Question

What is the oxidation state of Cr in cach compound? a. \(\mathrm{CrO} \quad\) b. \(\mathrm{CrO}_{3} \quad\) c. \(\mathrm{Cr}_{2} \mathrm{O}_{3}\)

Short answer

The oxidation states of Cr in the compounds are \( +2 \) in \(CrO\), \( +6 \) in \(CrO_3\), and \( +3 \) in \(Cr_2O_3\).

Step-by-step solution

Determine the Oxidation State of Oxygen

Oxygen usually has an oxidation state of -2 in most of its compounds (except in peroxides, superoxides, and when bonded to fluorine).

Calculate the Oxidation State of Cr in CrO

The compound is neutral, so the sum of oxidation states must equal 0. Let \(x\) be the oxidation state of Cr. Since oxygen has an oxidation state of -2: \(x + (-2) = 0\). Solving this equation gives \(x = +2\), which is the oxidation state of Cr in CrO.

Calculate the Oxidation State of Cr in CrO3

\(CrO_3\) is also a neutral compound. With three oxygen atoms each having an oxidation state of -2, their total is -6. Let \(x\) be the oxidation state of Cr: \(x + 3(-2) = 0\). Solving for \(x\) gives \(x = +6\), which is the oxidation state of Cr in \(CrO_3\).

Calculate the Oxidation State of Cr in Cr2O3

In \(Cr_2O_3\), the compound is neutral and contains two chromium atoms. The total oxidation state of the three oxygen atoms is -6. Let \(x\) be the oxidation state of each Cr atom: \(2x + 3(-2) = 0\). Solving the equation \(2x - 6 = 0\) leads to \(x = +3\), which is the oxidation state of each Cr in \(Cr_2O_3\).

Key concepts

Oxidation State of Chromium

Understanding the oxidation state of an element within a compound, such as chromium (Cr), is fundamental in grasping chemical reactions and bonding. The oxidation state, sometimes referred to as oxidation number, is a measure of the degree of oxidation of an atom in a substance. It represents the hypothetical charge an atom would have if all bonds to atoms of different elements were completely ionic.

Oxidation states are typically represented by integers, which can be positive, negative, or zero, and they are guided by a set of rules. For metals like chromium, multiple oxidation states are possible due to its ability to lose different numbers of electrons. In compounds, chromium can exhibit a variety of states such as +2, +3, +6, and others. Determining the correct oxidation state is a matter of balancing the overall charges, as displayed in the exercise, based on the premise that the sum of oxidation states in a neutral compound must equal zero.

Compound Neutrality

The concept of compound neutrality plays a critical role in the determination of oxidation states. Compounds are neutral entities, meaning that the sum of the positive and negative charges within a compound must cancel each other out, leading to an overall charge of zero. This rule is the cornerstone of solving for unknown oxidation states in compounds.

In the provided exercise, compound neutrality is used to find the oxidation state of chromium in different compounds. By setting the sum of the oxidation states multiplied by their respective number of atoms to zero, we can algebraically solve for the oxidation state of chromium. Ignoring this rule would lead to incorrect results, as it is the core principle that ensures the electrical neutrality of the compound.

Chemical Formulas

Chemical formulas are concise ways to represent chemical substances. They consist of the symbols of the elements present in the compound, accompanied by subscript numbers indicating the number of atoms of each element. These formulas not only provide information about the type and quantity of atoms but also serve as the basis for calculating molecular and molar masses, which are essential in stoichiometry.

Understanding how to read and interpret chemical formulas is crucial when determining oxidation states. In chromium compounds like CrO, CrO3, and Cr2O3, chemical formulas inform us about the ratio of chromium to oxygen, which is vital when applying the rule of compound neutrality to calculate oxidation states. For instance, in Cr2O3, the subscript '2' in front of Cr and '3' after O tells us there are two chromium atoms to three oxygen atoms, a ratio that drives the calculation process for chromium's oxidation state.