- Rate of Change of Intermediate (I) in Series Reactions
The rate of change of an intermediate (I) in a series reaction can be determined using the steady-state approximation. This approximation assumes that the concentration of the intermediate remains constant over a short period of time.
- Steady State Approximation
In a series reaction, the rate of formation of the intermediate (d[I]/dt) equals the rate of consumption of the intermediate by the subsequent reaction. This can be expressed as:
d[I]/dt = k1[A] - k2[I]
where k1 is the rate constant for the formation of the intermediate and k2 is the rate constant for its consumption.
- Applying the Steady State Approximation
By assuming that the concentration of the intermediate remains constant, we can set d[I]/dt = 0. This allows us to solve for the concentration of the intermediate at steady state:
0 = k1[A] - k2[I]
I = (k1[A])/k2
- Equation for Rate of Change of Intermediate (I)
To obtain the equation for the rate of change of the intermediate, we differentiate the steady-state concentration of the intermediate with respect to time:
dI/dt = (k1/k2)d[A]/dt
This equation shows how the concentration of the intermediate changes over time in a series reaction, taking into account the rate constants of formation and consumption.