Mole Concept Percentage Composition Question JEE Main 2026

Quick Summary

Question Type: Usual analysis and percentage composition calculation
Chapter: Mole Concept – Percentage Composition
Difficulty: ⭐⭐⭐ Medium
Time to Solve: 4-5 minutes
Key Formula: Percentage of element = (mass of element obtained from analysis / mass of sample) × 100
Correct Answer: (D) 50
Why: 1.79 g of magnesium pyrophosphate is Mg₂P₂O₇. Its molar mass is 222 g mol⁻¹, and phosphorus contributes 62 g per mole. So phosphorus mass = 1.79 × (62/222) ≈ 0.50 g. In a 1.00 g sample, percentage of phosphorus = 50%.

The Question

JEE Main 2026 (Online) Evening Shift – Mole Concept

By usual analysis, 1.00 g of compound (X) gave 1.79 g of magnesium pyrophosphate. The percentage of phosphorus in compound (X) is: (nearest integer)

Given: molar mass in g mol⁻¹: O = 16, Mg = 24, P = 31

Choose the correct answer from the options given below:
(A) 40
(B) 30
(C) 20
(D) 50

Quick Answer

Correct Option: (D) 50

Reasoning: Magnesium pyrophosphate has the formula Mg₂P₂O₇.

Its molar mass is:

• 2 × 24 + 2 × 31 + 7 × 16 = 222 g mol⁻¹

Mass of phosphorus in 222 g of Mg₂P₂O₇ is:

• 2 × 31 = 62 g

So phosphorus present in 1.79 g of Mg₂P₂O₇ is:

• 1.79 × 62/222 ≈ 0.50 g

Since the original compound sample is 1.00 g, percentage of phosphorus is:

• (0.50/1.00) × 100 = 50%

Therefore, the correct answer is (D) 50.

Why Other Options Are Wrong

• Option A (40): Incorrect because the phosphorus mass calculated from Mg₂P₂O₇ comes close to 0.50 g, not 0.40 g.
• Option B (30): Incorrect because this underestimates the phosphorus content significantly.
• Option C (20): Incorrect because it ignores the actual phosphorus mass contribution in magnesium pyrophosphate.
• Option D (50): Correct because the phosphorus content is approximately 49.95%, nearest integer 50.

Video Solution

If you want the full explanation in a clear step-by-step teaching format, watch the video solution below:

Watch Full Video Solution on YouTube

Understanding the Concept

How Usual Analysis Questions Work

In usual analysis questions, the element in the unknown compound is converted into a known stable compound. Then we use the mass of that known compound to calculate how much of the target element was originally present.

Here, phosphorus is finally obtained in the form of:

• magnesium pyrophosphate = Mg₂P₂O₇

So the main task is:

• find molar mass of Mg₂P₂O₇
• find how much phosphorus it contains
• use that fraction to calculate percentage in the original sample

The Key Principle

1. Find the formula and molar mass of the final compound
2. Find mass of the required element in 1 mole of that compound
3. Use mass ratio to calculate the required percentage

Detailed Step-by-Step Solution

Step 1: Write the Formula of Magnesium Pyrophosphate

• Magnesium pyrophosphate = Mg₂P₂O₇

Step 2: Calculate Its Molar Mass

• 2 × Mg = 2 × 24 = 48
• 2 × P = 2 × 31 = 62
• 7 × O = 7 × 16 = 112

So molar mass is:

• 48 + 62 + 112 = 222 g mol⁻¹

Step 3: Find the Mass of Phosphorus in 1.79 g of Mg₂P₂O₇

Download Handwritten Solution

In 222 g of Mg₂P₂O₇, mass of phosphorus = 62 g.

So in 1.79 g:

• Mass of P = 1.79 × 62/222
• Mass of P ≈ 0.4995 g

Step 4: Calculate Percentage of Phosphorus in Compound X

• Original sample mass = 1.00 g
• Mass of phosphorus in sample ≈ 0.4995 g

Therefore:

• Percentage of P = (0.4995/1.00) × 100
• Percentage of P ≈ 49.95%

Nearest integer:

• 50%

Step 5: Write Final Answer

So the correct option is (D).

Final Answer

Option (D): 50 ✓

The percentage of phosphorus in compound (X) is 50%.

