At equilibrium for a reaction `A harr B`.
correct representation is {`r_f `= rate of forward reaction, `r_b` = rate of backward reaction}`

Options

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Answer

To solve the problem regarding the equilibrium of the reaction \( A \rightleftharpoons B \) and the rates of the forward and backward reactions, we can follow these steps:

### Step 1: Understand the Concept of Equilibrium
At equilibrium, the rates of the forward and backward reactions become equal. This means that the concentration of reactants and products remains constant over time.

### Step 2: Define the Rates
- The rate of the forward reaction (\( r_f \)) is the rate at which reactant \( A \) is converted to product \( B \).
- The rate of the backward reaction (\( r_b \)) is the rate at which product \( B \) is converted back to reactant \( A \).

### Step 3: Set Up the Equilibrium Condition
At equilibrium, we can express the relationship mathematically:
\[ r_f = r_b \]
This indicates that the rate of formation of \( B \) from \( A \) is equal to the rate of formation of \( A \) from \( B \).

### Step 4: Conclusion
Since at equilibrium the rates of the forward and backward reactions are equal, we can conclude that:
\[ \text{At equilibrium, } r_f = r_b \]

### Final Answer
The correct representation at equilibrium for the reaction \( A \rightleftharpoons B \) is that the rate of the forward reaction (\( r_f \)) equals the rate of the backward reaction (\( r_b \)).

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