If the ratio of coordination number \(\mathrm{P}\) to that of \(\mathrm{Q}\) be \(\mathrm{Y}: \mathrm{Z}\), then the formula of the solid is: (a) \(\mathrm{P}_{\mathrm{z}} \mathrm{Q}_{\mathrm{Y}}\) (b) \(\mathrm{P} \mathrm{O}_{\mathrm{YZ}}\) (c) \(\mathrm{P}_{1 / \mathrm{Y}} \mathrm{Q}_{1 / Z}\) (d) \(\mathrm{P}_{\mathrm{Y}} \mathrm{Q}_{\mathrm{Z}}\)

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the elements and compounds involved in chemical reactions. It is based on the law of conservation of mass, which states that the total mass of reactants equals the total mass of products in a chemical reaction. To maintain these relationships, chemists use stoichiometric calculations to determine the proportions of reactants and products.

When applying stoichiometry to the problem of determining the formula of a solid based on coordination numbers, it's essential to understand that the ratio of the coordination numbers directly relates to the mole ratio of the ions in the compound. For instance, if element P has a coordination number of Y, and element Q has a coordination number of Z, then P and Q will combine in a Y:Z mole ratio to form a compound. The resulting chemical formula will reflect these ratios, ensuring that the proportions of each element are correct to preserve the stoichiometric balance.

A chemical formula represents the proportions of atoms of each element in a compound. It gives us information about the types of atoms present and their quantities. In ionic compounds, it is essential that the formula represents an electrically neutral entity. To achieve this, the formula is determined based on the stoichiometry of the compound which arises from the combination of ions in ratios that neutralize their respective charges.

For a solid with elements P and Q, the ratio of coordination numbers Y:Z denotes how many of each ion must be present to sustain the compound's structure. If P is surrounded by Z ions of Q and vice versa, the chemical formula would thus logically be represented as \( P_Y Q_Z \) because it displays the necessary proportions of each ion, accurately reflecting the structure and stoichiometry of the compound. To provide students with a more comprehensive understanding, it's important to explain that the subscripts in the chemical formula are derived from the coordination numbers, which are indicative of the number of opposite ions surrounding each ion in the solid's lattice structure.

The principle of electrical neutrality states that the total charge within a compound must be zero. In ionic compounds, this is achieved by combining positively charged ions (cations) and negatively charged ions (anions) in such a ratio that the charges balance each other out. This concept is crucial when determining the correct chemical formula for a compound.

Applying the principle of electrical neutrality to the exercise, we must remember that the chemical formula of the solid must reflect a neutral charge. Therefore, if we know the charge of the ions of P and Q, we multiply them by the respective coordination numbers (Y for P and Z for Q) to ensure the total charge is balanced. The correct chemical formula for an ionic compound arising from ions P and Q with a coordination number ratio Y:Z is \( P_Y Q_Z \) when both ions contribute to a neutral overall charge. When students are presented with coordination numbers and the task to determine the formula of a compound, they should always confirm that the result adheres to the rule of electrical neutrality.