Question

In \(1937,\) R. Schwartz and M. Schmiesser prepared a yellow-orange bromine oxide (BrO,) by treating Br with ozone in a fluorocarbon solvent. Many years later, J. Pascal found that, on heating, this oxide decomposed to two other oxides, a less volatile golden yellow oxide (A) and a more volatile deep brown oxide (B). Oxide B was later identified as \(\mathrm{Br}_{2} \mathrm{O}\). To determine the formula for oxide \(\mathrm{A},\) a sample was treated with sodium iodide. The reaction liberated iodine, which was titrated to an equivalence point with \(17.7 \mathrm{mL}\) of 0.065 M sodium thiosulfate. $$\mathrm{I}_{2}(\mathrm{aq})+2 \mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq}) \rightarrow 2 \mathrm{I}^{-}(\mathrm{aq})+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}(\mathrm{aq})$$ Compound A was also treated with AgNO \(_{3},\) and 14.4 mL of 0.020 M AgNO \(_{3}\) was required to completely precipitate the bromine from the sample. (a) What is the formula of the unknown bromine oxide A? (b) Draw Lewis structures for \(A\) and \(B r_{2} O .\) Speculate on their molecular geometry.

Short answer

The formula of bromine oxide A is \( \text{BrO}_3 \).

Step-by-step solution

Analyze Reaction with Sodium Thiosulfate

Given the reaction \( \text{I}_2 + 2\text{S}_2\text{O}_3^{2-} \rightarrow 2\text{I}^- + \text{S}_4\text{O}_6^{2-} \), determine the moles of sodium thiosulfate used: \[\text{Moles of } \text{S}_2\text{O}_3^{2-} = \text{Volume (L)} \times \text{Molarity} = 0.0177 \times 0.065 = 0.0011515 \text{ moles}\]This implies that 0.00057575 moles of \( \text{I}_2 \) reacted, as 1 mol \( \text{I}_2 \) needs 2 mols \( \text{S}_2\text{O}_3^{2-} \).

Analyze Reaction with Silver Nitrate

The reaction with silver nitrate precipitates bromine as silver bromide: \[\text{Ag}^+ + \text{Br}^- \rightarrow \text{AgBr}\]Calculate the moles of silver nitrate used: \[\text{Moles of AgNO}_3 = 0.0144 \text{ L} \times 0.020 \text{ M} = 0.000288 \text{ moles}\]This also represents the moles of \( \text{Br}^- \) in the sample.

Establish Ratio and Identify Formula of A

With iodine liberated from 0.00057575 moles of \( \text{I}_2 \) and 0.000288 moles of \( \text{Br}^- \), relate this to the decomposition of compound A.The empirical formula is derived from the stoichiometric ratio of the iodine liberated and bromine precipitated. Since the stoichiometry is 2:1 iodine to bromine, and the reaction liberates 1 mol of \( \text{I}_2 \) for every 2 moles of \( \text{Br}^- \), the formula of A is deduced as \( \text{BrO}_3 \).

Draw Lewis Structures and Discuss Molecular Geometry

For \( \text{BrO}_3 \), each oxygen is singly bonded to the bromine, and bromine carries a partial positive charge due to its high oxidation state. Its molecular geometry can be speculated to be trigonal planar.For \( \text{Br}_2 \text{O} \), oxygen bridges the two bromines; the Lewis structure shows single bonds from oxygen to each bromine. The molecular geometry of \( \text{Br}_2 \text{O} \) is bent due to electron pair repulsion around oxygen.

Key concepts

Lewis Structures

Understanding Lewis structures helps us visualize the arrangement of electrons in molecules. For compound \( \text{BrO}_3 \), each oxygen atom is singly bonded to a central bromine atom. In a Lewis structure, you represent valence electrons as dots. The bonds are depicted as lines between two atoms.
This depiction helps us see where extra electrons might create formal charges. For \( \text{Br}_2 \text{O} \), oxygen forms a bridge between the two bromines. This structure indicates that each bromine atom shares electron pairs with the oxygen.

• Draw dots for each valence electron.
• Connect with lines to show shared electron pairs.
• Check that the overall structure satisfies the octet rule (where applicable).

Identifying the correct Lewis structure is crucial for predicting molecular shapes and understanding chemical reactions.

Molecular Geometry

Molecular geometry describes the three-dimensional arrangement of atoms in a molecule. It considers not just the bonds between atoms, but also the space taken up by unbonded electron pairs.
For \( \text{BrO}_3 \), the central bromine atom is surrounded by the three oxygen atoms, leading to a trigonal planar geometry. This shape arises because the three oxygens are spaced evenly around the bromine.
For \( \text{Br}_2 \text{O} \), with oxygen forming a bridge, the molecule adopts a bent shape. The lone pairs on the oxygen push away the bromine atoms, creating this V-like shape.

• Trigonal planar: 120-degree angles, all atoms in a flat plane.
• Bent: less than 120 degrees, due to lone pair repulsion.

Understanding these shapes is key in predicting molecular properties and reactions.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It's based on the principles of conservation of mass. In our exercise, stoichiometry helps determine the formula for the mystery oxide A.
By analyzing the amount of iodine and bromine involved in the reactions, the stoichiometric calculations lead to the logical conclusion of the formula \( \text{BrO}_3 \). This is because it balances the number of atoms on both sides of the equation.

• Calculate moles using volume and molarity.
• Analyze mole ratio in reactions to deduce chemical formulas.
• Satisfy conservation of mass by ensuring reactants equal products in moles.

Stoichiometric calculations provide a quantitative basis for the analyses and predictions we make in chemistry.

Chemical Analysis Techniques

Chemical analysis techniques are essential tools for identifying and quantifying components in a sample. In this scenario, techniques like titration and precipitation reactions reveal important information about the unknown compound.
The titration of iodine with sodium thiosulfate calculates how much iodine is present, thereby indirectly helping determine the amount and nature of compound A. Through this process, chemical equivalence is established.
Additionally, the precipitation of bromine with silver nitrate gives further insight into the quantity of bromine present.

• Titration measures concentration via known volumes of reagent.
• Precipitation reactions can be used to isolate or measure specific ions.

These techniques are powerful for solving real-world chemistry problems, from determining unknown compounds to quantifying components accurately.