Question

What is the anhydride for each of the following acids: (a) \(\mathrm{H}_{2} \mathrm{SO}_{4}\), (b) \(\mathrm{HClO}_{3}\) (c) \(\mathrm{HNO}_{2}\), (d) \(\mathrm{H}_{2} \mathrm{CO}_{3}\) (e) \(\mathrm{H}_{3} \mathrm{PO}_{4} ?\)

Short answer

The anhydrides for the given acids are: (a) \(\mathrm{H}_{2}\mathrm{S}_{2}\mathrm{O}_{7}\) (b) \(\mathrm{Cl}_{2}\mathrm{O}_{6}\) (c) \(\mathrm{N}_{2}\mathrm{O}_{3}\) (d) No anhydride (decomposes into \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\)) (e) \(\mathrm{H}_{4}\mathrm{P}_{2}\mathrm{O}_{7}\)

Step-by-step solution

(a) Anhydride of \(\mathrm{H}_{2}\mathrm{SO}_{4}\)

To find anhydride of \(\mathrm{H}_{2}\mathrm{SO}_{4}\), we will combine two molecules of this acid and remove one water molecule (H₂O). \(2 \times \mathrm{H}_{2}\mathrm{SO}_{4} - \mathrm{H}_{2}\mathrm{O}\) Now, subtract the H₂O from it and simplify: \(\mathrm{H}_{2}\mathrm{S}_{2}\mathrm{O}_{7}\) So, the anhydride of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) is \(\mathrm{H}_{2}\mathrm{S}_{2}\mathrm{O}_{7}\).

(b) Anhydride of \(\mathrm{HClO}_{3}\)

To find anhydride of \(\mathrm{HClO}_{3}\), we will combine two molecules of this acid and remove one water molecule (H₂O). \(2 \times \mathrm{HClO}_{3} - \mathrm{H}_{2}\mathrm{O}\) Now, subtract the H₂O from it and simplify: \(\mathrm{Cl}_{2}\mathrm{O}_{6}\) So, the anhydride of \(\mathrm{HClO}_{3}\) is \(\mathrm{Cl}_{2}\mathrm{O}_{6}\).

(c) Anhydride of \(\mathrm{HNO}_{2}\)

To find anhydride of \(\mathrm{HNO}_{2}\), we will combine two molecules of this acid and remove one water molecule (H₂O). \(2 \times \mathrm{HNO}_{2} - \mathrm{H}_{2}\mathrm{O}\) Now, subtract the H₂O from it and simplify: \(\mathrm{N}_{2}\mathrm{O}_{3}\) So, the anhydride of \(\mathrm{HNO}_{2}\) is \(\mathrm{N}_{2}\mathrm{O}_{3}\).

(d) Anhydride of \(\mathrm{H}_{2}\mathrm{CO}_{3}\)

To find anhydride of \(\mathrm{H}_{2}\mathrm{CO}_{3}\), we will combine two molecules of this acid and remove one water molecule (H₂O). \(2 \times \mathrm{H}_{2}\mathrm{CO}_{3} - \mathrm{H}_{2}\mathrm{O}\) Now, subtract the H₂O from it and simplify: \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{5}\) However, carbonic acid doesn't form a stable anhydride; instead, it decomposes into \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\). Therefore, there is no anhydride for this acid.

(e) Anhydride of \(\mathrm{H}_{3}\mathrm{PO}_{4}\)

To find anhydride of \(\mathrm{H}_{3}\mathrm{PO}_{4}\), we will combine two molecules of this acid and remove one water molecule (H₂O). \(2 \times \mathrm{H}_{3}\mathrm{PO}_{4} - \mathrm{H}_{2}\mathrm{O}\) Now, subtract the H₂O from it and simplify: \(\mathrm{H}_{4}\mathrm{P}_{2}\mathrm{O}_{7}\) So, the anhydride of \(\mathrm{H}_{3}\mathrm{PO}_{4}\) is \(\mathrm{H}_{4}\mathrm{P}_{2}\mathrm{O}_{7}\).

Key concepts

Understanding Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into new substances, called products. This transformation involves the breaking and forming of chemical bonds, often with noticeable changes such as color change, temperature change, gas production, or precipitate formation.

In the case of acid anhydrides, the chemical reaction we are particularly interested in is a dehydration synthesis reaction. This reaction type involves the combining of reactants, in this instance, acid molecules, with the elimination of water (H₂O) to form an anhydride. Anhydrides are chemicals that can react with water to form acids or bases, depending on their structure.

To visualize this concept, let's take the dehydration synthesis of sulfuric acid (H₂SO₄), which combines two molecules of H₂SO₄ and removes one molecule of water, resulting in the formation of sulfuric anhydride (H₂S₂O₇). This reaction is important in organic chemistry and industrial applications such as the manufacturing of pharmaceuticals and agrochemicals.

Exploring Acid-Base Chemistry

Acid-base chemistry is a fundamental aspect of chemical science, dealing with the reactions between acids and bases. Acids are substances that can donate a proton (H⁺) to another substance, while bases are capable of accepting a proton.

When discussing acid anhydrides, we're looking at compounds that form acids upon the addition of water. This relationship can be understood in terms of the Bronsted-Lowry acid-base theory, which defines an acid as a proton donor and a base as a proton acceptor. Anhydrides act as acid progenitors because upon hydrolysis, they release the protons that were lost as water in their formation.

For instance, phosphoric anhydride (H₄P₂O₇), when reacted with water, regenerates phosphoric acid (H₃PO₄). Acid anhydrides can also react with bases to form salts and water, illustrating their role in acid-base reactions and their relevance in chemical synthesis.

Decoding Molecular Formulas

Molecular formulas provide concise information about the type and number of atoms in a molecule, serving as fundamental identifiers in the study of chemistry. They are critical for understanding the composition of chemical compounds, predicting the properties of substances, and balancing chemical equations.

In the context of acid anhydrides, the molecular formula is an expression of the non-water constituents of the corresponding acid. To discern the anhydride's molecular formula, a common technique is to double the acid's formula (since anhydrides typically come from two acid molecules) and subtract the elements that would make up a water molecule (H₂O).

For example, nitrous acid (HNO₂) has the anhydride dinitrogen trioxide (N₂O₃), derived by doubling HNO₂ to get H₂N₂O₄ and then removing H₂O. Understanding molecular formulas is vital as it helps in the visualization and manipulation of chemical substances during reactions, and thus, in the mastery of solving chemistry problems.