Which one is the correct representation for the reaction
`2SO_(2)(g)+O_(2)(g) hArr 2SO_(3)(g)`

Options

A. `K_(p)=([p_(SO_(3))]^(2))/([p_(SO_(2))]^(2)[p_(O_(2))])`
B. `K_(c)=([SO_(3)]^(2))/([SO_(2)]^(2)[O_(2)])`
C. `K_(p)=([n_(SO_(3))]^(2))/([n_(SO_(2))]^(2)[n_(O_(2))])xx[(P)/("Total mole")]^(-1)`
D. All the above

Answer

To determine the correct representation for the reaction \(2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)\), we need to analyze the equilibrium expressions for both \(K_c\) and \(K_p\).

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction is given as:
\[ 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) \]

2. **Write the Expression for \(K_c\)**:
The equilibrium constant \(K_c\) is defined in terms of the concentrations of the products and reactants. For the given reaction:
\[ K_c = \frac{[SO_3]^2}{[SO_2]^2 \times [O_2]} \]
Here, the concentration of each species is raised to the power of its coefficient in the balanced equation.

3. **Write the Expression for \(K_p\)**:
The equilibrium constant \(K_p\) is defined in terms of the partial pressures of the gases. For the same reaction:
\[ K_p = \frac{(P_{SO_3})^2}{(P_{SO_2})^2 \times (P_{O_2})} \]
Again, the partial pressure of each species is raised to the power of its coefficient.

4. **Relate \(K_c\) and \(K_p\)**:
The relationship between \(K_c\) and \(K_p\) can be expressed as:
\[ K_p = K_c \times (RT)^{\Delta n} \]
where \(\Delta n\) is the change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants). In this case:
\[ \Delta n = 2 - (2 + 1) = -1 \]
Therefore, the relationship becomes:
\[ K_p = K_c \times (RT)^{-1} \]

5. **Conclusion**:
Since both \(K_c\) and \(K_p\) have been derived correctly, the correct representation for the reaction is that both expressions are valid. Thus, if the options provided include both \(K_c\) and \(K_p\) representations, the correct answer would be that all representations are correct.

### Final Answer:
The correct representation for the reaction \(2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)\) is that all the expressions for \(K_c\) and \(K_p\) are valid.

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