Essential Formulas for This Topic

Primary Rules

1. Percentage Formula:
   • Percentage of element = (mass of element / mass of sample) × 100
2. Mass Ratio Rule:
   • Mass of element in compound = given mass × (mass of element in 1 mole / molar mass of compound)
3. Usual Analysis Logic:
   • Convert the unknown compound data into a known compound formula and then use stoichiometric mass relation

Important Notes

• Magnesium pyrophosphate formula must be written correctly as Mg₂P₂O₇
• Phosphorus contributes 62 g in 222 g of Mg₂P₂O₇
• The final answer must be rounded to the nearest integer

Common Mistakes to Avoid

❌ Mistake 1: Writing the Wrong Formula of Magnesium Pyrophosphate

Wrong Thinking: “Magnesium pyrophosphate may be MgPO₄ or Mg₃(PO₄)₂.”

Correct Approach: Use the correct formula given by usual analysis result: Mg₂P₂O₇.

❌ Mistake 2: Using Wrong Molar Mass

Wrong Thinking: “Only phosphorus mass matters, so total molar mass is not needed.”

Correct Approach: First calculate full molar mass of Mg₂P₂O₇, then use phosphorus mass fraction.

❌ Mistake 3: Forgetting There Are Two Phosphorus Atoms

Wrong Thinking: “Mass of phosphorus is 31 g in one mole of Mg₂P₂O₇.”

Correct Approach: There are two phosphorus atoms, so total phosphorus mass is 62 g.

❌ Mistake 4: Not Rounding to the Nearest Integer

Wrong Thinking: “49.95 is not exactly 50, so answer cannot be 50.”

Correct Approach: The question asks for the nearest integer, so 49.95 becomes 50.

Key Concept Summary

1. Identify the final compound correctly: Mg₂P₂O₇
2. Find its molar mass: 222 g mol⁻¹
3. Find phosphorus mass in it: 62 g per mole
4. Use mass fraction: 1.79 × 62/222 gives phosphorus mass
5. Final percentage is 50%: nearest integer value

The Golden Rule for Usual Analysis Questions

“Find the formula of the final compound first, then use the element’s mass fraction to calculate percentage.”

Frequently Asked Questions

Q1: What is the formula of magnesium pyrophosphate?

A: Mg₂P₂O₇.

Q2: Why is phosphorus mass taken as 62 g?

A: Because there are two phosphorus atoms in Mg₂P₂O₇, so total mass = 2 × 31 = 62 g.

Q3: What is the molar mass of Mg₂P₂O₇?

A: 222 g mol⁻¹.

Q4: How is the percentage of phosphorus calculated?

A: First find mass of phosphorus in 1.79 g of Mg₂P₂O₇, then divide by original sample mass and multiply by 100.

Q5: What is the correct answer?

A: Option (D), 50.

Prerequisites to Solve This Question

1. Mole concept: Basic molar mass calculation
2. Percentage composition: Element mass percentage formula
3. Formula interpretation: Reading atomic count in compounds correctly
4. Ratio method: Using mass fraction from a known compound

After Solving This, You Can:

✅ Solve usual analysis based percentage questions
✅ Calculate element percentage from precipitate mass
✅ Use molar mass and mass fraction confidently
✅ Avoid common percentage composition mistakes

Study Tips for This Topic

For JEE Main:

1. Memorize the percentage formula: It saves time in direct calculation questions
2. Always count atoms carefully: Missing one phosphorus atom can change the whole answer
3. Write the molar mass step clearly: It reduces silly mistakes
4. Read the final instruction: Questions may ask for nearest integer

Common JEE Variants:

• Percentage of an element from usual analysis
• Mass of precipitate based composition questions
• Formula-based mass fraction problems
• Nearest integer Mole Concept questions

Difficulty Rating & Exam Frequency

Difficulty Level: ⭐⭐⭐ (3/5) – Medium
JEE Main Frequency: Medium – Percentage composition and usual analysis appear regularly in Mole Concept
JEE Advanced Frequency: Low to Medium – Usually combined with analytical chemistry ideas
Topic Importance: High – Builds strong command over composition and mass relation problems

Written by Nishant Kumar Gupta
Chemistry Educator with 12+ Years of Experience Teaching JEE Aspirants
Founder – PadhoLikhoJEE

Last Updated: April 2026
Question Source: JEE Main 2026 PYQ
Topic: Mole Concept – Percentage Composition by Usual Analysis