Problem 54 - General Chemistry: Principles and Modern Applications

Question

What is the oxidation state of sulfur in the following compounds? (a) \(\mathrm{S}_{2} \mathrm{Br}_{2}\) (b) \(\mathrm{SCl}_{2}\) (c) \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) (d) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{S}_{4} \mathrm{O}_{6}\).

Step-by-Step Solution

Answer

The oxidation states of sulfur in the compounds are (a) +1, (b) +2, (c) +2, and (d) +5.

Step 1: Calculation for \( \mathrm{S}_{2} \mathrm{Br}_{2} \)

Given that bromine is usually -1 in compounds and since the compound is neutral, the total of all oxidation states should be zero. Therefore, we assign bromine an oxidation state of -1 and find sulfur's oxidation number by subtracting the total oxidation state of bromine from zero. This gives us that the oxidation state of sulfur is +1.

Step 2: Calculation for \(\mathrm{SCl}_{2}\)

The total oxidation state of a neutral molecule must be zero. Given that chlorine usually has an oxidation number of -1 in compounds, this means that the sulfur must have an oxidation state of +2.

Step 3: Calculation for \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\)

Sodium is always +1, and oxygen is usually -2. This means each sulfur atom must have an oxidation state of +2 to achieve overall neutrality.

Step 4: Calculation for \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{S}_{4} \mathrm{O}_{6}\)

The ammonium cation, \( \mathrm{NH}_{4}^{+} \), always has a charge of +1. Oxygen usually has an oxidation number of -2. Thus, considering the total charge in the molecule to be zero, the sulfur atoms must have an oxidation number of +5.

Key Concepts

Understanding Sulfur Compounds

Sulfur compounds are formed when sulfur combines with other elements, showcasing a variety of oxidation states. Sulfur can form a wide range of compounds, from simple binary compounds like sulfides to complex oxoanions. These compounds are important in different chemical and industrial applications. In binary compounds, sulfur often forms compounds with halogens (like chlorine and bromine). They showcase different oxidation states, influencing the reactivity and properties of each compound. Exploring sulfur compounds is essential, especially since they appear frequently in both natural and synthetic chemical processes.

• Sulfur and Bromine: Compounds like \( S_2Br_2 \) are interhalogen compounds, where sulfur achieves an oxidation state of +1. Here, sulfur interacts intimately with bromine.
• Sulfur and Chlorine: In compounds like \( SCl_2 \), sulfur assumes an oxidation state yet higher than in \( S_2Br_2 \), demonstrating the dynamic chemistry of sulfur.

In these compounds, the variance in oxidation states of sulfur points to its adaptability and major role in both industrial and biological systems.

Oxidation Number Calculations

Calculating oxidation numbers helps determine how electrons are distributed in compounds. It is a fundamental concept for understanding redox reactions. By following a set of rules, these numbers can be calculated, allowing us to predict reactions.

• Generally, any elemental state of a compound has an oxidation number of zero.
• For ions, the oxidation number equals the ion charge.
• Oxygen is usually assigned an oxidation number of -2, and in neutral compounds, the sums must equal zero.

Consider \( Na_2S_2O_3 \), where calculating the oxidation numbers involves recognizing the \( +1 \) oxidation state of sodium, \( -2 \) of oxygen, resulting in a critical insight about sulfur hosting the oxidation state of +2.

• Such calculations show how electrons shift or share among atoms, thereby clarifying the chemical behavior of compounds.

Neutral Molecules

Neutral molecules are those where the sum of all oxidation numbers equals zero. This balance is vital to maintaining stable compounds. Understanding neutral molecules helps in predicting the formation and stability of various chemical compounds.

• Balance: Achieving a neutral state demands balanced oxidation states across constituent atoms.
• Predicting Reactions: Through these calculations, one can infer how atoms swap or share electrons during reactions.

In \( (NH_4)_2S_4O_6 \), finding neutrality involves checking ammonium's contribution and balancing it against sulfur's oxidation number of +5. This balance solidifies a molecule's status as neutral.The understanding and identification of these neutral chemical entities lay the foundation for deeper engagement with chemical kinetics and dynamics.

Importance of Chemical Formulas

Chemical formulas represent the composition and proportions of elements within a compound. They serve as a crucial tool in chemical analysis and showcase the simplest representation of a substance.

• Molecular Composition: They indicate the exact number of atoms of each element in a molecule.
• Role in Oxidation Numbers: Essential in deducing oxidation states, which showcase electron distribution within molecules.
• Guiding Reactions: Guide chemists in predicting the outcomes of chemical reactions.

For instance, in compounds like \( S_2Br_2 \) and \( SCl_2 \), chemical formulas allow us to easily denote sulfur and halogen count, aiding in the quick calculation of sulfur's oxidation state.Precisely understanding these formulas opens the path to mastering complex chemical interactions and expands our capability to innovate across disciplines allied with chemistry.