If the rate of reaction, `2SO_2(g)+O_2(g)overset(Pt)to2SO_3(g)` is given by :
Rate=`K([SO_2])/([SO_3]^(1//2))`
which statement are correct :

Options

A. The overall order of reaction is `-1//2`
B. The overall order of reaction is `+1//2`
C. The reaction slows down as the product `SO_3` is build up
D. The rate of reaction does not depend upon concentration of `SO_3` formed

Explanation

To solve the problem, we need to analyze the given rate equation for the reaction:

\[ 2SO_2(g) + O_2(g) \overset{Pt}{\rightarrow} 2SO_3(g) \]

The rate of the reaction is given by:

\[ \text{Rate} = K \left( \frac{[SO_2]}{[SO_3]^{1/2}} \right) \]

### Step 1: Determine the overall order of the reaction
The overall order of a reaction is determined by summing the powers of the concentration terms in the rate equation.

- The power of \([SO_2]\) is 1.
- The power of \([SO_3]\) is \(-\frac{1}{2}\).

Thus, the overall order of the reaction is:

\[ \text{Overall Order} = 1 + \left(-\frac{1}{2}\right) = \frac{1}{2} \]

### Step 2: Analyze the effect of increasing \([SO_3]\) on the rate
From the rate equation, we can see that \([SO_3]\) is in the denominator. If the concentration of \([SO_3]\) increases, the overall rate of the reaction will decrease because the rate is inversely proportional to the concentration of \([SO_3]\).

### Step 3: Check the dependency of the rate on \([SO_3]\)
Since \([SO_3]\) appears in the rate equation, the rate of the reaction does depend on the concentration of \([SO_3]\). Therefore, if \([SO_3]\) is formed, it will affect the rate of the reaction.

### Conclusion:
Based on the analysis, we can summarize the correctness of the statements:

1. **Overall order of reaction is \(-\frac{1}{2}\)** - **Incorrect** (it is \(\frac{1}{2}\)).
2. **The reaction slows down as product \([SO_3]\) builds up** - **Correct** (because increasing \([SO_3]\) decreases the rate).
3. **The rate of reaction does not depend upon the concentration of \([SO_3]\)** - **Incorrect** (the rate does depend on \([SO_3]\)).
4. **Overall order of reaction is \(\frac{1}{2}\)** - **Correct**.

### Final Answer:
The correct statements are:
- The reaction slows down as product \([SO_3]\) builds up.
- The overall order of the reaction is \(\frac{1}{2}\).