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A reaction is represented by : A to B...

A reaction is represented by :
`A to B` slow and `A+B to C` (fast) where `k_1 and k_2` are the rate constants of the mechanistic steps. The rate of production of B will be given by :

A

`K_1[A][B]`

B

`K_1[A]`

C

`K_1K_2[A]`

D

`K_2[A][B]`

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To find the rate of production of B in the given reaction mechanism, we need to analyze the steps involved: ### Step-by-Step Solution: 1. **Identify the Reaction Steps**: - The first step is the conversion of A to B, which is a slow step: \[ A \rightarrow B \quad \text{(slow, rate constant } k_1\text{)} \] - The second step is the conversion of A and B to C, which is a fast step: \[ A + B \rightarrow C \quad \text{(fast, rate constant } k_2\text{)} \] 2. **Determine the Rate Law for the Slow Step**: - Since the first step is the slow step, it is the rate-determining step. The rate of production of B can be expressed using the rate law for this step: \[ \text{Rate} = k_1 [A] \] - Here, \([A]\) is the concentration of A. 3. **Relate the Change in Concentration of A to B**: - As A is converted to B, the change in concentration of A is related to the change in concentration of B: \[ -\frac{d[A]}{dt} = \frac{d[B]}{dt} \] - This means that the rate of decrease of A is equal to the rate of increase of B. 4. **Express the Rate of Production of B**: - From the rate law derived from the slow step, we can express the rate of production of B: \[ \frac{d[B]}{dt} = k_1 [A] \] 5. **Final Expression**: - Therefore, the rate of production of B is given by: \[ \frac{d[B]}{dt} = k_1 [A] \] ### Conclusion: The rate of production of B is directly proportional to the concentration of A and the rate constant \(k_1\).
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