Question

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2. Reaction: 2 NOCI (g) 2 NO (g) +Cl2(g) Its rate constants are 9.3x 106 s1 at 77 C and 6.9 x 104 s1 at 127 C, respectively. (a) Calculate the activation energy Ea for this reaction. (b) Calculate eER at 77 'C and 127 C, respectively. (c) What is the rate constant at 200 °C? (30 points)

Answer 1

2.a)

Arrhenius equation provides the dependence of rate constant with absolute temperature of a chemical reaction.

the equation is

K = A. e^-Ea^/RT (1)

K is rate constant , T is absolute temperature , A is frequency factor.

given, at T₁ = 77⁰ c = 273+77 = 350 K, K₁ = 9.3*10^-6 s^-1  

and, T₂ = 127⁰ c = 273+127 = 400 K, K₂ = 6.9*10^-4 s^-1

now applying Eq. 1

K₁ = A. e^-Ea^/RT1 (2)

K₂ = A. e^-Ea^/RT2 (3)

=
e-Ea/RT -Ea/RT2

_2.1
= - e^{(E_a/R) * ()}

^{or , ln}
2.1
= -
Ea 1
( )

now, putting the given values in above equation

ln
6.9 104 9.3 * 10-6
= -
Ea 8.314
(
400
-
350
)

or, ln (74.19) = -   (- 0.000357)

Ea 8.314

or, 4.306 =
_{Ea 8.314}
*0.000357

or, E_a = (4.306*8.314)/0.000357

or, E_a = 100280.34 J

Hence activation energy = 100.28 KJ

b)

now,at 77 ⁰c ; e^-Ea^/RT₁ = e^{-100280.34/(8.314*350)} = e^-34.46 = 1.08*10^-15

at 1270c , e-Ea/RT2 = e-100280.34/(8.314*400) = 8.054*10-14

c)

Let at T₂ = 200⁰ c = 273+200 = 473 K , rate constant is K₂  

at, T₁ = 400 K, K₁ = 6.9*10^-4 s^-1

^ln
2.1
= -
Ea 1
( )

or, ^ln =
Ea 1
( )

or, ln (6.9*10^-4/K₂ ) =  
100280.34 8.314
(
473
-  
400
)

or, ln (6.9*10^-4/K2 ) = 12061.62*(-0.000385)

or, ln 6.9*10^-4/K₂ )= - 4.643

or,  (6.9*10^-4/K₂ ) = e^-4.643

or,  (6.9*10^-4/K₂ ) = 0.0096

or, K₂ = 6.9*10^-4/ 0.0096

or, K₂ = 0.0718 = 7.18*10^-2 s^-1