} + \mathrm{HSO}_{4}^{-} + \mathrm{OH}^{-} \rightarrow \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{SO}_{4}^{2-} + \mathrm{HSO}_{4}^{-}\] Since we have \(\mathrm{HSO}_{4}^{-}\) on both sides of the equation, we can cancel it out to simplify: \[\mathrm{H}_{2}\mathrm{SO}_{4} + \mathrm{OH}^{-} \rightarrow \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{SO}_{4}^{2-}\]

Identify the conjugate acid-base pairs

Now to identify the conjugate acid-base pairs in the reaction, we look for species that differ only by a single proton: 1. \(\mathrm{H}_{2}\mathrm{SO}_{4} \leftrightarrow \mathrm{HSO}_{4}^{-}\): Conjugate acid-base pair (sulfuric acid and its conjugate base, bisulfate ion). 2. \(\mathrm{OH}^{-} \leftrightarrow \mathrm{H}_{3}\mathrm{O}^{+}\): Conjugate acid-base pair (hydroxide ion and its conjugate acid, hydronium ion). Thus, the balanced equation for the acid-base reaction is: \[\mathrm{H}_{2}\mathrm{SO}_{4} + \mathrm{OH}^{-} \rightarrow \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{SO}_{4}^{2-}\] And the conjugate acid-base pairs are: 1. \(\mathrm{H}_{2}\mathrm{SO}_{4} \leftrightarrow \mathrm{HSO}_{4}^{-}\) 2. \(\mathrm{OH}^{-} \leftrightarrow \mathrm{H}_{3}\mathrm{O}^{+}\)

Key concepts

Conjugate Acid-Base Pairs

In an acid-base reaction, conjugate acid-base pairs are essential to grasping the transformation process. They consist of two substances that differ by only one proton (H⁺). When an acid donates a proton, it transforms into its conjugate base, and when a base accepts a proton, it transforms into its conjugate acid.

In the given reaction,

• Sulfuric acid (\(\mathrm{H}_{2}\mathrm{SO}_{4}\)) acts as the acid, donating a proton to become its conjugate base, the bisulfate ion (\(\mathrm{HSO}_{4}^{-}\)).
• The hydroxide ion (\(\mathrm{OH}^{-}\)) acts as the base, accepting a proton to become its conjugate acid, the hydronium ion (\(\mathrm{H}_{3}\mathrm{O}^{+}\)).

Recognizing these pairs helps emphasize the balance in a reaction, where a proton's journey defines the interaction of acids and bases.

Hydronium Ion

The hydronium ion (\(\mathrm{H}_{3}\mathrm{O}^{+}\)) plays a crucial role in acid-base chemistry, serving as a marker for acidity in a solution. It is created when a water molecule (\(\mathrm{H}_{2}\mathrm{O}\)) accepts a proton (H⁺) from an acid. This transformation heightens the acidic property of the solution, as hydronium's presence directly correlates with the solution's pH level.

This ion is significant because it showcases how acids function in water. Acids don't merely donate protons in a vacuum—they do so in the context of water, forming the hydronium ion as a result. In our reaction, the creation of \(\mathrm{H}_{3}\mathrm{O}^{+}\)) from hydroxide ion demonstrates the natural connection between acid and base actions.

Sulfuric Acid

Sulfuric Acid (\(\mathrm{H}_{2}\mathrm{SO}_{4}\)) is a potent acid that is widely used in chemical reactions due to its ability to donate two protons. This is why it's often described as a diprotic acid. When it donates its first proton, it transforms into the bisulfate ion (\(\mathrm{HSO}_{4}^{-}\)), and when the second proton is lost, the sulfate ion (\(\mathrm{SO}_{4}^{2-}\)) forms.

In our balanced reaction, \(\mathrm{H}_{2}\mathrm{SO}_{4}\) acts as the acid, donating a proton to react with a base, showcasing its primary function in acid-base chemistry. Its capacity to release protons makes sulfuric acid a key component in industrial applications, while also forming the foundation of many lab reactions.

Sulfate Ion

The sulfate ion (\(\mathrm{SO}_{4}^{2-}\)) emerges after sulfuric acid has donated both of its protons. This ion is noted for its stability, which contributes to sulfuric acid's characteristics as a strong acid. Formed from the complete dissociation of sulfuric acid, it is an important product in acid-base reactions.

In the depicted reaction, \(\mathrm{SO}_{4}^{2-}\) represents the end state of sulfuric acid after releasing protons. It highlights how acids like \(\mathrm{H}_{2}\mathrm{SO}_{4}\) evolve through successive proton donations, reinforcing the importance of proton transfer in determining reaction dynamics.