Q.82 Chemistry ⭐ 360° Option Elimination Active

NEET 2021 Chemistry Question 82 Solution

Topic: States of Matter · Official NTA Booklet Code M1

Question

Choose the correct option for graphical representation of Boyle's law, which shows a graph of pressure vs. volume of a gas at different temperatures:

✓

Verified Against NTA Final Answer Key

Option (4) : Graph (4) (Rectangular hyperbolas with 600 K highest, 200 K lowest)

📚 States of Matter Easy

📋 Given Parameters & Problem Setup

Governing Law Boyle's Law (P vs V at constant T)

Temperatures 200 K, 400 K, 600 K

⚡

The 30-Second Exam Hall Shortcut: ⚡ Higher T = Higher Curve (P ∝ T at constant V)

⏱️ Save ~15 seconds

From ideal gas equation $PV = nRT$ , at any fixed volume $V$ , pressure is directly proportional to temperature: $P \propto T$ . Thus, the highest temperature isotherm ( $600\text{ K}$ ) must lie at the highest pressure, followed by $400\text{ K}$ , and the lowest is $200\text{ K}$ . The curves are rectangular hyperbolas. This corresponds uniquely to Graph (4)! Match Option (4)!

1 Boyle's law states

P \propto \frac{1}{V}

at constant

T

, producing rectangular hyperbolic isotherms.

2 Draw a vertical line of constant volume

V_0

3 At constant volume:

P = \left(\frac{nR}{V_0}\right) T \implies P \propto T

4 As

T

increases (

200\text{ K} \to 400\text{ K} \to 600\text{ K}

), the pressure must increase.

5 The uppermost curve is

600\text{ K}

, middle is

400\text{ K}

, and lowest is

200\text{ K}

6 Match Graph (4).

🛡️

Why You Can 100% Trust This Shortcut: Canonical NCERT States of Matter Fig. 5.1 (P vs V isotherms of Boyle's Law).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Mathematical Formulation of Boyle's Law Isotherms

Boyle's law states that at constant temperature $T$ , the pressure of a fixed mass of gas is inversely proportional to its volume: $P = \frac{k_1}{V} \implies PV = k_1 = nRT$ A plot of $P$ versus $V$ at constant temperature gives a rectangular hyperbola called an isotherm.

Step 2

Temperature Dependence of the Constant k1 = nRT

The constant $k_1$ is directly proportional to the absolute temperature $T$ . A higher temperature corresponds to a larger value of $k_1 = nRT$ . For any given volume $V$ on the horizontal axis:

P = \frac{nRT}{V} \implies P_{600\text{ K}} > P_{400\text{ K}} > P_{200\text{ K}}

Step 3

Identifying the Correct Graph

- Graph (1): Inverted temperature labels ( $200\text{ K}$ is shown at top and $600\text{ K}$ at bottom), which violates thermodynamics. - Graph (2): Shows pressure independent of volume (horizontal line), which is false. - Graph (3): Shows linear increase ( $P \propto V$ ), which is isobaric/Charles law plot type, not $P$ vs $V$ . - Graph (4): Shows three hyperbolic isotherms with $600\text{ K}$ on top, $400\text{ K}$ in the middle, and $200\text{ K}$ at the bottom. This is the exact NCERT textbook plot.

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✗ Incorrect

Verdict & Scientific Reason:

Inverted temperature order (places $200\text{ K}$ above $600\text{ K}$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Assuming lower temperature has higher curve.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Horizontal line implies pressure is independent of volume, completely violating Boyle's law.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing

PV

P

plot with

P

V

plot.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Straight lines through origin represent direct proportionality ( $P \propto V$ ), not inverse.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing

P

1/V

plot with

P

V

plot.

4 4

✓ 100% Correct

Verdict & Scientific Reason:

Flawless representation of Boyle's law isotherms with $600\text{ K} > 400\text{ K} > 200\text{ K}$ .

💡

Why this is airtight: None; canonical NCERT isotherm diagram.

⚠️

NTA Trap Alert: Graph (1) Inverted Temperature Trap

Candidates who know the curves are hyperbolas often rush and pick Graph (1) without checking the temperature labels. Graph (1) places $200\text{ K}$ at the top, which is physically impossible. At higher temperature, gas particles have higher kinetic energy and exert GREATER pressure, shifting the curve UPWARDS (Graph 4).

🛡️ How to avoid the -1 mark: Fix a vertical line at constant V: higher temperature MUST give higher pressure (

600\text{ K}

on top).

📖

Core NEET Syllabus Standard

NCERT Chemistry · States of Matter Standard Benchmark

Core Scientific Principle Tested:

"Each curve on a P-V graph corresponds to a different constant temperature and is known as an isotherm. Higher curves correspond to higher temperatures."

Syllabus Focus: The Gas Laws (Boyle's Law - Pressure-Volume Relationship)

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Chemistry Question 82 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Higher T = Higher Curve (P ∝ T at constant V)

Step-by-Step Rigorous Workflow & Mathematical Proof

Mathematical Formulation of Boyle's Law Isotherms

Temperature Dependence of the Constant k1 = nRT

Identifying the Correct Graph

360° Option Elimination Engine Key Feature

NTA Trap Alert: Graph (1) Inverted Temperature Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — States of Matter

Classification of Intermolecular Forces (Exclusion of Covalent Bonding)

Boyle’s Law Graphical Isotherms: P vs 1/V Linear Representation

Dalton's Law of Partial Pressures: Partial Pressure of N2 in N2-Ar Mixture

Ideal Gas Equation: Total Pressure of a Non-Reacting Gaseous Mixture

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