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Q36

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type=NAT · page=15–16 · marks=1 · content_conf=0.7999999999999999 · math_conf=0.55

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file: GATE CH 2020 (with Solutions).pdf

pages: 15–16

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The decomposition of acetaldehyde (x) to methane and carbon monoxide follow four step free radical

1 /text{mechanism} . /text{The} /text{overall} /text{rate} /text{of} /text{decomposition} /text{of} X /text{is} , −r=Kk₁/2 K₃ C²=KCx². Where

A2()2X3overall3

[VISUAL / REVIEW — NO INVENTED LATEX] Source math clip

KJ/mol) of 320,40 and 0 respectively. The temperature dependency of the rate constant is described by Arrhenius equation. Cₓ denotes the concentration of a acetaldehyde. The rate constant for the overall reaction is Kₒᵥₑᵣₐₗₗ. The activation energy for the overall reaction (in KJ/mol) is ____

Options

none

Answer

200

Solution

E_1 = 320

E_2 = 40

E_3 = 0

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ₐ₂()^{23}[/frac{₀(−E)}{RT}]

−r = /frac{kK_1}{2}K_3./mathrm{Cx}^2K = Ke

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−r = /frac{/frac{/frac{/frac{Ke^{-}E_2}{R_{/mathrm{TK}}_{01}}e^{-}E_1}{RT}}{2}K_0e^{-}E_3}{RT./mathrm{Cx}^{32}_a}(₀₂)(₃)^1

−−r_a = /frac{/frac{K_0e_{40}}{RT}(/frac{(K_{01})^{12}.e(−320)}{RT})}{(/frac{(2K_0)^{12}.e(−0)}{2}RT)./mathrm{Cx}^{32}}

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−r = /frac{/frac{K_{02}.K_{01}^{12}}{(2k_0)^{12}}(/frac{.(³[40-/frac{320}{2}])}{(eR-T_0)})}{e}]Cx² ₐ[₃³

(−200)/RT33

−rA = K_0_{/text{overall}} . e.C x^2 = K_0_{/text{overall}} . /mathrm{Cx}^2

⇒ E =200 Hence, the correct answer is 200.

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K₁ ,K₂,K₃ denotes the rate constant of the elementary steps with corresponding activation energy (in

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Source PDF: GATE CH 2020 (with Solutions).pdf

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