JEE Main · 2020 · Shift-IImediumCK-103

The rate constant (k) of a reaction is measured at different temperature (T), and the data are plotted in the given…

Chemical Kinetics · Class 12 · JEE Main Previous Year Question

Question

The rate constant (kk) of a reaction is measured at different temperature (TT), and the data are plotted in the given figure. The activation energy of the reaction in kJmol1\mathrm{kJ\,mol^{-1}} is ____\_\_\_\_: (RR is gas constant) image

Options
  1. a

    2/R2/R

  2. b

    1/R1/R

  3. c

    RR

  4. d

    2R2R

Correct Answerd

2R2R

Detailed Solution

From the Arrhenius equation: lnk=lnAEaRT\ln k = \ln A - \frac{E_a}{RT}

The slope of lnk\ln k vs 1T\frac{1}{T} is EaR-\frac{E_a}{R}.

From the graph, the slope =2= -2 (reading the graph: change in lnk\ln k per unit change in 1/T1/T).

EaR=2Ea=2R-\frac{E_a}{R} = -2 \Rightarrow E_a = 2R

Answer: Option (4) — 2R2R

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