Problem 3 - Chemistry The Molecular Nature of Matter

Question

In the compound \(\mathrm{As}_{4} \mathrm{O}_{6}\), arsenic has an oxidation \(\mathrm{num}\) ber of +3 . What is the oxidation state of arsenic in this compound?

Step-by-Step Solution

Answer

The oxidation state of arsenic in the compound \(\mathrm{As}_{4} \mathrm{O}_{6}\) is +3.

Step 1: Understanding the Exercise

The exercise gives the chemical formula \(\mathrm{As}_{4} \mathrm{O}_{6}\) and tells us that in this compound, arsenic (As) has an oxidation number of +3. The goal is to confirm the oxidation state of arsenic in this compound. Since the compound is neutral, the sum of the oxidation states of all the atoms must equal zero.

Step 2: Determine the Oxidation State of Oxygen

Oxygen generally has an oxidation state of -2 (except in peroxides, superoxides, or when it's bonded to fluorine). Since there is no indication of an unusual situation here, we can assume that each oxygen atom has an oxidation state of -2.

Step 3: Calculate the Total Oxidation State of Oxygen

Multiply the oxidation state of a single oxygen atom by the number of oxygen atoms in the compound: \(6 \times -2 = -12\).

Step 4: Set Up the Equation

The total oxidation state of the compound is zero. Let the oxidation state of As be 'x'. There are four arsenic atoms, which means \(4x\) for arsenic and \(6 \times -2\) for oxygen. Setting up the equation: \(4x + (6 \times -2) = 0\).

Step 5: Solve for the Oxidation State of Arsenic

Solve the equation \(4x - 12 = 0\) for 'x' to find the oxidation state of arsenic. Adding 12 to both sides of the equation gives \(4x = 12\). Dividing both sides by 4 gives \(x = 3\).

Key Concepts

Chemical Formula

A chemical formula is a representation of a substance using symbols for its constituent elements and numerals to indicate the proportions of each element. In the compound \textbf{As\(_4\)O\(_6\)}, arsenic (As) and oxygen (O) are combined in a specific ratio. The numerical subscript after the element symbol indicates how many atoms of each are present in a single molecule of the compound.

Understanding the formula is crucial as it gives immediate information about the composition of the compound, which is the foundation for analyzing its properties and reactions. The particular arrangement of atoms within a chemical formula can also suggest the structure of the compound, although a more detailed representation, such as a structural formula, is often needed to convey the full three-dimensional shape.

Oxidation Number

The oxidation number, often called the oxidation state, is a numerical indicator of the number of electrons an atom has gained, lost, or shared when forming a chemical bond. In the exercise, the challenge was to confirm that the oxidation state of arsenic in \textbf{As\(_4\)O\(_6\)} is +3.

To deduce this, it's important to remember that the sum of oxidation states in a neutral compound must be zero. Typically, oxygen has a consistent oxidation state of -2. Hence, by understanding the expected oxidation states of common elements, we can set up an equation based on the stoichiometry of the compound to solve for an unknown oxidation state. This fundamental concept of oxidation number is essential for predicting the types of chemical reactions a compound can undergo, such as redox reactions.

Compound Stoichiometry

Compound stoichiometry pertains to the quantitative relationships of elements within a chemical formula. It involves the mole concept, which provides a method for translating between mass and number of atoms, given the fact that the atomic masses are scaled relative to carbon-12 (\(^{12}C\)).

In the context of the exercise, stoichiometry was used to help deduce the oxidation number of arsenic by balancing the sum of the oxidation states within the compound. Using stoichiometry, we can deduce that the four arsenic atoms must collectively have a total positive charge that cancels out the total negative charge of the six oxygen atoms. This kind of stoichiometric calculation is vital in all areas of chemistry, from balancing equations to determining the proportions of reactants and products in a chemical reaction.