Rate of the given reaction,
(1) `A + B overset(r_(1)=0.05) to X`
(2) `X + B overset(r_(2)=0.89) to Y`
(3) `Y + A overset(r_(3)=0.001) to AY`
(4) `AY + B overset(r_(4)=0.10) to AYB` will be determined by

Options

A. Step 1 : because the reaction starts with the formation of X
B. Step 2 : because it is the fatest step
C. Step 3 : because it is the slowest step
D. Step 4 : because it ends the reaction

Answer

To determine which step of the given reactions will dictate the overall rate of the reaction, we need to analyze the rates of each individual step. Here are the steps to arrive at the solution:

### Step-by-Step Solution:

1. **Identify the Given Reactions and Their Rates:**
- Reaction (1): \( A + B \overset{(r_1=0.05)}{\rightarrow} X \)
- Reaction (2): \( X + B \overset{(r_2=0.89)}{\rightarrow} Y \)
- Reaction (3): \( Y + A \overset{(r_3=0.001)}{\rightarrow} AY \)
- Reaction (4): \( AY + B \overset{(r_4=0.10)}{\rightarrow} AYB \)

2. **Compare the Rates of Each Reaction:**
- \( r_1 = 0.05 \)
- \( r_2 = 0.89 \)
- \( r_3 = 0.001 \) (slowest)
- \( r_4 = 0.10 \)

3. **Determine the Slowest Step:**
- The rate-determining step (RDS) is the step with the lowest rate because it takes the longest time to complete, thus controlling the overall rate of the reaction.
- From the rates compared, \( r_3 = 0.001 \) is the lowest.

4. **Conclusion:**
- Therefore, the step that determines the rate of the reaction is **Step 3**: \( Y + A \overset{(r_3=0.001)}{\rightarrow} AY \).

### Final Answer:
The step that determines the rate of the reaction is **Step 3**.

---