For the reaction `2SO_(2(g))+O_(2(g))hArr2SO_(3(g))`, if
`K_(p)=K_(c)(RT)^(X)` then the value of `X` is

Options

A. `-1`
B. `-(1)/(2)`
C. `+(1)/(2)`
D. `+1`

Explanation

To solve the problem, we need to determine the value of \( X \) in the equation \( K_p = K_c (RT)^X \) for the reaction:

\[ 2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)} \]

### Step 1: Identify the reaction and write down the equilibrium constant relationships

For the given reaction, we can express the relationship between \( K_p \) and \( K_c \) using the formula:

\[ K_p = K_c (RT)^{\Delta n} \]

where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta n \) is the change in the number of moles of gas, calculated as the number of moles of products minus the number of moles of reactants.

### Step 2: Calculate \( \Delta n \)

Now, we need to calculate \( \Delta n \):

- **Products**: From the reaction, we have 2 moles of \( SO_3 \) (2 moles).
- **Reactants**: We have 2 moles of \( SO_2 \) and 1 mole of \( O_2 \) (total 3 moles).

So, we can calculate \( \Delta n \):

\[ \Delta n = \text{(moles of products)} - \text{(moles of reactants)} = 2 - 3 = -1 \]

### Step 3: Substitute \( \Delta n \) into the equation

Now that we have \( \Delta n = -1 \), we can substitute this value into the equation:

\[ K_p = K_c (RT)^{-1} \]

### Step 4: Relate this to the given equation \( K_p = K_c (RT)^X \)

From our substitution, we can see that:

\[ K_p = K_c (RT)^{-1} \implies X = -1 \]

### Conclusion

Thus, the value of \( X \) is:

\[ \boxed{-1} \]