Q.60 Chemistry · Section A ⭐ 360° Option Elimination Active
NEET 2024 Chemistry Question 60 Solution
Topic: Chemical Kinetics · Official NTA Booklet Code T1
Question
Which plot of ln k vs 1/T is consistent with Arrhenius equation?
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Verified Against NTA Final Answer Key
Option (2) : Plot (2): Straight line with negative slope and positive intercept
📚 Chemical Kinetics Easy
📋 Given Parameters & Problem Setup
Plotted function ln k on y-axis versus (1 / T) on x-axis
Theoretical basis Arrhenius equation: k = A e^(-E_a / RT)
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⏱️ Save ~30 seconds The 30-Second Exam Hall Shortcut: ⚡ Arrhenius Slope Identification
ln k = ln A - (E_a / R)(1/T) -> y = c + mx where slope m = -E_a/R is STRICTLY NEGATIVE -> Straight line sloping downward!
1 Linear form of Arrhenius equation: ln k = ln A - (E_a / R) · (1/T).
2 Match to standard straight line y = mx + c:
3 y = ln k, x = 1/T, Intercept c = ln A > 0, Slope m = -E_a / R < 0.
4 Because E_a > 0 and R > 0, the slope is negative: as 1/T increases (temperature cools), ln k decreases.
5 Plot (2) is the only plot showing a downward-sloping straight line with negative slope.
6 Option (2) in under 3 seconds!
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Why You Can 100% Trust This Shortcut: NCERT Chemistry · Chemical Kinetics (Arrhenius equation and determination of activation energy from graphical slope: Slope = -E_a / R).
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Step-by-Step Rigorous Workflow & Mathematical Proof
Step 1
Derivation of the Linear Equation
Taking the natural logarithm of both sides of the Arrhenius rate expression:
Step 2
Comparison with Standard Linear Form y = mx + c
Aligning variables to identify graphical features: - Dependent variable: y = ln k - Independent variable: x = 1 / T - Slope: m = -Ea / R (strictly negative) - Y-intercept: c = ln A (positive finite value when extrapolated to 1/T = 0)
Step 3
Graphical Interpretation
As absolute temperature T increases, 1/T decreases, and the reaction rate constant k increases (ln k rises). Conversely, moving along the positive x-axis (increasing 1/T, meaning cooling), ln k falls linearly. The graph must therefore be a straight line sloping downward from left to right, exactly as illustrated in Plot (2).
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4-Option Deep Scan
360° Option Elimination Engine Key Feature
Diagnose every choice: Know exactly why the right option works and why distractors fail.
1 (1)
✗ Incorrect Verdict & Scientific Reason:
Violates Arrhenius equation: positive slope implies reaction slows down upon heating.
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Student Fallacy (Why candidates pick this trap): Assuming rate constant is directly proportional to 1/T.
2 (2)
✓ 100% Correct Verdict & Scientific Reason:
Matches Arrhenius slope m = -Ea/R < 0 and intercept c = ln A.
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Why this is airtight: None.
3 (3)
✗ Incorrect Verdict & Scientific Reason:
Slope must be negative.
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Student Fallacy (Why candidates pick this trap): Flipping sign of Ea/R.
4 (4)
✗ Incorrect Verdict & Scientific Reason:
Incorrect positive slope.
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Student Fallacy (Why candidates pick this trap): Plotting ln k versus T instead of 1/T.
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NTA Trap Alert: Confusing 1/T with Temperature T
Rate constant k increases with T (positive correlation), but 1/T is inversely related to T. Therefore, ln k decreases as 1/T increases!
🛡️ How to avoid the -1 mark: Higher 1/T means colder temperature, so the reaction is slower and ln k must be smaller.
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Core NEET Syllabus Standard
Chemistry Core Physical Chemistry · Chemical Kinetics Standard Benchmark
Core Scientific Principle Tested:
"The plot of ln k versus 1/T gives a straight line with slope = -Ea / R and intercept = ln A."
Syllabus Focus: Arrhenius Equation: Graphical Representation and Activation Energy
✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗
As 1/T climbs, temperature goes low: The Arrhenius line must slope down below!
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