Q.132 Chemistry ⭐ 360° Option Elimination Active

NEET 2020 Chemistry Question 132 Solution

Topic: Chemical Kinetics · Official NTA Booklet Code E1

Question

The rate constant for a first order reaction is 4.606×10⁻³ s⁻¹. The time required to reduce 2.0 g of the reactant to 0.2 g is:

✓

Verified Against NTA Final Answer Key

Option (3) : 500 s

📚 Chemical Kinetics Easy

📋 Given Parameters & Problem Setup

Reaction Order First order

Rate Constant (k) 4.606 × 10^-3 s^-1

Initial Amount [R]0 2.0 g

Remaining Amount [R] 0.2 g

Integrated Rate Formula t = (2.303 / k) × log([R]0 / [R])

⚡

The 30-Second Exam Hall Shortcut: ⚡ "Ratio [R]0/[R] = 2.0 / 0.2 = 10 -> log(10) = 1; t = 2.303 / (4.606 × 10^-3) = 500 s!"

⏱️ 25 seconds

The integrated rate equation for a first order reaction is $t = \frac{2.303}{k} \log\left(\frac{[R]_0}{[R]}\right)$ . Here, the concentration ratio is $\frac{2.0}{0.2} = 10$ , and $\log(10) = 1$ . Therefore, $t = \frac{2.303}{4.606 \times 10^{-3}} \times 1 = \frac{1}{2 \times 10^{-3}} = \frac{1000}{2} = 500\text{ s}$ ! Mark Option (3) in 10 seconds.

1 Formula: t = (2.303 / k) × log([R]0 / [R]).

2 Substitute concentrations: [R]0 = 2.0 g, [R] = 0.2 g.

3 Ratio: [R]0 / [R] = 2.0 / 0.2 = 10.

4 log(10) = 1.

5 Calculate: t = 2.303 / (4.606 × 10^-3) = 1 / (2 × 10^-3) = 500 s.

6 Select Option (3).

🛡️

Why You Can 100% Trust This Shortcut: NCERT Chemistry · Chemical Kinetics (Integrated Rate Equations: First Order Reactions)

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

State Integrated Rate Law for First Order Reaction

For a first order reaction $R \to \text{Products}$ , the integrated rate equation in common logarithmic form is: $k = \frac{2.303}{t} \log\left(\frac{[R]_0}{[R]}\right) \implies t = \frac{2.303}{k} \log\left(\frac{[R]_0}{[R]}\right)$

Step 2

Insert Given Quantities

Given: - Rate constant $k = 4.606 \times 10^{-3}\text{ s}^{-1}$ - Initial mass of reactant $[R]_0 = 2.0\text{ g}$ - Final mass of reactant remaining $[R] = 0.2\text{ g}$ (Notice that for a given volume, the ratio of masses is identical to the ratio of molar concentrations).

Step 3

Evaluate the Logarithmic Term

$\frac{[R]_0}{[R]} = \frac{2.0}{0.2} = 10$ $\log(10) = 1$

Step 4

Calculate Time (t)

$t = \frac{2.303}{4.606 \times 10^{-3}} \times 1$ Notice that $4.606 = 2 \times 2.303$ : $t = \frac{1}{2 \times 10^{-3}} = \frac{1000}{2} = 500\text{ seconds}$ This confirms Option (3).

⭐

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; arithmetic error in dividing 1000 by 2.

⚠️

Student Fallacy (Why candidates pick this trap): Dividing by 10 instead of 2.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; inverts the factor of 2 or forgets to account for $\log(10)$ .

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying by 2 instead of dividing.

3 C

✓ 100% Correct

Verdict & Scientific Reason:

Factually and mathematically exact; $t = \frac{2.303}{4.606 \times 10^{-3}} = 500\text{ s}$ .

💡

Why this is airtight: None; clean cancellation of 2.303 into 4.606.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; neglects the factor of 2 ( $4.606 / 2.303 = 2$ ) in the denominator.

⚠️

Student Fallacy (Why candidates pick this trap): Forgetting that 4.606 is double of 2.303.

⚠️

NTA Trap Alert: Numerical Cancellation Landmark

NTA intentionally uses $k = 4.606 \times 10^{-3}$ because $4.606 / 2.303 = 2$ exactly! Do not waste time doing long division by hand.

🛡️ How to avoid the -1 mark: Spot the multiple:

2.303 / 4.606 = 1/2

📖

Core NEET Syllabus Standard

Chemistry · Chemical Kinetics Standard Benchmark

Core Scientific Principle Tested:

Syllabus Focus: First Order Kinetics: Time Required for 90% Reactant Reduction

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2020 Chemistry Question 132 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ "Ratio [R]0/[R] = 2.0 / 0.2 = 10 -> log(10) = 1; t = 2.303 / (4.606 × 10^-3) = 500 s!"

Step-by-Step Rigorous Workflow & Mathematical Proof

State Integrated Rate Law for First Order Reaction

Insert Given Quantities

Evaluate the Logarithmic Term

Calculate Time (t)

360° Option Elimination Engine Key Feature

NTA Trap Alert: Numerical Cancellation Landmark

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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