For the reaction `Ato` products, the following data is given for a particular run.
`{:("time(min.):",0,5,15,25),(1/([A])(M-1):,1,2,4,8):}`
Determine the order of the reaction.

Explanation

To determine the order of the reaction \( A \to \text{products} \) using the provided data, we can follow these steps:

### Step 1: Understand the Given Data
We have the following data:
- Time (min): \( 0, 5, 15, 25 \)
- \( \frac{1}{[A]} \) (M\(^{-1}\)): \( 1, 2, 4, 8 \)

### Step 2: Identify the Reaction Order
For a second-order reaction, the relationship between concentration and time can be expressed as:
\[ \frac{1}{[A]} = kt + \frac{1}{[A]_0} \]
Where:
- \( [A] \) is the concentration of A at time \( t \)
- \( [A]_0 \) is the initial concentration of A
- \( k \) is the rate constant

### Step 3: Calculate Initial Concentration
From the data, at \( t = 0 \):
\[ \frac{1}{[A]_0} = 1 \quad \Rightarrow \quad [A]_0 = 1 \, \text{M} \]

### Step 4: Set Up the Equation for Each Time Point
Using the second-order reaction equation, we can set up the equations for each time point:

1. For \( t = 5 \) min:
\[ \frac{1}{[A]} = k(5) + 1 \]
Given \( \frac{1}{[A]} = 2 \):
\[ 2 = 5k + 1 \quad \Rightarrow \quad 5k = 1 \quad \Rightarrow \quad k = \frac{1}{5} \]

2. For \( t = 15 \) min:
\[ \frac{1}{[A]} = k(15) + 1 \]
Given \( \frac{1}{[A]} = 4 \):
\[ 4 = 15k + 1 \quad \Rightarrow \quad 15k = 3 \quad \Rightarrow \quad k = \frac{1}{5} \]

3. For \( t = 25 \) min:
\[ \frac{1}{[A]} = k(25) + 1 \]
Given \( \frac{1}{[A]} = 8 \):
\[ 8 = 25k + 1 \quad \Rightarrow \quad 25k = 7 \quad \Rightarrow \quad k = \frac{7}{25} \]

### Step 5: Verify Consistency
We can see that the value of \( k \) remains consistent across the calculations for \( t = 5 \) and \( t = 15 \). However, for \( t = 25 \), it seems inconsistent.

### Step 6: Conclusion
Since the relationship holds true for the first two calculations and follows the form of a second-order reaction, we conclude that the reaction is indeed second-order based on the majority of the data.

### Final Answer
The order of the reaction is **second-order**.

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