Question

Phosphorus can have several different oxidation numbers ranging in value from \(-3\) to \(+5\). (a) When phosphorus burns in air or oxygen, it yields either tetraphosphorus hexoxide or tetraphosphorus decoxide. Write the formula and give the oxidation number in each compound. (b) Based on oxidation numbers, which phosphorus oxide compound from part (a) was formed by combustion with a limited supply of oxygen?

Short answer

(a) \(\text{P}_4\text{O}_6\): oxidation +3, \(\text{P}_4\text{O}_{10}\): oxidation +5. (b) \(\text{P}_4\text{O}_6\) formed with limited oxygen.

Step-by-step solution

Identify the Compounds

Phosphorus can form two oxides when it reacts with oxygen: **Tetraphosphorus hexoxide** and **Tetraphosphorus decoxide**. These are represented by their chemical formulas as \( \text{P}_4\text{O}_6 \) and \( \text{P}_4\text{O}_{10} \) respectively.

Determine the Oxidation Numbers in Tetraphosphorus Hexoxide \((\text{P}_4\text{O}_6)\)

The oxidation number of oxygen is generally \(-2\). In \(\text{P}_4\text{O}_6\), there are 6 oxygen atoms, so the total contribution to the oxidation number from oxygen is \(-2 \times 6 = -12\). Let the oxidation number of phosphorus be \(x\). We have:\[4x + (-12) = 0\]Solving for \(x\), we get:\[4x = 12\]\[x = 3\]Thus, the oxidation number of phosphorus in \(\text{P}_4\text{O}_6\) is \(+3\).

Determine the Oxidation Numbers in Tetraphosphorus Decoxide \((\text{P}_4\text{O}_{10})\)

Similarly, in \(\text{P}_4\text{O}_{10}\): There are 10 oxygen atoms contributing to an oxidation number of \(-2 \times 10 = -20\). Let the oxidation number of phosphorus be \(x\). The equation becomes:\[4x + (-20) = 0\]Solving for \(x\), we obtain:\[4x = 20\]\[x = 5\]Therefore, the oxidation number of phosphorus in \(\text{P}_4\text{O}_{10}\) is \(+5\).

Determine the Compound Formed with Limited Oxygen

The lower the oxidation number of phosphorus, the less oxygen was available for the reaction. Thus, tetraphosphorus hexoxide \(\text{P}_4\text{O}_6\) formed when there was a limited supply of oxygen, as it has an oxidation number of \(+3\), which is lower than \(+5\) in \(\text{P}_4\text{O}_{10}\).

Key concepts

phosphorus oxides

Phosphorus, a versatile element, can form various oxides, primarily depending on its oxidation number. When phosphorus is combusted, it forms phosphorus oxides such as tetraphosphorus hexoxide and tetraphosphorus decoxide. These oxides arise due to different oxidation states of phosphorus, indicating how many electrons are lost, gained, or shared in bonding. Tetraphosphorus hexoxide, with the formula \( \text{P}_4\text{O}_6 \), reflects a +3 oxidation state for phosphorus. In contrast, tetraphosphorus decoxide, \( \text{P}_4\text{O}_{10} \), shows phosphorus in a +5 oxidation state. The formation of these distinct oxides is influenced by the availability of oxygen during the reaction. The process highlights how phosphorus can adaptively bond with oxygen to form stable compounds.

chemical formulas

The chemical formulas \( \text{P}_4\text{O}_6 \) and \( \text{P}_4\text{O}_{10} \) are a way to represent the composition of phosphorus oxides. Let's break down what these formulas tell us:

• \( \text{P}_4\text{O}_6 \) means each molecule consists of 4 phosphorus atoms and 6 oxygen atoms.
• \( \text{P}_4\text{O}_{10} \) indicates a composition of 4 phosphorus atoms bonded with 10 oxygen atoms.

These formulas not just show the types of atoms present but also the ratio in which these atoms combine to form the molecules. Understanding chemical formulas is vital for analyzing and predicting the properties of chemical compounds. They help in understanding the variations in oxidation numbers and the nature of the chemical bonds in the compounds.

limited oxygen supply

When phosphorus burns, the reaction can result in different products based on the amount of oxygen available. Having a limited oxygen supply means fewer oxygen molecules are available to react with phosphorus. This limitation is crucial in determining which phosphorus oxide will form.With limited oxygen, tetraphosphorus hexoxide \( \text{P}_4\text{O}_6 \) is more likely to be produced due to its lower oxygen to phosphorus ratio. This is indicated by its oxidation number of +3. On the other hand, if there is plenty of oxygen, tetraphosphorus decoxide \( \text{P}_4\text{O}_{10} \), showing a +5 oxidation state, is formed due to a higher incorporation of oxygen atoms.

oxidation state determination

Determining the oxidation state of an element within a compound, like phosphorus in its oxides, is crucial to understand its chemical behavior. The oxidation state indicates how many electrons an atom has donated or accepted during the formation of the compound.For instance, in \( \text{P}_4\text{O}_6 \):

• Oxygen typically has an oxidation state of -2.
• With 6 oxygen atoms, the total oxidation state from oxygen is -12.
• Letting the oxidation state of phosphorus be \( x \), the equation \( 4x + (-12) = 0 \) can be solved to find \( x = 3 \).

This shows phosphorus in \( \text{P}_4\text{O}_6 \) has an oxidation state of +3.In \( \text{P}_4\text{O}_{10} \), a similar calculation shows:

• The total contribution from 10 oxygen atoms is -20.
• Solving the equation \( 4x + (-20) = 0 \) results in \( x = 5 \).

Thus, phosphorus in \( \text{P}_4\text{O}_{10} \) has an oxidation state of +5. Understanding these calculations helps in determining the nature of chemical reactions and the formation of products.