Problem 85 - Chemistry The Central Science

Question

Consider the collection of nonmetallic elements \(\mathrm{O}, \mathrm{P}\) , Te, \(\mathrm{I},\) and \(\mathrm{B} .\) (a) Which two would form the most polar single bond? (b) Which two would form the longest single bond? (c) Which two would be likely to form a compound of formula \(\mathrm{XY}_{2} ?(\mathbf{d})\) Which combinations of elements would likely yield a compound of empirical formula \(\mathrm{X}_{2} \mathrm{Y}_{3}\) ?

Step-by-Step Solution

Answer

(a) The most polar single bond will be formed between O and B, as they have the highest electronegativity difference. (b) The longest single bond will be formed between I and O, as they have the largest atomic radii. (c) B and O can form a compound with the formula \(BO_2\), as O has a valency of 2, and B has a valency of 3. (d) The possible combinations of elements yielding a compound of empirical formula X2Y3 are B2O3, B2Te3, and B2I3.

Step 1: Identify the most polar single bond

A polar bond occurs when there is a significant difference in electronegativity between the two atoms in the bond. To find the most polar bond, we need to find the combination of elements with the highest electronegativity difference. (a) Among the given elements, O has the highest electronegativity (\(3.44\)) and B has the lowest electronegativity (\(2.04\)). Therefore, the most polar single bond will be formed between O and B.

Step 2: Identify the longest single bond

The bond length typically increases as the atomic size increases. We need to find the combination of elements with the largest atomic radii. (b) Among the given elements, I has the largest atomic radius (\(140\,pm\)) and O has the smallest atomic radius (\(60\,pm\)). Therefore, the longest single bond will be formed between I and O.

Step 3: Identify which elements will form a compound with the formula XY2

A compound with the formula XY2 will form if one element can accept two electrons from the other element. (c) Among the given elements, O has a valency of 2, which can accept two electrons from an element like B, which has a valency of 3. Therefore, B and O can form a compound with the formula \(BO_2\).

Step 4: Identify the combinations of elements yielding a compound of empirical formula X2Y3

An empirical formula of X2Y3 indicates that two atoms of element X bond with three atoms of element Y. (d) In the given elements, B has a valency of 3 and can form compounds with elements having a valency of 2. Elements with valency 2 in the given list are O, Te, and I. Therefore, there are possible combinations of elements that can yield a compound of empirical formula X2Y3: 1. B2O3 2. B2Te3 3. B2I3

Key Concepts

Electronegativity

Electronegativity is a chemical property that describes an atom's ability to attract and bind with electrons. This property plays a crucial role in determining how atoms will interact and bond with each other.

• The higher the electronegativity, the more an atom attracts electrons.
• Electronegativity values range from 0 to 4, with fluorine having the highest value.

This concept is particularly important in chemical bonding because it helps predict bond types:

• If two atoms have a large difference in electronegativity, the bond is likely to be polar, meaning the electrons are not shared equally.
• A small difference in values often results in a nonpolar bond, where electrons are shared more equally.

In our exercise, oxygen and boron form the most polar bond because they have the greatest difference in electronegativity among the listed elements. This difference makes oxygen more "electron-greedy," pulling shared electrons toward itself.

Bond Length

Bond length is the distance between the nuclei of two bonded atoms. It is influenced by several factors, including the type of atoms involved and the nature of bonds between them. Bond lengths are usually measured in picometers (\(pm\)) or angstroms (\(Å\)).

• Generally, the larger the atoms, the longer the bond length, as the nuclei are further apart.
• Bond length decreases with multiple bonds (double, triple), resulting in shorter distances compared to a single bond.

Analyzing our set of elements, iodine (\(I\)) and oxygen (\(O\)) could make one of the longest single bonds due to iodine's large atomic radius, compared to the smaller size of other atoms in the set. The bond length affects the bond strength; longer bonds tend to be weaker and more reactive.

Chemical Formulas

Understanding chemical formulas is essential in representing compounds. Formulas convey the types and numbers of atoms present within a molecule. They help in pinpointing the stoichiometry and structure of a compound, critical for reactions and understanding the composition.For instance, in the given problem, the potential compounds like \(BO_2\) or \(B_2O_3\) illustrate different combinations and ratios within the compounds.

• \(XY_2\) formulas indicate one atom of \(X\) bonded to two atoms of \(Y\). This might suggest a molecule like water, \(H_2O\).
• In \(X_2Y_3\) compounds, it shows a 2:3 atomic ratio, critical in materials like aluminum oxide (\(Al_2O_3\)), representing how different atoms can be arranged to achieve stable compounds.

Chemical formulas are keys to unlocking the understanding of compounds and their potential properties.

Valency

Valency is the combining power of an element, particularly seen in forming bonds. It refers to how many electrons an atom can gain, lose, or share to achieve a full outer shell, usually corresponding to achieving a stable electronic configuration like that of noble gases.

• Group elements generally have a predictable valency, like halogens with a valency of 1.
• Oxygen, with a valency of 2, needs two electrons to fill its outer shell.

In our case study, valency helps identify which elements can form specific compounds:

• Boron (\(B\)) often exhibits a valency of 3. This makes it a candidate for forming multiple bonds with elements like oxygen, which seeks additional electrons.
• Understanding valency allows the prediction of chemical formula possibilities, as observed with the examples of \(B_2O_3\) or \(BO_2\), where the stoichiometric balance reflects this intrinsic chemical characteristic.

This knowledge of valency is foundational in exploring how different elements can combine to form diverse and complex chemical structures.