The equilibrium constant `K_c` for the following reaction will be
`K_2CO_3(aq)+BaSO_4(s) hArr BaCO_3(s) +K_2SO_4(aq)`

Options

A. `([CO_3^(2-)])/([SO_4^(2-)])`
B. `([K_2CO_3])/([K_2SO_4])`
C. `([BaSO_4])/([CO_3^(2-)])`
D. `([SO_4^(2-)])/([CO_3^(2-)])`

Answer

To determine the equilibrium constant \( K_c \) for the reaction:

\[ K_2CO_3(aq) + BaSO_4(s) \rightleftharpoons BaCO_3(s) + K_2SO_4(aq) \]

we follow these steps:

### Step 1: Identify the components of the reaction
The reaction consists of reactants and products:
- Reactants: \( K_2CO_3 \) (aqueous) and \( BaSO_4 \) (solid)
- Products: \( BaCO_3 \) (solid) and \( K_2SO_4 \) (aqueous)

### Step 2: Write the general expression for the equilibrium constant \( K_c \)
The equilibrium constant \( K_c \) is given by the formula:

\[ K_c = \frac{[\text{Products}]^{\text{stoichiometric coefficients}}}{[\text{Reactants}]^{\text{stoichiometric coefficients}}} \]

### Step 3: Exclude solids from the expression
In the expression for \( K_c \), we only include the concentrations of the aqueous and gaseous species. Solids do not appear in the equilibrium expression because their activities are considered to be constant. Therefore, we exclude \( BaSO_4 \) and \( BaCO_3 \) from the expression.

### Step 4: Write the expression for \( K_c \)
From the reaction, we have:
- Product: \( K_2SO_4 \) (aqueous)

Thus, the equilibrium expression simplifies to:

\[ K_c = [K_2SO_4] \]

### Step 5: Consider the dissociation of \( K_2SO_4 \)
If we consider the dissociation of \( K_2SO_4 \):

\[ K_2SO_4(aq) \rightleftharpoons 2K^+(aq) + SO_4^{2-}(aq) \]

We can express \( K_2SO_4 \) in terms of its ions:

\[ K_c = [K^+]^2 [SO_4^{2-}] \]

### Conclusion
The final expression for the equilibrium constant \( K_c \) for the given reaction is:

\[ K_c = [K^+]^2 [SO_4^{2-}] \]