Problem 171 - A Complete Resource Book in Chemistry for JEE Main

Question

How many moles of magnesium phosphate, \(\mathrm{Mg}_{3}\) \(\left(\mathrm{PO}_{4}\right)_{2}\) will contain \(0.25\) mole of oxygen atoms? [2006] (a) \(0.02\) (b) \(3.125 \times 10^{-2}\) (c) \(1.25 \times 10^{-2}\) (d) \(2.5 \times 10^{-2}\)

Step-by-Step Solution

Answer

The answer is (b) \(3.125 \times 10^{-2}\).

Step 1: Identify Oxygen Atoms in Compound

Magnesium phosphate, \( \text{Mg}_3(\text{PO}_4)_2 \), contains phosphate groups. Each \( \text{PO}_4 \) unit has 4 oxygen atoms, thus the compound has \( 2 \times 4 = 8 \) oxygen atoms in total.

Step 2: Calculate Moles of Compound for Given Moles of Oxygen

Since each mole of \( \text{Mg}_3(\text{PO}_4)_2 \) contains 8 moles of oxygen atoms, it will take \( \frac{0.25}{8} \) moles of \( \text{Mg}_3(\text{PO}_4)_2 \) to have \( 0.25 \) mole of oxygen atoms.

Step 3: Perform Division to Find Mole

Divide the given moles of oxygen atoms by the number of oxygen atoms per mole of \( \text{Mg}_3(\text{PO}_4)_2 \):\[\text{Moles of } \text{Mg}_3(\text{PO}_4)_2 = \frac{0.25}{8} = 0.03125.\]

Step 4: Match With Given Options

Compare the calculated value of \( 0.03125 \) with the given options to identify the correct answer. The correct option is closest to \( 3.125 \times 10^{-2} \).

Key Concepts

Molecular Composition

Molecular composition refers to the types and quantities of atoms that make up a molecule. In the case of magnesium phosphate, represented chemically as \( \mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2} \), we have a compound made of magnesium, phosphorus, and oxygen atoms. Understanding the composition helps us determine not only the molecular formula but also the structure of the compound.

• Magnesium phosphate contains three magnesium atoms, two phosphate groups, and each phosphate group consists of one phosphorus atom and four oxygen atoms, totaling eight oxygen atoms in two phosphate groups.
• The ability to break down molecules into their constituent atoms is essential for understanding chemical reactions and molecular interactions.

Grasping the concept of molecular composition is crucial because it serves as the foundation for the more advanced topics of stoichiometry and problem-solving in chemistry. Once you know the components of a compound, you can move on to calculate relationships between these molecules.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical equation. This relationship helps chemists determine how much of each substance is necessary, or produced, in a reaction. It is directly related to the concept of moles, a standard unit for measuring chemical substances.

• In the problem of determining moles of magnesium phosphate related to the given moles of oxygen atoms, stoichiometry allows us to use the molecular composition to find these relationships.
• Since magnesium phosphate has 8 oxygen atoms per mole, we use stoichiometry to determine how many moles of the entire compound would provide 0.25 moles of oxygen.
• This involves simple division of the moles of oxygen we have by the number of oxygen atoms in one mole of the compound: \( \frac{0.25}{8} \).

This is a practical application of stoichiometry, showing how we can transition from atom-level understanding to entire molecules and reactants, thereby preparing students for more complex problem-solving tasks.

Chemistry Problem Solving

Solving chemistry problems efficiently often boils down to understanding a few central principles and applying them methodically. For this type of question, problem-solving involves breaking down the task into manageable steps, much like in mathematics or any analytical process.

• The initial step is understanding the components of your compounds, as demonstrated in analyzing magnesium phosphate's contents.
• Once you evaluate the elements present and their quantities, stoichiometry aids in converting between scales, from atoms to entire compounds.
• Finally, execute the necessary calculations, verifying your end result with given choices or additional context if provided.

For instance, the solution here involves recognizing the composition of the compound and how this influences the amount of substance needed. This skill of understanding and logically solving problems is invaluable, not just in chemistry, but in all scientific endeavors.