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 the number of oxygen atoms in one formula unit of magnesium phosphate

Magnesium phosphate, \(\mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2}\), contains two phosphate ions. Each \(\mathrm{PO}_{4}^{3-}\) ion has four oxygen atoms, so there are a total of \(2 \times 4 = 8\) oxygen atoms in one formula unit of \(\mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2}\).

Step 2: Calculate moles of magnesium phosphate for 0.25 moles of oxygen atoms

Since each mole of \(\mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2}\) contains 8 moles of oxygen atoms, we need to find the moles of \(\mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2}\) that contain 0.25 mole of oxygen atoms. We use the ratio \(\frac{1 \text{ mole of } \mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2}}{8 \text{ moles of oxygen}}\). Then: \[ \text{Moles of } \mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2} = \frac{0.25 \text{ moles of oxygen}}{8} = 0.03125 \text{ moles.} \]

Step 3: Match to the closest option

The calculated moles of \(\mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2}\) is \(0.03125\), which matches option \((b)\) \(3.125 \times 10^{-2}\).

Key Concepts

Understanding Moles in Chemistry

The concept of "moles" is fundamental in chemistry and helps standardize how we count particles like atoms and molecules, which are often incredibly small. A mole is a unit of measurement used to express amounts of a chemical substance. It is exactly equal to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles per mole. This means that one mole of any substance contains \(6.022 \times 10^{23}\) representative particles, whether they are atoms, molecules, or ions.
In the context of magnesium phosphate, we often need to transition from counting individual atoms to larger quantities that are countable, making moles very useful. For example, when we talk about 0.25 moles of oxygen atoms, we are essentially referring to 1/4 of Avogadro's number of oxygen atoms. This conversion can then be used to determine the amount of magnesium phosphate as seen in the exercise. By understanding that moles provide a bridge between the molecular level and amounts we can physically measure, it becomes much easier to work through complex chemical calculations.

Chemical Formulas in Determining Composition

Chemical formulas are shorthand representations of chemical compounds using element symbols and numbers that indicate the proportions of each element present. For example, the chemical formula for magnesium phosphate is \( \text{Mg}_3(\text{PO}_4)_2 \). This tells us that in every formula unit of magnesium phosphate, there are:

• Three magnesium (Mg) atoms
• Two phosphate (\(\text{PO}_4^{3-}\)) ions
• Each phosphate ion contains four oxygen (O) atoms

Knowing the chemical formula allows you to work out the compound's composition and count the exact number of each type of atom in a given formula unit. As seen in the exercise, understanding the chemical formula was crucial to finding how many moles of oxygen are present, which then allowed the calculation of the moles of magnesium phosphate.

Role of Phosphate Ions in Chemistry

Phosphate ions, represented as \(\text{PO}_4^{3-}\), are polyatomic ions consisting of one phosphorus atom covalently bonded to four oxygen atoms, and the entire group carries a \(-3\) charge. This ion is a building block in many compounds and frequently encountered in biochemical and industrial processes.
In magnesium phosphate, the role of phosphate ions is crucial as they form the core segments of the compound. Each phosphate ion has three negative charges, which are balanced by positive charges from magnesium ions to form a neutral compound. Recognizing the number and arrangement of phosphate ions within a compound's chemical formula allows chemists to deduce structural and compositional details, like determining the number of oxygen atoms in magnesium phosphate.
Thus, phosphate ions are integral to both the structure and reactions of phosphate-containing compounds. Understanding their composition helps one grasp how different chemicals interact and react with one another.