Question

Write the formula for the conjugate acid of each of the following bases: (a) HS", (b) \(\mathrm{HCO}_{3}^{-}\) (c) \(\mathrm{CO}_{3}^{2-}\), (d) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) (h) \(\mathrm{SO}_{4}^{2-}\) (e) \(\mathrm{HPO}_{4}^{2-}\), (f) \(\mathrm{PO}_{4}^{3-},(\mathrm{g}) \mathrm{HSO}_{4}^{-}\) (i) \(\mathrm{SO}_{3}^{2-}\).

Short answer

The conjugate acids are: (a) H₂S, (b) H₂CO₃, (c) HCO₃⁻, (d) H₃PO₄, (h) HSO₄⁻, (e) H₂PO₄⁻, (f) HPO₄²⁻, (g) H₂SO₄, (i) HSO₃⁻.

Step-by-step solution

Understanding Conjugate Acids

A conjugate acid is formed when a base gains a proton (H⁺). Therefore, to find the conjugate acid of a given base, we add an H⁺ to its formula.

Conjugate Acid of HS⁻

Add an H⁺ to HS⁻:\[ \mathrm{HS}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{2}\mathrm{S} \]Thus, the conjugate acid is \( \mathrm{H}_{2}\mathrm{S} \).

Conjugate Acid of HCO₃⁻

Add an H⁺ to \( \mathrm{HCO}_{3}^{-} \):\[ \mathrm{HCO}_{3}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{2}\mathrm{CO}_{3} \]Thus, the conjugate acid is \( \mathrm{H}_{2}\mathrm{CO}_{3} \).

Conjugate Acid of CO₃²⁻

Add an H⁺ to \( \mathrm{CO}_{3}^{2-} \):\[ \mathrm{CO}_{3}^{2-} + \mathrm{H}^{+} \rightarrow \mathrm{HCO}_{3}^{-} \]Thus, the conjugate acid is \( \mathrm{HCO}_{3}^{-} \).

Conjugate Acid of H₂PO₄⁻

Add an H⁺ to \( \mathrm{H}_{2} \mathrm{PO}_{4}^{-} \):\[ \mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4} \]Thus, the conjugate acid is \( \mathrm{H}_{3} \mathrm{PO}_{4} \).

Conjugate Acid of SO₄²⁻

Add an H⁺ to \( \mathrm{SO}_{4}^{2-} \):\[ \mathrm{SO}_{4}^{2-} + \mathrm{H}^{+} \rightarrow \mathrm{HSO}_{4}^{-} \]Thus, the conjugate acid is \( \mathrm{HSO}_{4}^{-} \).

Conjugate Acid of HPO₄²⁻

Add an H⁺ to \( \mathrm{HPO}_{4}^{2-} \):\[ \mathrm{HPO}_{4}^{2-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{2} \mathrm{PO}_{4}^{-} \]Thus, the conjugate acid is \( \mathrm{H}_{2} \mathrm{PO}_{4}^{-} \).

Conjugate Acid of PO₄³⁻

Add an H⁺ to \( \mathrm{PO}_{4}^{3-} \):\[ \mathrm{PO}_{4}^{3-} + \mathrm{H}^{+} \rightarrow \mathrm{HPO}_{4}^{2-} \]Thus, the conjugate acid is \( \mathrm{HPO}_{4}^{2-} \).

Conjugate Acid of HSO₄⁻

Add an H⁺ to \( \mathrm{HSO}_{4}^{-} \):\[ \mathrm{HSO}_{4}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4} \]Thus, the conjugate acid is \( \mathrm{H}_{2} \mathrm{SO}_{4} \).

Conjugate Acid of SO₃²⁻

Add an H⁺ to \( \mathrm{SO}_{3}^{2-} \):\[ \mathrm{SO}_{3}^{2-} + \mathrm{H}^{+} \rightarrow \mathrm{HSO}_{3}^{-} \]Thus, the conjugate acid is \( \mathrm{HSO}_{3}^{-} \).

Key concepts

Base

In chemistry, a base is a substance that can accept hydrogen ions (protons) or more broadly, donate electron pairs. This ability to interact with protons is what defines a base in the context of acid-base reactions. When a base gains a proton, it transforms into its conjugate acid.
For example, consider the hydroxide ion ( ext{OH}^-). As a base, it can accept a proton to form water ( ext{H}_2 ext{O}), which is its conjugate acid.

• A base is crucial in chemical reactions as it balances acids, which are proton donors.
• A common household example of a base is baking soda, chemically known as sodium bicarbonate ( ext{NaHCO}_3).

If a substance can receive a proton, it behaves as a base. As in the exercise, hydrogen sulfate ( ext{HSO}_4^-) acts as a base when adding a proton becomes sulfuric acid ( ext{H}_2 ext{SO}_4). This is a great example of how bases are important participants in forming new substances in reactions.

Proton Transfer

Proton transfer is the movement of protons (hydrogen ions, ext{H}^+) between atoms, molecules, or ions. It is fundamental to many chemical reactions, particularly in acid-base chemistry. The process can cause significant changes in chemical bonds and structures in the involved substances.

• For bases in acid-base reactions, gaining a proton means transforming into a conjugate acid.
• A proton's high reactivity is essential in processes like digestion and metabolism within living organisms.

Let's illustrate with bicarbonate ( ext{HCO}_3^-). When it receives a proton, a new chemical bond forms, turning it into carbonic acid ( ext{H}_2 ext{CO}_3). This exchange exemplifies proton transfer leading to the dramatic change from base to conjugate acid.
Proton transfer is not just a simple switch; it's a cornerstone for many dynamics in chemical and biological systems, explaining responsibility in energy transfer and driving reactions forward.

Acid-Base Reaction

Acid-base reactions are chemists' way of explaining how acids and bases interact. They involve the exchange of protons from an acid to a base. The result is a conjugate pair forming from the original acid and base. These reactions can be found spanning various areas from industrial applications to daily life.
For instance, when hydrochloric acid ( ext{HCl}) reacts with sodium hydroxide ( ext{NaOH}), they form the neutral compound sodium chloride and water. Here's why these reactions are vital:

• The balance they offer is used in creating products like fertilizers and cleaning products.
• They play a significant role in the body's pH balance, crucial for maintaining homeostasis.

Acid-base reactions also occur in a controlled manner in laboratory settings to study materials and their properties. Understanding how bases turn into conjugate acids is a small but essential part of learning how these reactions operate in broader chemical contexts.

Chemical Formula

A chemical formula represents the elements within a compound and their relative ratios. The formula is a shorthand way of conveying detailed information quickly. For acids and bases, understanding their chemical formulas is vital for predicting their behavior in reactions.
Consider the bicarbonate ion ( ext{HCO}_3^-). Its formula reveals its makeup: one hydrogen atom, one carbon atom, and three oxygen atoms, carrying an overall negative charge. Here are reasons why chemical formulas are indispensable:

• They allow chemists to predict how substances will interact by looking closely at components and their charges.
• Formulas are a universal language, enabling scientists worldwide to communicate complex ideas simply.

Knowing the formula for a compound tells you much of what you need to know about how it will act in a chemical reaction, such as an acid-base reaction. When breaking down exercises like deriving conjugate acids, the chemical formula guides you in adding protons to form new compounds.