Q.91 Chemistry · Section B ⭐ 360° Option Elimination Active

NEET 2024 Chemistry Question 91 Solution

Topic: Thermodynamics · Official NTA Booklet Code T1

Question

The work done during reversible isothermal expansion of one mole of hydrogen gas at 25°C from pressure of 20 atmosphere to 10 atmosphere is: (Given R = 2.0 cal K⁻¹ mol⁻¹)

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Verified Against NTA Final Answer Key

Option (4) : -413.14 calories

📚 Thermodynamics Medium

📋 Given Parameters & Problem Setup

Amount of hydrogen gas (n) 1 mole

Temperature (T) 25°C = 298.15 K

Initial pressure (P1) 20 atm

Final pressure (P2) 10 atm

Gas constant (R) 2.0 cal K^-1 mol^-1

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The 30-Second Exam Hall Shortcut: ⚡ Sign Convention & Expansion Formula Hack

⏱️ Save ~45 seconds

Gas EXPANDS from 20 atm to 10 atm -> Work is done BY the gas -> w is strictly NEGATIVE (-413.14 cal)! Eliminate positive options immediately!

1 Formula for reversible isothermal work (IUPAC convention): w = -2.303 · n R T · log10(P1 / P2).

2 Pressure drops from 20 atm to 10 atm -> volume expands -> w must be negative.

3 Substitute values: w = -2.303 × (1 mol) × (2.0 cal K⁻¹ mol⁻¹) × (298.15 K) × log10(20 / 10).

4 log10(2) = 0.3010.

5 w = -2.303 × 2.0 × 298.15 × 0.3010 = -4.606 × 298.15 × 0.3010 = -413.14 calories.

6 Match Option (4) in 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: NCERT Chemistry · Thermodynamics (First Law of Thermodynamics: work done in reversible isothermal process w = -2.303 nRT log(P1/P2)).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Thermodynamic Work Formula (IUPAC Sign Convention)

In chemistry, work done on the system is positive, and work done by the system (such as during expansion against external pressure) is negative. For a reversible isothermal expansion of an ideal gas:

w = -\int_{V_1}^{V_2} P_{ext}\, dV = -nRT \ln\left(\frac{V_2}{V_1}\right) = -nRT \ln\left(\frac{P_1}{P_2}\right)

Step 2

Conversion to Common Logarithm (Base 10)

Expressing natural logarithm in terms of base-10 logarithm using the factor 2.303:

w = -2.303\, n R T \log_{10}\left(\frac{P_1}{P_2}\right)

Step 3

Substitution of Given Parameters

Given: - n = 1 mole - R = 2.0 cal K⁻¹ mol⁻¹ - T = 25 + 273.15 = 298.15 K (or 298 K) - P1 = 20 atm, P2 = 10 atm ⟹ P1/P2 = 2.0 - log10(2) = 0.30103

w = -2.303 \times 1 \times 2.0 \times 298.15 \times \log_{10}(2)

Step 4

Numerical Evaluation

Multiplying the terms step by step: 2.303 × 2.0 = 4.606 4.606 × 298.15 = 1373.28 1373.28 × 0.30103 = 413.14 calories. With the negative sign for expansion work:

w = -413.14\;\text{calories}

⭐

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:

Physics sign convention; in chemical thermodynamics, expansion work is strictly negative.

⚠️

Student Fallacy (Why candidates pick this trap): Using physics work convention (w = +P dV) instead of IUPAC chemical convention (w = -P dV).

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Arbitrary incorrect value.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing pressure difference with work.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Internal energy change ΔU = 0 for isothermal process, but work w is non-zero.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing work w with internal energy change ΔU.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Exact magnitude and correct IUPAC negative sign for expansion work.

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Why this is airtight: None.

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NTA Trap Alert: Option (1) Sign Convention Trap

Option (1) offers +413.14 cal. Remember that in chemistry, WORK DONE BY THE GAS IN EXPANSION IS ALWAYS NEGATIVE (w = -413.14 cal).

🛡️ How to avoid the -1 mark: Expansion = Volume increases = Gas does work on surroundings = w < 0.

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Core NEET Syllabus Standard

Chemistry Core Physical Chemistry · Thermodynamics Standard Benchmark

Core Scientific Principle Tested:

"Work done in a reversible isothermal expansion of an ideal gas is negative under IUPAC convention: w = -2.303 nRT log(P1/P2)."

Syllabus Focus: First Law of Thermodynamics: Reversible Isothermal Work

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Gas expands and pushes wide: negative work on chemistry’s side (-413.14 cal)!

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NEET 2024 Chemistry Question 91 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Sign Convention & Expansion Formula Hack

Step-by-Step Rigorous Workflow & Mathematical Proof

Thermodynamic Work Formula (IUPAC Sign Convention)

Conversion to Common Logarithm (Base 10)

Substitution of Given Parameters

Numerical Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Option (1) Sign Convention Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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Entropy Changes in Isothermal Free Expansion of an Ideal Gas

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