A reaction proceeds by the following three-step mechanism with elementary rate coefficients,
k.
A + B → C k 1
C → A + B k -1
C → B + D k 2
(C is a chemical radical)
(ii) By applying the Steady State Approximation determine the overall order of the
reaction.
(iii)What is the value of kOBS, the observed rate coefficient, at 800K given that the
elementary rate coefficients are as follows:
k l = 1011 exp -( 1 0 0 0 0 / RT )dm3mol-1s-1.
k-1 = 1015 exp –(40000/RT) s-1
k2 = 1013exp –(30000/RT) s-1
To solve this problem, we need to apply the steady-state approximation and determine the overall order of the reaction and the value of kOBS at 800K.
(i) Steady-State Approximation:
The steady-state approximation assumes that the concentration of the intermediate species remains approximately constant during the reaction. In this case, the intermediate species is C.
The rate of formation of C in the first step is given by:
Rate1 = k1 * [A] * [B]
The rate of consumption of C in the second and third steps is given by:
Rate2 = k-1 * [C] = k2 * [C]
Since the concentration of C is assumed to be approximately constant, the rates of formation and consumption of C should be equal:
Rate1 = Rate2
Substituting the rate expressions:
k1 * [A] * [B] = k-1 * [C] = k2 * [C]
Simplifying the above equation:
k1 * [A] * [B] = (k-1 + k2) * [C]
This equation represents the steady-state approximation for this reaction mechanism.
(ii) Overall Order:
The overall order of the reaction is determined by the sum of the exponents of the concentration terms in the rate equation. From the steady-state approximation equation, we can see that the concentration of A, B, and C all have an exponent of 1. Therefore, the overall order of the reaction is 1 + 1 + 1 = 3.
(iii) kOBS at 800K:
To find the value of kOBS at 800K, we need to calculate the values of k1, k-1, and k2 at that temperature.
Given:
k1 = 1011 exp (-10000/RT) dm3mol-1s-1
k-1 = 1015 exp (-40000/RT) s-1
k2 = 1013 exp (-30000/RT) s-1
We can substitute the temperature (800K) into these equations and calculate the values of k1, k-1, and k2.
k1 = 1011 exp (-10000/(8.314 * 800)) dm3mol-1s-1
k-1 = 1015 exp (-40000/(8.314 * 800)) s-1
k2 = 1013 exp (-30000/(8.314 * 800)) s-1
After substituting the values and evaluating the exponential terms, you will get the values of k1, k-1, and k2 at 800K.