Composite Reactions & the Steady State Approximation

DECOMPOSITION OF AZOMETHANE

Hint

To back substitute the equation

A = BC + D . . . {1}
into the equation
X = YA + Z . . . {2}
Replace A, where it appears in Equation {2} with (BC + D); giving
X = Y(BC + D) + Z

So in the case of the Azomethane Example, anytime [AZO*] appears in the overall rate of Nitrogen production expression

d[N2]/dt = +k2[AZO*]
it should be replaced with
k1[AZO]2 / (k-1[AZO] + k2)

Eliminating [AZO*] from the Rate Expression for the Production of Nitrogen {+d[N2]/dt}

Having obtained the Steady State Concentration of (Azomethane)*

[AZO*]SS = k1[AZO]2 / (k-1[AZO] + k2)

(Note: The SS subscript is used to denote a Steady State term.)

this relationship can now be back-substituted into the expression for the overall rate of production of Nitrogen

d[N2]/dt = +k2[AZO*]

giving the result

d[N2]/dt = k1[AZO]2 / (k-1[AZO] + k2)

d[N2]/dt = k2k1[AZO]2 / (k-1[AZO] + k2)

d[N2]/dt = +k2[AZO*]k1[AZO]2 / (k-1[AZO] + k2)