Problem 55 - Chemistry and Chemical Reactivity

Question

Review the structure of phosphorous acid in Table 21.7 (a) What is the oxidation number of the phosphorus atom in this acid? (b) Draw the structure of diphosphorous acid, \(\mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{5}\) What is the maximum number of protons this acid can dissociate in water?

Step-by-Step Solution

Answer

(a) +3, (b) 2 protons dissociate.

Step 1: Determine Oxidation Number of Phosphorus in Phosphorous Acid

In phosphorous acid, which is represented by the formula \( ext{H}_3 ext{PO}_3\), the oxidation states of hydrogen and oxygen are +1 and -2 respectively. Let \(x\) be the oxidation number of phosphorus. Set up the equation for the sum of oxidation numbers as: \(3(+1) + x + 3(-2) = 0\). This simplifies to \(3 + x - 6 = 0\), giving \(x = +3\). Hence, the oxidation number of phosphorus in phosphorous acid is +3.

Step 2: Draw the Structure of Diphosphorous Acid

Diphosphorous acid has the formula \( ext{H}_4 ext{P}_2 ext{O}_5\). In this structure, two phosphorous atoms are connected by an oxygen atom bridge (P-O-P), each phosphorus atom is bonded to one OH group and one double-bonded oxygen atom. Visually it looks like: H(O)P(=O)(OH) O P(=O)(OH) H.

Step 3: Determine Maximum Number of Protons that Can Dissociate

In diphosphorous acid \( ext{H}_4 ext{P}_2 ext{O}_5\), each of the four hydrogen atoms accounts for potential dissociation. However, only the two hydroxyl groups (OH) can donate a proton each, resulting in a maximum dissociation of 2 protons in water.

Key Concepts

Diphosphorous Acid Structure

Diphosphorous acid, known by its chemical formula \(\mathrm{H}_4\mathrm{P}_2\mathrm{O}_5\), is an intriguing molecule owing to its unique arrangement of atoms. This acid consists of two phosphorus atoms that are connected by a bridging oxygen atom. Imagine the structure as a pair of phosphorus atoms (P) sitting side by side, each linked by an oxygen (O) bridge forming a P-O-P bond. In addition to this, each phosphorus atom is surrounded by one double-bonded oxygen and one hydroxyl group (OH). This results in the formula H(O)P(=O)(OH) O P(=O)(OH)H. Breaking down the composition of this structure reveals the precise organization and connection of atoms and offers insights into the chemical behavior of diphosphorous acid.

Proton Dissociation

The concept of proton dissociation relates to the ability of certain hydrogens in an acid to release protons (\(\mathrm{H}^+\)) into a solution, which defines the acid's strength. In diphosphorous acid, \(\mathrm{H}_4\mathrm{P}_2\mathrm{O}_5\), with four hydrogen atoms, one might expect a potential release of all four protons. However, only certain protons, specifically those being part of the hydroxyl (OH) groups, are capable of dissociating in water. This means only two protons are capable of dissociation, contributing to the acidity of the solution. Here’s why:

• Each OH group is more ready to release its proton due to the polarity of the OH bond.
• The remaining hydrogen atoms are involved in more stable or less polar covalent bonds and do not dissociate as easily.

Thus, the maximum number of protons that diphosphorous acid can contribute to a solution is two.

Oxidation State Determination

Understanding oxidation states is vital for analyzing chemical reactions and properties. It indicates the degree of oxidation of an atom in a compound. In phosphorous acid \(\mathrm{H}_3\mathrm{PO}_3\), the oxidation states of atoms are categorized as follows: hydrogen as +1, oxygen as -2. To find phosphorus's oxidation state, we label it as \(x\) and set up the equation: \(3(+1) + x + 3(-2) = 0\).
Solving this equation results in:

• \(3 + x - 6 = 0\)
• \(x = +3\)

Thus, phosphorus in phosphorous acid holds an oxidation state of +3. This calculation method helps us conclude how electrons are distributed in the molecule and predicts the reactivity and interaction within chemical environments.