Problem 53 - General Chemistry: Principles and Modern Applications

Question

Chromium forms three principal oxides. Write appropriate formulas for these compounds in which the oxidation states of Cr are \(+3,+4,\) and \(+6,\) respectively.

Step-by-Step Solution

Answer

The formulas for Chromium oxides where Chromium has oxidation states of +3, +4, and +6 are \(Cr_2O_3\), \(CrO_2\), and \(CrO_3\) respectively.

Step 1: Identify Elements and Their Oxidation States

The elements involved here are Chromium (Cr) and Oxygen (O). They will form an ionic compound, with Chromium carrying positive charges of +3, +4, and +6 at different times, and Oxygen having a -2 charge continuously.

Step 2: Form Compound for Oxidation State +3

For Chromium in oxidation state +3, it forms a Cr³⁺ ion. Oxygen on the other hand forms O²⁻ ions. Since the total positive charges must balance the total negative charges, we need 2 Chromium ions for every 3 Oxygen ions to balance the formula. Hence, the formula for this compound is \(Cr_2O_3\)

Step 3: Form Compound for Oxidation State +4

Chromium in oxidation state +4 forms Cr⁴⁺ ions. To balance the charges, we need 2 Chromium ions for each 4 Oxygen ions. Thus, the formula for this compound is \(Cr_2O_4\). In order to standardize the formula, we cut down the ratio to the simplest form. Hence, the formula becomes \(CrO_2\).

Step 4: Form Compound for Oxidation State +6

For Chromium in oxidation state of +6, it forms Cr⁶⁺ ions. We need 1 Chromium ion for each 3 Oxygen ions to balance the charges, since Oxygen carries a -2 charge. Therefore, the appropriate formula is \(CrO_3\).

Key Concepts

Oxidation States

Oxidation states are an essential concept in chemistry that denote the degree of oxidation of an atom within a compound. They are characterized by the number of electrons an atom loses, gains, or appears to use when participating in a chemical reaction.

• Positive oxidation states indicate the atom has lost electrons.
• Negative oxidation states indicate the atom has gained electrons.

In this exercise, we see Chromium (Cr) with oxidation states of +3, +4, and +6. This means Chromium can lose 3, 4, or 6 electrons, respectively, to form different ions in various compounds with oxygen. Understanding oxidation states helps in determining the chemical formulas of compounds by balancing the total positive and negative charges within the compound. This ensures that compounds are electrically neutral overall.

Chemical Formulas

Chemical formulas are symbolic representations of chemical compounds, showing the elements involved and their relative number of atoms. They provide a straightforward way of expressing how atoms are bonded together in molecules.
Chemists use oxidation states to derive chemical formulas. In the case of Chromium oxides:

• For the +3 oxidation state, Chromium forms a compound with oxygen as \(Cr_2O_3\).
• In the +4 state, it forms \(CrO_2\).
• With a +6 state, Chromium combines with oxygen to form \(CrO_3\).

Each of these formulas is derived by balancing the positive charge of chromium ions with the negative charge from oxide ions, aiming for a neutral compound. This is crucial for the stability of the compound.

Ionic Compounds

Ionic compounds are substances made of charged particles held together by ionic bonds. These particles, or ions, are atoms or molecules that have gained or lost electrons, resulting in positive or negative charges.
In the context of Chromium oxides, the ions involved are chromium ions (\(Cr^{3+}\), \(Cr^{4+}\), \(Cr^{6+}\)) and oxide ions (\(O^{2-}\)).

• Positive chromium ions are cations.
• Negative oxide ions are anions.

In ionic compounds, the sum of the charges must be zero to ensure electric neutrality. This is achieved by balancing the number of positive and negative ions, as seen in the formulas for Chromium oxides like \(Cr_2O_3\), \(CrO_2\), and \(CrO_3\). Understanding the formation of ionic compounds helps in predicting compound formulas and properties, aiding in their practical application in various chemical reactions.