Question

Predict the formulae of the binary compounds formed by combination of the following pairs of elements: (i) Magnesium and nitrogen (ii) Silicon and oxygen (a) \(\mathrm{MgN}_{2}, \mathrm{SiO}_{2}\) (b) \(\mathrm{Mg}_{3} \mathrm{~N}_{2}, \mathrm{SiO}_{2}\) (c) \(\mathrm{Mg}_{2} \mathrm{~N}_{3}, \mathrm{Si}_{2} \mathrm{O}_{3}\) (d) \(\mathrm{MgN}, \mathrm{SiO}_{2}\)

Short answer

The correct formulae for the binary compounds are (b) \textrm{Mg}_{3}N_{2} and SiO_{2}.

Step-by-step solution

Determine the valencies of the elements

Identify the valencies (or oxidation states) of magnesium (Mg), nitrogen (N), silicon (Si), and oxygen (O). Magnesium typically has a valency of +2 (Mg^{2+}), nitrogen typically has a valency of -3 (N^{3-}), silicon typically has a valency of +4 (Si^{4+}), and oxygen typically has a valency of -2 (O^{2-}).

Write the chemical formulas using the crisscross method

Use the crisscross method to balance the charges by crossing over the valencies of the combining elements to become the subscript of the other element. For Mg (valency +2) combining with N (valency -3), their formula becomes Mg_{3}N_{2}. Similarly for Si (valency +4) and O (valency -2), the formula is SiO_{2}.

Determine the correct formulae

The correct formula for magnesium nitride is Mg_{3}N_{2}, as 3 magnesium atoms (each with a 2+ charge) are required to balance the charge of 2 nitrogen atoms (each with a 3- charge). The correct formula for silicon dioxide is SiO_{2}, as one silicon atom (with a 4+ charge) balances the charges of two oxygen atoms (each with a 2- charge).

Key concepts

Valency

Understanding the concept of valency is crucial when dealing with chemical compounds. Valency refers to the combining power of an element, particularly how many electrons an atom can lose, gain, or share to achieve a full outer shell, resembling a noble gas configuration. For elements such as metals, the valency is typically positive, representing the number of electrons they can donate. Non-metals often have negative valencies, indicating the number of electrons they can accept to form a stable electronic arrangement. It's this principle that governs the combinations of elements to form compounds, as atoms strive to reach a state of electrical neutrality.

For example, in the exercise provided, magnesium (Mg), a metal, has a valency of +2, meaning it can lose two electrons to achieve stability. Nitrogen (N), a non-metal, has a valency of -3, indicating it can gain three electrons. By understanding these valencies, we pave the way for predicting compound formulas accurately.

Crisscross Method

The crisscross method is a straightforward technique for determining the formula of a compound based on the valencies of its constituent elements. To apply it, you simply 'crisscross' the valencies of the two combining elements and use them as subscripts for one another.

Using our exercise as an instance, let's look at magnesium and nitrogen. The valency of magnesium is +2, while that of nitrogen is -3. By crisscrossing the valencies, magnesium requires three atoms (from nitrogen's valency) to match up with two atoms of nitrogen (from magnesium's valency). You end up with a subscript of 3 for magnesium and 2 for nitrogen, thus resulting in the chemical formula Mg₃N₂. This balances out the charges, leading to a neutral compound. The process improves comprehension of how compounds are formed and reinforces the underlying principle of charge neutrality in chemical formations.

Binary Compounds

Binary compounds are composed of two different elements. These can range from simple ionic compounds, where one element donates electrons and the other accepts them, to covalent compounds, where the atoms share electrons. Recognizing that binary compounds consist of only two elements simplifies the process of predicting their formulas. In many cases, binary compounds are also ionic compounds, meaning they consist of a metal and a non-metal.

In the provided exercise, magnesium nitride and silicon dioxide are both binary compounds. Magnesium nitride is made of magnesium (Mg) and nitrogen (N), while silicon dioxide consists of silicon (Si) and oxygen (O). For chemical formula prediction, knowing the composition of binary compounds is an essential first step before applying other principles like valency and the crisscross method to determine the precise formula.

Oxidation States

Oxidation states, also referred to as oxidation numbers, represent the degree of oxidation of an atom within a compound. They are very similar to valencies, providing insight into the loss or gain of electrons during chemical reactions. An oxidation state can be thought of as a more formal version of valency. Positive oxidation states indicate a loss of electrons (typically metals), whereas negative oxidation states demonstrate a gain of electrons (non-metals).

It is critical to note that the oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were completely ionic. This concept is key to balancing chemical equations and determining compound formulas. For instance, as seen in the exercise, magnesium has an oxidation state of +2, and nitrogen has an oxidation state of -3. Recognizing the oxidation states aids in accurately predicting how these atoms will combine to form a chemical compound, leading to the discovery of their precise formulas, such as Mg₃N₂ for magnesium nitride.