What is the value of slope, if $\log _{10} \mathrm{~K}$ (y-axis) is plotted versus $1 / \mathrm{T}$ (x-axis)…

What is the value of slope, if $\log _{10} \mathrm{~K}$ (y-axis) is plotted versus $1 / \mathrm{T}$ (x-axis) for Arrhenius equation?
  1. $\log _{10} \mathrm{~A}$
  2. $\frac{2 \cdot 303 \mathrm{R}}{\mathrm{E}_{\mathrm{a}}}$
  3. $\frac{-\mathrm{E}_{\mathrm{a}}}{2 \cdot 303 \mathrm{R}}$
  4. $-\log _{10} \mathrm{~A}$

Solution

Arrhenius equation is $k=A e^{-E_a / R T}$ $\therefore \quad \ln \mathrm{k}=-\frac{\mathrm{E}_{\mathrm{a}}}{\mathrm{RT}}+\ln \mathrm{A}$ $\therefore \quad \log _{10} \mathrm{k}=-\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{R}} \frac{1}{\mathrm{~T}}+\log _{10} \mathrm{~A}$
Thus, the slope of the line is $-\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{R}}$

Asked in: MHT CET 2024 (02 May Shift 2)

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