Question

Assign an oxidation state to each atom in each polyatomic ion. (a) \(\mathrm{CrO}_{4}^{2-}\) (b) \(\mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}\) (c) \(\mathrm{PO}_{4}{ }^{3-}\) (d) \(\mathrm{MnO}_{4}^{-}\)

Short answer

The oxidation states are (a) Cr: +6, (b) Cr: +6, (c) P: +5, (d) Mn: +7.

Step-by-step solution

Assigning Oxidation State to Oxygen

In most compounds, oxygen is assigned an oxidation state of -2. Since there are four oxygens in \(\mathrm{CrO}_{4}^{2-}\), seven oxygens in \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\), four oxygens in \(\mathrm{PO}_{4}^{3-}\), and four oxygens in \(\mathrm{MnO}_{4}^{-}\), multiply -2 by the number of oxygen atoms to calculate the total oxidation state contributed by the oxygen atoms in each polyatomic ion.

Determining Total Charge of Polyatomic Ion

Use the charge of the polyatomic ion to determine the total oxidation state that must be accounted for by the non-oxygen atoms in the ion. For \(\mathrm{CrO}_{4}^{2-}\) the total charge is -2, for \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\) it is also -2, for \(\mathrm{PO}_{4}^{3-}\) it is -3, and for \(\mathrm{MnO}_{4}^{-}\) it is -1.

Assigning Oxidation State to Chromium in \(\mathrm{CrO}_{4}^{2-}\)

The sum of the oxidation states of all atoms in the ion must equal the overall charge of the ion. For \(\mathrm{CrO}_{4}^{2-}\), we have: \(-2 \times 4 + \mathrm{Cr} = -2\). Solve for the oxidation state of Cr, which gets us \(+6\) for chromium.

Assigning Oxidation State to Chromium in \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\)

Following a similar method for \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\), we have: \(-2 \times 7 + 2 \times \mathrm{Cr} = -2\). Solve for the oxidation state of Cr, which gives us \(+6\) for each chromium atom.

Assigning Oxidation State to Phosphorus in \(\mathrm{PO}_{4}^{3-}\)

For \(\mathrm{PO}_{4}^{3-}\), the calculation follows: \(-2 \times 4 + \mathrm{P} = -3\). Solve for the oxidation state of P, which gives an oxidation state of \(+5\) for phosphorus.

Assigning Oxidation State to Manganese in \(\mathrm{MnO}_{4}^{-}\)

For \(\mathrm{MnO}_{4}^{-}\), we do: \(-2 \times 4 + \mathrm{Mn} = -1\). Solve for the oxidation state of Mn, which leads to an oxidation state of \(+7\) for manganese.

Key concepts

Assigning Oxidation Numbers

Understanding how to assign oxidation numbers is essential in the study of redox reactions and chemical bonding. It provides insight into the electron distribution in compounds, helping to predict how atoms will behave in a chemical reaction. When assigning oxidation numbers to the atoms in a polyatomic ion, always start by considering the known values of certain elements, like oxygen, which typically has an oxidation number of -2. However, it's important to remember that there are exceptions, such as in peroxides where oxygen is -1 or in compounds with fluorine where it can be positive.

Following this, calculate the total oxidation number for all oxygen atoms. Then, considering the overall charge of the ion, determine the remaining oxidation numbers for the other atoms in the ion. The sum of the oxidation numbers in the ion should equal the ion's charge. This systematic approach to assigning oxidation numbers aids in maintaining the electron balance which is a critical concept in redox chemistry.

Polyatomic Ion Charge

Polyatomic ions are charged species composed of two or more atoms covalently bonded together. The charge on a polyatomic ion is not arbitrary but is the result of the difference between the number of protons and electrons within the ion. When asked to assess the charge on a polyatomic ion, it's essential to count the total number of electrons that have been lost or gained relative to the number of protons in the atoms that make up the ion.

To determine the charge, use the assigned oxidation numbers for each atom and balance them in such a way that the overall charge matches the charge on the polyatomic ion. It is also crucial in understanding chemical reactions and stoichiometry, as the charge affects the ratio in which ions combine to form neutral compounds.

Redox Chemistry

Redox chemistry deals with the flow of electrons between atoms and molecules during chemical reactions. This involves oxidation, where an atom or molecule loses electrons, and reduction, where one gains electrons. The oxidation numbers assigned to atoms allow chemists to keep track of these electron transfers. In the context of polyatomic ions, the changes in oxidation numbers imply that a redox reaction may have occurred to form the ion.

Understanding redox chemistry is crucial when predicting the feasibility of reactions, their products, and their energetics. As oxidation numbers change, they can tell us not only the direction of electron flow but also about the transformation of energy within the reaction, making redox concepts fundamental in both inorganic and organic chemistry.

Chemical Bonding

Chemical bonding is what holds atoms together in molecules and compounds. In polyatomic ions, covalent bonds are typically what keep the atoms associated. These bonds involve the sharing of electrons between the atoms, yet the electrons are not always shared equally. Electronegativity, or the attraction an atom has for electrons, can cause an uneven distribution of electron density.

The oxidation number of an atom in a molecule gives a rough measure of its electron possession relative to the atom in its elemental state. In polyatomic ions, understanding the chemical bonding and distribution of valence electrons is essential for predicting the molecule's geometry, reactivity, and even physical properties. Knowledge of bonding helps determine molecular polarity, intermolecular forces, and the resultant macroscopic behavior of the substance.