Question

Write the formulas of the conjugate bases of the following Brønsted-Lowry acids: (a) \(\mathrm{HCN}\) (b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}_{2}^{+}\) (c) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) (d) \(\mathrm{HSeO}_{3}^{-}\)

Short answer

The conjugate bases are: (a) \(\mathrm{CN}^-\), (b) \((\mathrm{CH}_{3})_{2} \mathrm{NH}\), (c) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\), (d) \(\mathrm{SeO}_{3}^{2-}\).

Step-by-step solution

Understanding the Brønsted-Lowry Acid-Base Concept

In the Brønsted-Lowry theory, acids are substances that donate a proton (\(\mathrm{H}^+\)), while bases are substances that accept a proton. The conjugate base of an acid is what remains after the acid donates a proton.

Determining the Conjugate Base for \(\mathrm{HCN}\)

The acid \(\mathrm{HCN}\) donates a proton, forming its conjugate base. This means removing a \(\mathrm{H}^+\) ion from \(\mathrm{HCN}\), resulting in \(\mathrm{CN}^-\), which is the conjugate base of \(\mathrm{HCN}\).

Determining the Conjugate Base for \(\left(\mathrm{CH}_{3}\right)_{2}\mathrm{NH}_{2}^{+}\)

The acid \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}_{2}^{+}\) donates a proton. When it loses \(\mathrm{H}^+\), it forms \(\left(\mathrm{CH}_{3}\right)_{2}\mathrm{NH}\), its conjugate base.

Determining the Conjugate Base for \(\mathrm{H}_{3} \mathrm{PO}_{4}\)

The acid \(\mathrm{H}_{3} \mathrm{PO}_{4}\) donates a proton, losing \(\mathrm{H}^+\), and becomes \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\), which is its conjugate base.

Determining the Conjugate Base for \(\mathrm{HSeO}_{3}^{-}\)

The acid \(\mathrm{HSeO}_{3}^{-}\) donates a proton. By removing \(\mathrm{H}^+\), it forms \(\mathrm{SeO}_{3}^{2-}\), the conjugate base of \(\mathrm{HSeO}_{3}^{-}\).

Key concepts

Conjugate Bases

In the Brønsted-Lowry theory of acids and bases, understanding conjugate bases is crucial. When an acid donates a proton (\(\mathrm{H}^+\)), it transforms into its conjugate base. A simple way to think of a conjugate base is as the remnant or the leftover species after the acid gives away a proton. For instance:

• For the acid \(\mathrm{HCN}\), after losing \(\mathrm{H}^+\), it results in \(\mathrm{CN}^-\), its conjugate base.
• The acid \((\mathrm{CH}_3)_2 \mathrm{NH}_2^+\) donates a proton, forming the conjugate base \((\mathrm{CH}_3)_2 \mathrm{NH}\).
• As \(\mathrm{H}_3 \mathrm{PO}_4\) donates a proton, it becomes \(\mathrm{H}_2 \mathrm{PO}_4^-\), its conjugate base.
• Similarly, \(\mathrm{HSeO}_3^-\) loses a proton to form \(\mathrm{SeO}_3^{2-}\).

This transformation effectively demonstrates the principle of conjugate acid-base pairs within proton transfer reactions.

Proton Donation

At the heart of Brønsted-Lowry acid-base reactions is the concept of proton donation. Acids by definition are proton donors, a central idea in understanding how these reactions proceed. When an acid donates a proton, it generally reduces its positive charge by one unit. Let's delve deeper:- **Proton Donors in Action**: When \(\mathrm{HCN}\) donates a proton, it loses its \(\mathrm{H}^+\) and becomes \(\mathrm{CN}^-\). This neutral molecule turns into a negatively charged ion. Similarly, \((\mathrm{CH}_3)_2 \mathrm{NH}_2^+\) donates a \(\mathrm{H}^+\) and transitions into a neutral species, \((\mathrm{CH}_3)_2 \mathrm{NH}\).- **Charge Changes**: It's essential to note the changes in charge that accompany proton donation. With \(\mathrm{H}_3 \mathrm{PO}_4\), dropping the \(\mathrm{H}^+\) reduces its charge, forming the negatively charged \(\mathrm{H}_2 \mathrm{PO}_4^-\). Likewise, for \(\mathrm{HSeO}_3^-\), losing a proton results in \(\mathrm{SeO}_3^{2-}\), a more negatively charged species.By examining these transformations, we see that acids, through proton donation, become their respective conjugate bases with a distinct change in their charge state.

Acid-Base Reactions

Acid-base reactions as defined by the Brønsted-Lowry theory revolve around proton transfer. In these reactions:

• An acid donates a proton to a base, effectively transferring an \(\mathrm{H}^+\) from one molecule to another.
• This creates two new species: a conjugate base from the acid and a conjugate acid from the base. These paired species are what we term conjugate pairs.

Consider the general reaction: \[\text{Acid}_1 + \text{Base}_2 \rightarrow \text{Conjugate Base}_1 + \text{Conjugate Acid}_2\]This proceeding is evident in our examples:- For \(\mathrm{HCN}\), the \(\mathrm{CN}^-\) ion acts as the conjugate base while the substance accepting this proton becomes its conjugate acid.- With \((\mathrm{CH}_3)_2 \mathrm{NH}_2^+\), the leftover \((\mathrm{CH}_3)_2 \mathrm{NH}\) is the conjugate base.These reactions exhibit the dynamic interplay between acids and bases where protons play the pivotal role. They define the changes and relationships within the pairs, emphasizing the necessity of viewing them in balance rather than isolation.