Write the formula of a compound formed by combining (a) \(\mathrm{Al}\) and \(S\); (b) Na and \(\mathrm{O}\); (c) \(\mathrm{Mg}\) and \(S\); (d) \(\mathrm{Ba}\) and \(\mathrm{I}\).

Understanding valency is crucial for anyone delving into the field of chemistry. Valency, sometimes referred to as 'valence', is the measure of an element's ability to bond with other elements. It represents the number of electrons an atom can lose, gain, or share to achieve a full outer shell – that is, to become stable. For example, the valency of hydrogen is 1, because it can form a bond by sharing or losing one electron. Similarly, oxygen has a valency of 2, indicating it can form two bonds.

Valency is determined by the number of valence electrons present in an atom's outer shell. Group 1 elements in the periodic table, like sodium (Na), have a valency of 1. Group 2 elements like magnesium (Mg) have a valency of 2. This pattern continues across the table, though exceptions exist, particularly among transition metals and non-metals. Knowing the valency of elements helps predict how they combine to form compounds, and as a rule of thumb, the total number of electrons lost is equal to the total number gained when atoms combine to form compounds.

Once you grasp the concept of valency, writing chemical formulas becomes a more intuitive process. Chemical formulas are shorthand representations of compounds, indicating which elements and how many of each are present. When writing chemical formulas, the first step is to determine the valency of each element, similar to Step 1 of our example problem.

Next, use the valencies to figure out the lowest ratio of atoms that balance out to a neutral compound. Chemical formulas are not just a random assortment of symbols and numbers; they follow precise rules. In our example, aluminum (Al) with a valency of 3 and sulfur (S) with a valency of 2 combine to form aluminum sulfide with the formula \(\mathrm{Al}_2S_3\), reflecting a balanced exchange of electrons.

It's helpful to remember that the 'cross-over method' can be applied as a quick way to balance charges between atoms by swapping their valencies to develop subscripts in the chemical formula. For instance, Na (with a valency of 1) and O (with a valency of 2) cross over to give us \(\mathrm{Na}_2O\), a neutral compound.

After mastering valency and the writing of chemical formulas, the next step in chemical problem solving is balancing chemical equations. A chemical equation represents a chemical reaction with reactants on the left-hand side and products on the right. To balance an equation, ensure the same number of each type of atom exists on both sides of the reaction.

Start by writing down the unbalanced equation, then adjust the coefficients (the numbers placed before compounds and elements in the equation) to balance the atoms. Never alter subscripts within a chemical formula, as this changes the identity of the substance itself. For example, in the combustion of methane (\(\mathrm{CH}_4 + 2\mathrm{O}_2 \rightarrow \mathrm{CO}_2 + 2\mathrm{H}_2\mathrm{O}\)), we carefully adjust coefficients to conserve carbon, hydrogen, and oxygen atoms across the equation.

Just like balancing a mathematical equation, what you do to one side, you must do to the other. Balancing chemical equations requires practice and a good understanding of the preceding concepts of valency and chemical formulas, but with time it becomes second nature.