Problem 9 - Chemistry Principles and Practice

Question

Assign the oxidation numbers of all atoms in the following species. (a) \(\mathrm{ClO}_{3}^{-}\) (b) \(\mathrm{PF}_{3}\) (c) \(\mathrm{CO}\)

Step-by-Step Solution

Answer

(a) Cl: +5, O: -2; (b) P: +3, F: -1; (c) C: +2, O: -2.

Step 1: Determine the Oxidation Number of Oxygen in ClO3-

Oxygen typically has an oxidation number of -2. Since the chlorate ion (\(\mathrm{ClO}_{3}^{-}\)) contains 3 oxygen atoms, the total contribution from oxygen is \(3 \times (-2) = -6\).

Step 2: Calculate the Oxidation Number of Chlorine in ClO3-

The overall charge on the chlorate ion is -1. Let the oxidation number of chlorine be \(x\). The sum of the oxidation numbers is: \[x + 3(-2) = -1\], which simplifies to \[x - 6 = -1\]. Solving for \(x\), we find \(x = +5\). Therefore, the oxidation number of chlorine is +5.

Step 3: Determine the Oxidation Number of Fluorine in PF3

Fluorine always has an oxidation number of -1. In \(\mathrm{PF}_{3}\), there are 3 fluorine atoms contributing \(3 \times (-1) = -3\).

Step 4: Calculate the Oxidation Number of Phosphorus in PF3

Since the molecule \(\mathrm{PF}_{3}\) is neutral, the sum of the oxidation numbers must be zero. Let the oxidation number of phosphorus be \(y\). Then, \[y + 3(-1) = 0\], which simplifies to \[y - 3 = 0\]. Solving for \(y\), we get \(y = +3\). Therefore, phosphorus has an oxidation number of +3.

Step 5: Determine the Oxidation Number of Oxygen in CO

Similar to previous cases, oxygen typically has an oxidation number of -2. In carbon monoxide (\(\mathrm{CO}\)), this remains unchanged.

Step 6: Calculate the Oxidation Number of Carbon in CO

Since carbon monoxide is a neutral molecule, the sum of the oxidation numbers should be zero. Let the oxidation number of carbon be \(z\). Then, \[z + (-2) = 0\], which simplifies to \[z - 2 = 0\]. Solving for \(z\), we find \(z = +2\). Therefore, carbon has an oxidation number of +2.

Key Concepts

Chlorate Ion

The chlorate ion, written as \(\mathrm{ClO}_{3}^{-}\), is a polyatomic ion comprised of one chlorine atom covalently bonded to three oxygen atoms. It carries an overall charge of -1. Understanding the configuration of chlorate is crucial for accurately determining oxidation numbers. To find the oxidation state of chlorine within this ion, note that oxygen typically has an oxidation state of -2. With three oxygen atoms, their cumulative contribution to the charge sums up to \(3 \times (-2) = -6\). The overall charge of the ion is -1, so the oxidation state of chlorine must counterbalance the charge introduced by oxygen.The sum of the oxidation states of chlorine and the three oxygens in \(\mathrm{ClO}_{3}^{-}\) must equal the charge of the ion:- For chlorine, let its oxidation number be \(x\). We set up the equation \(x + 3(-2) = -1\).- Solving for \(x\), we find \(x = +5\).This calculation reveals chlorine’s role in stabilizing the negative charge, which may seem high but is due to the electron-withdrawing effect of the bonded oxygen atoms.

Oxidation States

Oxidation states, or oxidation numbers, provide insight into the electron distribution within chemical species. They are essential for balancing chemical reactions and understanding redox processes.Each element has standard oxidation states based on its electronegativity and typical bonding scenarios:

• Oxygen, for example, is almost always found with an oxidation state of -2 due to its high electronegativity.
• Fluorine, being the most electronegative element, uniformly holds an oxidation state of -1 in compounds.

Consider the fluorine case found in \(\mathrm{PF}_{3}\):- There are three fluorine atoms, each contributing an oxidation number of -1.- For phosphorus, which tends to have varied oxidation states, the sum of the states in \(\mathrm{PF}_{3}\) must maintain the molecule's neutrality. Application of the formula for net oxidation states helps deduce phosphorus's state:- Let \(y\) be phosphorus's oxidation number.- The neutrality condition is written as \(y + 3(-1) = 0\), leading to \(y = +3\).These calculations demonstrate how oxidation states reflect the sharing of electrons in molecules.

Molecular Neutrality

Molecular neutrality means that the sum of oxidation numbers in a neutral molecule is zero. This principle is pivotal when determining unknown oxidation states in compounds.Let's understand this with the example of carbon monoxide (\(\mathrm{CO}\)), a simple diatomic molecule:- Oxygen, with its consistent oxidation state of -2, maintains this value in \(\mathrm{CO}\).- For the neutral molecule, carbon's oxidation number must equilibrate the effect of oxygen.Assigning the oxidation state of carbon involves ensuring the sum of the oxidation states equals zero:- Assume the oxidation state of carbon is \(z\).- Set up the neutrality equation: \(z + (-2) = 0\).- Solving gives \(z = +2\).This balancing act showcases the stability of molecular neutrality and explains how atoms achieve charge balance through electron sharing and transfer. Understanding this concept is fundamental in chemistry, ensuring proper charge balancing in various applications such as redox reactions.