Conisder the following statement for a second order reaction and score of each statement.
`2A rarr P`
`|{:(,,"Score"),(a.,[A]=([A_(0)])/(1+kt),3),(b.,"A plot of" 1//[A]^(2) "vs time will be straight line",2),(c.,"Half life is long when the concentration is low",1):}|`
Find the total score of the correct statements.

Explanation

To solve the question regarding the second-order reaction \(2A \rightarrow P\) and evaluate the correctness of the given statements, we will analyze each statement one by one.

### Step 1: Analyze Statement (a)
**Statement (a):** \([A] = \frac{[A_0]}{1 + kt}\)

For a second-order reaction, the integrated rate law is given by:
\[ \frac{1}{[A]} = \frac{1}{[A_0]} + kt \]
This means that the expression for \([A]\) is not correctly stated in statement (a). Therefore, statement (a) is **incorrect**.

**Score for (a): 3 (incorrect)**

### Step 2: Analyze Statement (b)
**Statement (b):** "A plot of \( \frac{1}{[A]^2} \) vs time will be a straight line."

For a second-order reaction, the correct plot is:
\[ \frac{1}{[A]} \text{ vs } t \]
This will yield a straight line. However, plotting \( \frac{1}{[A]^2} \) vs time does not yield a straight line. Therefore, statement (b) is **incorrect**.

**Score for (b): 2 (incorrect)**

### Step 3: Analyze Statement (c)
**Statement (c):** "Half-life is long when the concentration is low."

For a second-order reaction, the half-life (\(t_{1/2}\)) is given by:
\[ t_{1/2} = \frac{1}{k[A_0]} \]
This indicates that the half-life is inversely proportional to the initial concentration \([A_0]\). Therefore, if the concentration is low, the half-life will be long. Hence, statement (c) is **correct**.

**Score for (c): 1 (correct)**

### Step 4: Calculate Total Score
Now, we sum the scores of the correct statements:
- Score for (a): 3 (incorrect)
- Score for (b): 2 (incorrect)
- Score for (c): 1 (correct)

Total score = 0 (since only statement (c) is correct).

### Final Answer
The total score of the correct statements is **1**.

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