Question

Consider the collection of nonmetallic elements \(\mathrm{O}, \mathrm{P}, \mathrm{Te}\), I and 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 \(\mathrm{XY}_{2}\) ? (d) Which combinations of elements would likely yield a compound of empirical formula \(\mathrm{X}_{2} \mathrm{Y}_{3}\) ?

Short answer

The most polar single bond would be formed by O and B with an electronegativity difference of 1.4. The longest single bond would be formed by Te and I, as they are the largest atoms among the given elements. The possible compounds following the XY2 formula are PO2 and ITe2. The possible combinations of elements that would yield a compound of empirical formula X2Y3 are B2O3 and B2P3.

Step-by-step solution

(a) Most polar single bond

A bond is polar if there is a significant difference in electronegativity between the two atoms. To determine the most polar bond, we need to calculate the electronegativity difference between the pairs of elements. We can look up electronegativity values using a periodic table: O: 3.44 P: 2.19 Te: 2.1 I: 2.66 B: 2.04 Now we can calculate the electronegativity differences for all possible pairs of elements: 1. O - P = 1.25 2. O - Te = 1.34 3. O - I = 0.78 4. O - B = 1.4 5. P - Te = 0.09 6. P - I = 0.47 7. P - B = 0.15 8. Te - I = 0.56 9. Te - B = 0.06 10. I - B = 0.62 The largest electronegativity difference will result in the most polar bond. In this case, it's O - B with a difference of 1.4. Therefore, the most polar single bond is formed by O and B.

(b) Longest single bond

The bond length is determined by the atomic size of the elements involved. In general, the larger the atoms, the longer the bond. From the given elements, we analyze their atomic sizes using periodic trends: O: small P: medium Te: large I: large B: small From the periodic table, we can see that Te and I are the largest atoms among the given elements. So, the longest single bond would be formed by Te and I.

(c) Compound with formula XY2

A compound with the formula XY2 implies that element Y should have two valence electrons more than element X, in order to form stable bonds. Let's analyze the valence electrons of the given elements: O: 6 P: 5 Te: 6 I: 7 B: 3 To create the XY2 compound, we require that Y - X = 2. From the above values, we observe that (P, O) and (I, Te) are the pairs fulfilling this condition. So, the possible compounds following the XY2 formula are PO2 and ITe2.

(d) Compound with empirical formula X2Y3

A compound with the empirical formula X2Y3 implies that element X should donate 2 electrons each while element Y should donate 3 electrons each to form a stable bond. Let's analyze the valence electrons of the given elements once again: O: 6 P: 5 Te: 6 I: 7 B: 3 We need X donating 2 electrons and Y donating 3 electrons. From the above valence electron values, B fits the role of element X and both O and P can fit the role of element Y. Therefore, the possible combinations of elements that would yield a compound of empirical formula X2Y3 are B2O3 and B2P3.

Key concepts

Polarity of Bonds

Understanding the polarity of bonds is crucial in chemistry, as it affects a molecule's physical properties, reactivity, and interactions with other molecules. A polar bond arises due to an uneven distribution of electrical charge between the two atoms involved in the bond. This happens when one atom is more electronegative than the other, meaning it has a greater tendency to attract electrons towards itself.

For example, in the exercise, when we consider the bond between oxygen (O) and boron (B), the large electronegativity difference suggests that the bonding electrons are more strongly attracted to the oxygen atom. This results in a partial negative charge on oxygen and a partial positive charge on boron, leading to a polar bond. As a general rule, the greater the electronegativity difference, the more polar the bond.

Electronegativity Difference

The electronegativity difference between two atoms is a predictor of the type of bond they will form. Electronegativity is a measure of an atom's ability to attract and hold onto electrons. When atoms with different electronegativities form a bond, the one with the higher electronegativity will attract the shared electrons more strongly.

In the context of the exercise, by calculating the electronegativity differences between various pairs of elements, you can predict the bond polarity. For instance, the bond between oxygen and boron has the highest electronegativity difference, hence it's the most polar bond among the evaluated pairs. The significance of understanding this concept helps students realize that the bond type is not only about the presence of valence electrons but also about how they are shared or transferred between atoms.

Bond Length

The bond length is an important characteristic of a chemical bond and influences the molecule’s stability and reactivity. It is the distance between the nuclei of two bonded atoms. Generally, the larger the size of the atoms, the longer the bond length, because bigger atoms have more electron shells which result in the outer electrons being farther apart.

Referring back to our exercise, tellurium (Te) and iodine (I) are the two largest atoms given and thus, they form the longest single bond. If students visualize the atoms as spheres, where larger spheres need to be further apart to touch, this might aid in their understanding of why bond length increases with the size of the atoms.

Valence Electrons

The valence electrons are the electrons in the outermost shell of an atom that are available for bonding. They are responsible for the chemical properties of the atom as they are the ones that form chemical bonds with other atoms. In the exercise, the distribution of these electrons is pivotal to predicting the types of compounds that the elements can form.

For example, the exercise demonstrates that the compound formula XY2 requires element Y to have two more valence electrons than element X. This specific requirement is associated with the ability of the elements to achieve stable electronic configurations through bonding. Grasping the behavior of valence electrons simplifies complex concepts like bonding patterns, molecule shapes, and reactivity.

Empirical Formula

The empirical formula represents the simplest whole-number ratio of elements in a compound. It's an essential concept in chemistry as it conveys the composition of a compound without indicating the actual number or arrangement of atoms. During the exercise, analyzing the valence electrons allows us to match them in such a way that we find the simplest ratio conforming to stable bonds, resulting in empirical formulas such as X2Y3.

In our scenario, boron (B), with three valence electrons, can combine with oxygen (O) or phosphorus (P), both with five valence electrons, leading to the formation of compounds with an empirical formula B2O3 or B2P3. Recognizing the empirical formula helps students to predict and understand the composition and stoichiometry of chemical compounds.