Problem 16 - Chemistry The Central Science In Si Units

Question

(a) Give the conjugate base of the following BrønstedLowry acids: (i) \(\mathrm{H}_{2} \mathrm{SO}_{3},\) (ii) \(\mathrm{HSO}_{3}^{-}(\mathbf{b})\) Give the conjugate acid of the following Brønsted-Lowry bases: (i) \(\mathrm{CH}_{3} \mathrm{NH}_{2}\), (ii) \(\mathrm{CH}_{3} \mathrm{COO}^{-}\).

Step-by-Step Solution

Answer

Conjugate bases: (i) HSO₃⁻, (ii) SO₃²⁻; Conjugate acids: (i) CH₃NH₃⁺, (ii) CH₃COOH.

Step 1: Understand Conjugate Bases

A conjugate base is what remains of a Brønsted-Lowry acid after it donates a proton (H⁺). This means that to find the conjugate base of an acid, we simply need to remove one hydrogen atom from the acid's formula and adjust the charge accordingly.

Step 2: Determine the Conjugate Base of H₂SO₃

For the acid H₂SO₃, remove one hydrogen ion (H⁺). This gives us \[ \mathrm{H}_2\mathrm{SO}_3 \rightarrow \mathrm{HSO}_3^- + \mathrm{H}^+ \]Therefore, the conjugate base of H₂SO₃ is \(\mathrm{HSO}_3^-\).

Step 3: Determine the Conjugate Base of HSO₃⁻

For the acid HSO₃⁻, remove one hydrogen ion (H⁺). This gives us \[ \mathrm{HSO}_3^- \rightarrow \mathrm{SO}_3^{2-} + \mathrm{H}^+ \] Therefore, the conjugate base of HSO₃⁻ is \(\mathrm{SO}_3^{2-}\).

Step 4: Understand Conjugate Acids

A conjugate acid is formed when a Brønsted-Lowry base accepts a proton (H⁺). To find the conjugate acid of a base, add one hydrogen ion to the base's formula, and adjust the charge accordingly.

Step 5: Determine the Conjugate Acid of CH₃NH₂

For the base CH₃NH₂, add a hydrogen ion (H⁺). This gives us \[ \mathrm{CH}_3\mathrm{NH}_2 + \mathrm{H}^+ \rightarrow \mathrm{CH}_3\mathrm{NH}_3^+ \]Therefore, the conjugate acid of CH₃NH₂ is \(\mathrm{CH}_3\mathrm{NH}_3^+\).

Step 6: Determine the Conjugate Acid of CH₃COO⁻

For the base CH₃COO⁻, add a hydrogen ion (H⁺). This gives us\[ \mathrm{CH}_3\mathrm{COO}^- + \mathrm{H}^+ \rightarrow \mathrm{CH}_3\mathrm{COOH} \]The conjugate acid of CH₃COO⁻ is \(\mathrm{CH}_3\mathrm{COOH}\), which is acetic acid.

Key Concepts

Brønsted-Lowry Acid

A Brønsted-Lowry Acid is a substance that can donate a proton (H⁺) to another substance. In this definition, the proton donor plays a central role and is what distinguishes an acid in this context.
When an acid donates a proton, it transforms into its conjugate base. This process highlights a clear link between acids and their corresponding bases. For instance, let's look at sulfurous acid \(\mathrm{H}_2\mathrm{SO}_3\).

• When it donates a proton, it becomes \(\mathrm{HSO}_3^{-}\), which is its conjugate base.
• Similarly, if \(\mathrm{HSO}_3^{-}\) donates another proton, it turns into \(\mathrm{SO}_3^{2-}\).

This indicates that \(\mathrm{H}_2\mathrm{SO}_3\) has donated its protons in a stepwise manner. Each step shows the acid turning into its conjugate base. This interplay illustrates how acids and bases form pairs through the transfer of protons, a hallmark of Brønsted-Lowry Acid behavior.

Brønsted-Lowry Base

Under the Brønsted-Lowry theory, a base is defined as a substance that can accept a proton. The acceptance of a proton by a base results in the formation of its conjugate acid.
An example of a Brønsted-Lowry base is methylamine, \(\mathrm{CH}_3\mathrm{NH}_2\). When\(\mathrm{CH}_3\mathrm{NH}_2\) accepts a proton, the process can be represented as: \[\mathrm{CH}_3\mathrm{NH}_2 + \mathrm{H}^+ \rightarrow \mathrm{CH}_3\mathrm{NH}_3^+\] Here, the base \(\mathrm{CH}_3\mathrm{NH}_2\) has transformed into its conjugate acid, \(\mathrm{CH}_3\mathrm{NH}_3^+\). This proton acceptance demonstrates the essential role of bases in chemical reactions as agents that can convert into acids via proton gain.

• The acetate ion, \(\mathrm{CH}_3\mathrm{COO}^-\), is another clear example. It accepts a proton to form acetic acid, \(\mathrm{CH}_3\mathrm{COOH}\).
• This transformation emphasizes the capacity of a base to "receive" and stabilize an extra proton, thus altering its identity to become its conjugate acid.

Chemical Reactions

Chemical reactions involving Brønsted-Lowry acids and bases center around the exchange of protons. During these reactions:

• An acid \(\text{donates}\) a proton to a base.
• In response, the base \(\text{accepts}\) this proton.

This back-and-forth transfer is the driving force behind many important chemical processes.
This type of reaction can be visually encapsulated in a straightforward chemical equation. For example, when acetic acid \(\mathrm{CH}_3\mathrm{COOH}\) reacts with water \(\mathrm{H}_2\mathrm{O}\), \[\mathrm{CH}_3\mathrm{COOH} + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{CH}_3\mathrm{COO}^- + \mathrm{H}_3\mathrm{O}^+\]This equation demonstrates acetic acid donating a proton to water.
The products are acetate and the hydronium ion \(\mathrm{H}_3\mathrm{O}^+\), both illustrating the conjugate relationship formed during the reaction.
On a broader scale, this fundamental mechanism powers various biochemical reactions in nature, showcasing its pivotal role in transforming and transferring components at the molecular level.