Question

A transition metal \(X\) forms an oxide of formula \(\mathrm{X}_{2} \mathrm{O}_{3} .\) It is found that only \(50 \%\) of \(\mathrm{X}\) atoms in this compound are in the +3 oxidation state. The only other stable oxidation states of \(X\) are +2 and +5 . What percentage of \(\mathrm{X}\) atoms are in the +2 oxidation state in this compound?

Short answer

50% of X atoms are in the +2 oxidation state.

Step-by-step solution

Understand the Problem

The compound is given as \( \mathrm{X}_{2} \mathrm{O}_{3} \), meaning for every 2 atoms of \( X \), there are 3 atoms of oxygen. The problem states that 50% of \( X \) atoms are in the +3 oxidation state, and we need to find the percentage of \( X \) atoms in the +2 oxidation state.

Assign Oxidation States

The oxidation state for oxygen in compounds is typically \(-2\). Since there are 3 oxygen atoms, their total contribution in terms of oxidation state is \(-6\). The 2 atoms of \( X \) must balance this with a total charge of \(+6\).

Calculate Contribution of +3 Oxidation State

Since 50% of \( X \) atoms are in the +3 state, that means 1 out of the 2 \( X \) atoms is in the +3 state. This contributes \(+3\) to the total charge.

Determine Remaining Charge

The total positive charge needed is \(+6\), and \(+3\) has already been contributed by one \( X \) atom at +3 oxidation state. Therefore, \(+3\) more is needed from the remaining \( X \) atom.

Assign Oxidation State to Remaining X Atom

The remaining \( X \) atom must balance the remaining +3 charge, so it can be either in the +2 or +5 oxidation state. To make up for just +3, the remaining \( X \) atom must be in the +2 oxidation state since it would not balance if it were +5, exceeding the required +6 total.

Determine Percentage of +2 Oxidation State

As there are 2 \( X \) atoms total, and one is in the +2-state, the percentage of \( X \) atoms in the +2 oxidation state is \( \frac{1}{2} \times 100\% = 50\%\).

Key concepts

Oxidation State

The oxidation state, also known as oxidation number, is a concept used in chemistry to indicate the degree of oxidation of an atom in a chemical compound. It is represented by a number that signifies how many electrons an atom can lose, gain, or share when it forms a chemical bond.
To better understand, consider these key points:

• Oxidation involves an increase in oxidation state as atoms lose electrons.
• Reduction involves a decrease in oxidation state as atoms gain electrons.
• In most compounds, oxygen is assigned an oxidation state of (-2), and hydrogen is (+1).

In the given exercise, two oxidation states are primarily considered: (+2) and (+3), which help balance the overall charge of the compound. Balancing is crucial since the total charge of the compound must remain neutral by using appropriate oxidation states for both metal and non-metal elements.

Transition Metals

Transition metals are elements found in the d-block of the periodic table, distinguished by their ability to form several oxidation states, typically due to their d-electrons.
This ability makes them crucial in various chemical reactions and compounds. Let's explore the main features:

• They have partially filled d orbitals which allow them to form different oxidation states.
• Transition metals often form colored compounds and are good conductors of electricity.
• They can form complex ions with varied oxidation numbers, affecting their chemical and physical properties.

In the example from the exercise, the transition metal X can exist in multiple stable oxidation states, specifically (+2), (+3), and (+5). This multivalence allows the metal to effectively bond with oxygen to form stable compounds, highlighting the importance of selecting the appropriate oxidation states to balance the charges.

Chemical Formulas

Chemical formulas serve as shorthand notations to represent chemical substances. They convey important details about the elements involved and their ratios within compounds.
Here's what essential about them:

• They denote the types and numbers of atoms present in a molecule.
• Different prefixes (`subscripts`) in a chemical formula reflect the number of each type of atom present.
• They help track oxidation states in compounds, playing a crucial role in balancing reactions.

In our specific example, \( \mathrm{X}_2\mathrm{O}_3 \) reflects that the compound consists of 2 atoms of metal X and 3 atoms of oxygen. The subscripts help chemists understand how the atoms relate to each other and how they contribute to the overall oxidation state of the compound.