Problem 36 - A Complete Resource Book in Chemistry for JEE Main

Question

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) \(\mathrm{P}_{1 / \mathrm{Y}} \mathrm{Q}_{1 / 2}\) (d) \(\mathrm{P}_{\mathrm{Y}} \mathrm{Q}_{\mathrm{Z}}\)

Step-by-Step Solution

Answer

The formula of the solid is (d) \( \mathrm{P}_{\mathrm{Y}} \mathrm{Q}_{\mathrm{Z}} \).

Step 1: Understanding the Problem

The problem presents a ratio of coordination numbers between elements P and Q given as \( Y:Z \). We need to determine the correct chemical formula for the solid using this ratio.

Step 2: Translate the Ratio to Formula

In chemistry, if the coordination number of P to Q is given as \( Y:Z \), it implies that for every Y parts of P, there are Z parts of Q. This directly informs the stoichiometric relationship in the formula, giving us the form \( \mathrm{P}_Y \mathrm{Q}_Z \).

Step 3: Verify the Options

Review the options to see which matches the inferred formula \( \mathrm{P}_Y \mathrm{Q}_Z \). We can immediately see that option (d) \( \mathrm{P}_{\mathrm{Y}} \mathrm{Q}_{\mathrm{Z}} \) corresponds to our understanding.

Key Concepts

Coordination Number

In chemistry, the coordination number is a fundamental concept that refers to the number of atoms, ions, or molecules that a central atom or ion holds as its nearest neighbors in a chemical compound. It is crucial in determining the structure and properties of complex materials.
For instance, common coordination numbers for transition metals range from 2 to 12, with 6 being particularly common in octahedral structures. Understanding coordination numbers helps in visualizing the spatial arrangement of atoms in a compound, which is vital in predicting reactivity and stability.

• The coordination number gives insights into the geometry of a molecule or crystal.
• It also affects the material’s physical and chemical properties.
• For ions, it is influenced by factors such as ionic size and charge.

Thus, recognizing the coordination number in different compounds helps chemists in deriving properties and reactivity patterns effectively.

Stoichiometry

Stoichiometry is the science of measuring the quantitative ratios in which elements react and combine to form compounds. This involves calculations based on the balanced chemical equations that describe these combinations. It is essential for predicting the amounts of reactants needed or products formed in a chemical reaction.
In our exercise, the stoichiometric relationship is expressed by the ratio of coordination numbers, which translates into the empirical formula through the proportion of elements involved.

• Stoichiometry ensures that equations are balanced, reflecting the conservation of mass.
• It helps in calculating the yield of a product from given reactant quantities.
• It’s used in determining reactant/product ratios in industrial applications.

Through stoichiometry, we can efficiently deduce the correct chemical formula by analyzing given ratios, as applied in finding \( \mathrm{P}_Y \mathrm{Q}_Z \).

Chemical Ratios

Chemical ratios represent the fixed proportions in which elements combine to form a compound. These ratios are foundational in determining formulas of compounds, as seen in coordination complexes and ionic compounds. They ensure the correct combination necessary for stability and reaction balance.
In the given problem, the ratio of coordination numbers is depicted as \( Y:Z \), signifying how the elements P and Q combine. This straightforward translation into chemical formula encompasses understanding these intrinsic ratios:

• Ratios indicate the quantity relationship between reactants in reaction equations.
• Essential for confirming the composition of unknown compounds.
• Aid in discerning empirical formulas from experimental data.

Ultimately, understanding chemical ratios is key to deriving formulas like \( \mathrm{P}_Y \mathrm{Q}_Z \), making them indispensable in chemical compound determination.