An oxidation state measures the degree of oxidation of an atom within a chemical substance. This number represents the hypothetical charge an atom would have if all its bonds were purely ionic. Determining these values is fundamental to understanding how an element behaves in reactions involving electron transfer. This article determines the oxidation states for Potassium (K), Oxygen (O), and Chromium (Cr) in the compound potassium dichromate, \(\text{K}_2\text{Cr}_2\text{O}_7\).
Establishing the Rules for Assigning Oxidation States
To accurately calculate the oxidation state of an unknown element, one must rely on established hierarchical rules for assigning these numerical values. These rules are based on the periodic table position and the electronegativity of the elements involved.
Potassium (K) is an alkali metal in Group 1 of the periodic table, and it always exhibits an oxidation state of \(+1\) in its compounds. Potassium readily gives up its single valence electron to achieve a stable electron configuration. This fixed value provides the first known number for the calculation.
The second rule involves oxygen (O), which is highly electronegative and typically carries an oxidation state of \(-2\) in most compounds. This value reflects oxygen’s strong tendency to gain two electrons. The \(-2\) rule applies to the oxygen atoms within the dichromate structure.
The third rule is the Sum Rule, which states that the sum of the oxidation states for all atoms in a neutral compound must equal zero. Since \(\text{K}_2\text{Cr}_2\text{O}_7\) has no overall charge, the total contribution from the two potassium atoms, the two chromium atoms, and the seven oxygen atoms must sum to zero. These established values and the Sum Rule are used to algebraically solve for the unknown state of chromium.
Step-by-Step Calculation for Potassium Dichromate
The calculation for the oxidation state of chromium (Cr) in \(\text{K}_2\text{Cr}_2\text{O}_7\) begins by setting up an algebraic equation based on the Sum Rule. The compound contains two potassium atoms, two chromium atoms, and seven oxygen atoms. Since the total charge must be zero, this charge neutrality is the foundation of the equation.
The equation is formulated as: \((2 \times \text{Oxidation State of K}) + (2 \times \text{Oxidation State of Cr}) + (7 \times \text{Oxidation State of O}) = 0\). Since the oxidation states for potassium and oxygen are known, these values are substituted into the formula. Let \(X\) represent the unknown oxidation state of a single chromium atom.
Substituting the known values of \(+1\) for potassium and \(-2\) for oxygen yields the expression: \((2 \times +1) + (2 \times X) + (7 \times -2) = 0\). Performing the multiplication for the known elements simplifies the equation to: \(+2 + 2X – 14 = 0\).
The next step is to simplify the equation by combining the constant terms. Combining \(+2\) and \(-14\) results in a net charge of \(-12\). The equation is reduced to \(2X – 12 = 0\).
To isolate the variable \(X\), the constant \(-12\) is added to both sides of the equation, resulting in \(2X = +12\). The final step involves dividing the total charge by the two chromium atoms present. Dividing \(+12\) by two yields \(X = +6\).
Therefore, the oxidation state of each element in \(\text{K}_2\text{Cr}_2\text{O}_7\) is \(+1\) for potassium, \(-2\) for oxygen, and \(+6\) for chromium. The \(+6\) oxidation state for chromium is the highest possible for the element, which has implications for the compound’s chemical behavior.
Why Potassium Dichromate is a Powerful Oxidizer
The calculated \(+6\) oxidation state of chromium is the primary reason potassium dichromate functions as a powerful oxidizing agent. An oxidizing agent gains electrons from another substance, causing the other substance to be oxidized while the agent itself is reduced. Chromium in this hexavalent state is highly electron-deficient and strongly electron-seeking.
The \(+6\) state is the maximum oxidation state chromium can achieve, meaning it has a strong tendency to accept electrons and be reduced to a lower, more stable oxidation state, most commonly \(\text{Cr}^{+3}\). This transition from \(\text{Cr}^{+6}\) to \(\text{Cr}^{+3}\) involves the gain of three electrons per chromium atom. The stability of the resulting \(\text{Cr}^{+3}\) ion drives the reaction forward.
This high oxidizing power is frequently utilized in laboratory and industrial settings. Potassium dichromate is an effective reagent for oxidizing primary alcohols into aldehydes or carboxylic acids in organic synthesis. The compound is also employed in various analytical chemistry applications, such as chemical titrations, where its ability to accept electrons is precisely measured to determine the concentration of a reducing substance. The color change from the orange \(\text{Cr}^{+6}\) ion to the green \(\text{Cr}^{+3}\) ion also serves as a visible indicator of the reaction’s progress.