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? (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

(b) \(3.125 \times 10^{-2}\) moles.

Step 1: Determine Oxygen Atoms in One Molecule

The molecular formula for magnesium phosphate is \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\). Each phosphate group \(\mathrm{PO}_4\) contains 4 oxygen atoms, and with two phosphate groups in magnesium phosphate, there are \(2 \times 4 = 8\) oxygen atoms in each molecule of \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\).

Step 2: Calculate Moles of Mg3(PO4)2 Needed

Given that there are 8 oxygen atoms in one molecule, there will be 8 moles of oxygen atoms per mole of magnesium phosphate. To find the moles of magnesium phosphate that contain 0.25 moles of oxygen atoms, divide 0.25 moles of oxygen by the 8 moles of oxygen per mole of compound: \[ \text{Moles of } \mathrm{Mg}_3(\mathrm{PO}_4)_2 = \frac{0.25 \text{ moles of O}}{8 \text{ moles of O/mole of compound}} = 0.03125 \text{ moles of } \mathrm{Mg}_3(\mathrm{PO}_4)_2 \].

Step 3: Compare Answer to Options

The calculated number of moles of magnesium phosphate is 0.03125. To express this in scientific notation, it becomes \(3.125 \times 10^{-2}\). This matches option (b).

Key Concepts

Understanding Molecular Formulas

When studying chemistry, you often encounter the term "molecular formula." This formula provides crucial information about the composition of a molecule by indicating the number and type of atoms present. For example, the molecular formula of magnesium phosphate is \(\text{Mg}_3(\text{PO}_4)_2\). This tells us that each molecule of magnesium phosphate contains 3 magnesium (Mg) atoms and 2 phosphate \((\text{PO}_4)\) groups.

Examining the formula further, each \(\text{PO}_4\) group is made up of one phosphorus (P) atom and 4 oxygen (O) atoms. In magnesium phosphate, the presence of 2 \(\text{PO}_4\) groups means the molecule is richer in certain elements. Specifically, you end up with 2 phosphorus atoms and \(2 \times 4 = 8\) oxygen atoms in total. Understanding the breakdown of a molecular formula allows you to calculate how these atoms contribute to the entire molecule's composition.

Knowing molecular formulas is critical for calculating various properties, like the number of moles of a specific atom within a compound. It's a foundational skill for chemistry students!

Calculating Oxygen Atoms

To calculate the number of oxygen atoms in a given amount of a compound, it's important to understand what each part of the molecular formula means. In \(\text{Mg}_3(\text{PO}_4)_2\), each \(\text{PO}_4\) contains 4 oxygen atoms. So, if you have 2 \(\text{PO}_4\) groups in magnesium phosphate, you multiply to find the total: \(2 \times 4 = 8\) oxygen atoms.

This multiplication gives you the number of oxygen atoms in a single molecule. Knowing this, if you have a whole mole (which is \(6.022 \times 10^{23}\) entities) of magnesium phosphate, you would also have 8 moles of oxygen atoms. Understanding this concept helps when you need to find out how many moles of a particular element, like oxygen, are present in a known quantity of a compound.

For instance, the problem states there's 0.25 moles of oxygen atoms. To find how many moles of \(\text{Mg}_3(\text{PO}_4)_2\) correspond to this, you would use division: 0.25 moles of oxygen divided by 8 moles of oxygen per mole of compound provides 0.03125 moles of \(\text{Mg}_3(\text{PO}_4)_2\). This calculation is essential for linking specific atomic components back up to the larger compound.

The Role of Scientific Notation

Scientific notation is a key tool in chemistry, especially when dealing with very large or very small numbers. It allows us to write these numbers in a compact form that is easier to read and understand. For example, 0.03125 can be expressed in scientific notation as \(3.125 \times 10^{-2}\).

This method is particularly useful when comparing numbers, as scientific notation makes it immediately clear which values are larger or smaller. When your calculations in chemistry return decimals that have many places, scientific notation helps simplify results and maintain accuracy.

In the context of the original problem, using scientific notation allowed for easier comparison with the provided answer choices. Converting 0.03125 to \(3.125 \times 10^{-2}\) quickly showed it matched one of the options, simplifying the decision-making process. Thus, scientific notation is a valuable skill for both solving problems and presenting your answers clearly.