Final answer:
The rate of appearance of D in the given reaction mechanism can be expressed as (k3 * k1 / (k2 + k3[C]))[A][C], considering the steady state assumption for the intermediate B.
Step-by-step explanation:
To write an expression for the rate of appearance of product D in a reaction where A is converted to B and then B reacts with C to yield product D, we need to consider the steady state approximation for the intermediate B. According to the steady state hypothesis, the rate of formation of B from A is equal to the rate of consumption of B to form D. This can be described by the rates of the two elementary reactions:
- A ⇌ B (with rate constants k1 for the forward reaction and k2 for the reverse reaction).
- B + C → D (with rate constant k3).
By applying the steady state approximation (assuming that the concentration of B does not change over time), we can say that the rate of production of B is equal to its rate of consumption:
k1[A]= k2[B] + k3[B][C]
However, we are interested in the rate of appearance of D, hence the rate at which B reacts with C is our final rate:
Rate of appearance of D = k3[B][C]
Since we have assumed the steady state for B, we can solve for [B] from the steady state equation and substitute it into the rate law for D:
[B] = k1[A] / (k2 + k3[C])
Substituting this into the rate law for D gives us:
Rate of appearance of D = (k3 * k1 / (k2 + k3[C]))[A][C], which simplifies our expression.