Q.79 Chemistry ⭐ 360° Option Elimination Active

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NEET 2023 Chemistry Question 79 Solution

Topic: States of Matter · Official NTA Booklet Code G5

Question

Which amongst the following options is correct graphical representation of Boyle's Law?

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Verified Against NTA Final Answer Key

Option (3) : P vs 1/V straight lines with slopes T₃ > T₂ > T₁

📚 States of Matter Medium

📋 Given Parameters & Problem Setup

Gas Law Evaluated Boyle’s Law (constant n and T)

Temperature Ordering T₃ > T₂ > T₁

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The 30-Second Exam Hall Shortcut: ⚡ Linear Isotherm Slope Scan: P = (nRT) · (1/V) with Slope ∝ T

⏱️ Save ~35 seconds

Ideal gas law PV = nRT converts to P = (nRT)(1/V). Comparing with y = mx: plot of P vs 1/V is a straight line through the origin with slope = nRT. Higher T gives steeper slope! Since T₃ > T₂ > T₁, the slope order is slope₃ > slope₂ > slope₁. Graph (3) is instantly recognized!

1 Express Boyle’s law in terms of plotted variables: P = (nRT)(1/V).

2 This conforms to y = mx with intercept c = 0 (straight line passing through the origin).

3 Slope m = nRT is directly proportional to absolute temperature T.

4 Since T₃ > T₂ > T₁, the lines must be linear through (0,0) with steepest slope for T₃.

5 Graph (3) correctly displays this straight-line fan with slope₃ > slope₂ > slope₁.

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Why You Can 100% Trust This Shortcut: Direct functional mapping of Ideal Gas Law PV = nRT into Cartesian coordinates.

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

State Boyle’s Law and the Ideal Gas Equation

Boyle’s Law states that at constant temperature (T) and constant mass of gas (n), the pressure of a given mass of gas is inversely proportional to its volume:

P \propto \frac{1}{V} \implies PV = k = nRT

Step 2

Formulate Linear Equation for P vs 1/V

Rearranging the equation of state with y = P and x = 1/V yields a linear function:

P = (nRT) \left(\frac{1}{V}\right) \iff y = mx \quad (\text{where slope } m = nRT)

Step 3

Analyze Slope Variation with Temperature

Because slope m = nRT, the slope is directly proportional to absolute temperature:

T_3 > T_2 > T_1 \implies m_3 > m_2 > m_1

Step 4

Eliminate Alternative Graphs

Option (1) plots P vs T (Gay-Lussac’s isochores). Option (2) plots P vs V hyperbolas but inverts the temperature ordering. Option (4) shows a hyperbola for P vs 1/V, violating linearity. Graph (3) is uniquely correct:

\text{Correct graph: Straight lines through origin with } \text{slope}(T_3) > \text{slope}(T_2) > \text{slope}(T_1)

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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:

Represents Gay-Lussac’s law (isochores), not Boyle’s law.

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Student Fallacy (Why candidates pick this trap): Candidate confused isochoric pressure-temperature variation with isothermal pressure-volume variation.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

The curves are hyperbolic, but the upper isotherm has a higher PV product, so the top curve should be T₃, not T₁.

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Student Fallacy (Why candidates pick this trap): Candidate overlooked the temperature label ordering on the P vs V curves.

3 (3)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate: P = (nRT)(1/V) is a straight line through the origin whose slope increases with absolute temperature.

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Why this is airtight: None. Candidate correctly analyzed the linear functional form and temperature dependence of slope.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

P is directly proportional to 1/V, so the plot must be linear, not hyperbolic.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused the hyperbolic shape of P vs V with the linear shape of P vs 1/V.

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NTA Trap Alert: Confusing P vs V with P vs 1/V

P vs V is a rectangular hyperbola (isotherm). P vs 1/V is a straight line passing through the origin. Furthermore, at higher temperature, any given volume sustains a higher pressure, meaning isotherms shift upward and outward.

🛡️ How to avoid the -1 mark: Identify the axis variables first: if the x-axis is 1/V, the relationship is strictly linear with slope = nRT.

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · States of Matter Standard Benchmark

Core Scientific Principle Tested:

"At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: P = k/V."

Syllabus Focus: The Gaseous State – Boyle’s Law and Isotherms

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Chemistry Question 79 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Linear Isotherm Slope Scan: P = (nRT) · (1/V) with Slope ∝ T

Step-by-Step Rigorous Workflow & Mathematical Proof

State Boyle’s Law and the Ideal Gas Equation

Formulate Linear Equation for P vs 1/V

Analyze Slope Variation with Temperature

Eliminate Alternative Graphs

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing P vs V with P vs 1/V

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — States of Matter

Boyle's Law: Pressure vs. Volume Isotherms at Different Temperatures

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

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

Classification of Intermolecular Forces (Exclusion of Covalent Bonding)

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