Q.56 Chemistry ⭐ 360° Option Elimination Active

NEET 2025 Chemistry Question 56 Solution

Topic: Chemical Kinetics · Official NTA Booklet Code 45

Question

If the half-life (t₁/₂) for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is closest to:

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Verified Against NTA Final Answer Key

Option (4) : 10 minutes

📚 Chemical Kinetics Easy

📋 Given Parameters & Problem Setup

Order of Reaction First order

Half-Life (t_{1/2}) 1 minute

Completion Percentage 99.9%

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The 30-Second Exam Hall Shortcut: ⚡ Canonical 10 × t_{1/2} Identity

⏱️ Save ~40 seconds

For any first order reaction, t_{99.9%} = 10 × t_{1/2}! Since t_{1/2} = 1 minute, t_{99.9%} = 10 × 1 min = 10 minutes!

1 Memorize canonical first-order milestone: t_{99.9%} ≈ 10 × t_{1/2}.

2 Mathematical reason: At 99.9% completion, remaining amount is 0.1% = 1/1000 = 10⁻³ of initial.

3 Since (1/2)¹⁰ = 1/1024 ≈ 1/1000, exactly 10 half-lives have elapsed.

4 Given t_{1/2} = 1 minute ⟹ t_{99.9%} = 10 × 1 = 10 minutes.

5 Select Option (4) in under 5 seconds!

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Why You Can 100% Trust This Shortcut: Rate Law & Integrated Rate Equations (NCERT Chemistry · Chemical Kinetics: t_1/2 = 0.693/k).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulate Integrated Rate Law for 99.9% Completion

For a first-order reaction with rate constant k, the time t required for reactant concentration to decrease from [R]₀ to [R]_t is:

t = \frac{2.303}{k} \log_{10}\left(\frac{[R]_0}{[R]_t}\right)

• For 99.9% completion, [R]_t = [R]₀ - 0.999 [R]₀ = 0.001 [R]₀ = 10⁻³ [R]₀.
• Therefore: [R]₀ / [R]_t = 1 / 10⁻³ = 10³ = 1000.

Step 2

Relate Rate Constant k to Half-Life

Substitute k = 2.303 log(2) / t_{1/2} = 0.693 / t_{1/2} into the integrated rate equation:

t_{99.9\%} = \frac{2.303}{\frac{0.693}{t_{1/2}}} \log_{10}(10^3) = \frac{2.303 \times 3}{0.693} t_{1/2} = \frac{6.909}{0.693} t_{1/2} \approx 9.97 \times t_{1/2} \approx 10 \times t_{1/2}

• This is a fundamental theorem of first-order chemical kinetics.

Step 3

Calculate Time for Given Half-Life

Substitute t_{1/2} = 1 minute:

t_{99.9\%} = 10 \times 1\text{ minute} = 10\text{ minutes}

• Matches Option (4) exactly.

⭐

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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. 2 half-lives corresponds to 75% completion ((1/2)² = 1/4 remaining).

⚠️

Student Fallacy (Why candidates pick this trap): Confusing 99.9% with 75%.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. 4 half-lives corresponds to 93.75% completion.

⚠️

Student Fallacy (Why candidates pick this trap): Guessing 4 half-lives.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. 5 half-lives corresponds to 96.875% completion.

⚠️

Student Fallacy (Why candidates pick this trap): Arithmetic slip.

4 D

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. Canonical relation t_{99.9%} = 10 × t_{1/2} = 10 minutes.

💡

Why this is airtight: None; textbook kinetics mastery.

⚠️

NTA Trap Alert: Confusing 99% (t = 2 × t_{90%}) with 99.9%

t_{99%} ≈ 6.64 × t_{1/2}, whereas t_{99.9%} = 10 × t_{1/2}. Always count the nines: three nines (99.9%) means 10⁻³ remaining, which requires 10 half-lives (2¹⁰ = 1024)!

🛡️ How to avoid the -1 mark: Remember: 99.9% = 10 half-lives; 99% = 6.64 half-lives; 75% = 2 half-lives.

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Core NEET Syllabus Standard

NEET Chemistry Core Syllabus · Chemical Kinetics Standard Benchmark

Core Scientific Principle Tested:

"For a first order reaction, t_{99.9%} = 10 × t_{1/2}."

Syllabus Focus: Integrated Rate Equations & Half-Life of Reactions

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

3 Nines (99.9%) ⟹ 10⁻³ left ⟹ 2¹⁰ ≈ 1000 ⟹ 10 Half-Lives = 10 minutes!

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NEET 2025 Chemistry Question 56 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Canonical 10 × t_{1/2} Identity

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulate Integrated Rate Law for 99.9% Completion

Relate Rate Constant k to Half-Life

Calculate Time for Given Half-Life

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing 99% (t = 2 × t_{90%}) with 99.9%

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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