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 find the equilibrium constant \( K_c \) for the reaction:

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

we will follow these steps:

### Step 1: Write the expression for \( K_c \)

The equilibrium constant \( K_c \) is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their coefficients in the balanced equation.

For the given reaction, the expression for \( K_c \) is:

\[ K_c = \frac{[K_2SO_4]}{[K_2CO_3]} \]

### Step 2: Identify the states of the reactants and products

In the reaction:
- \( K_2CO_3 \) is in the aqueous state (aq).
- \( BaSO_4 \) is in the solid state (s).
- \( BaCO_3 \) is in the solid state (s).
- \( K_2SO_4 \) is in the aqueous state (aq).

### Step 3: Consider the contribution of solids to the equilibrium constant

In the expression for \( K_c \), only the species in the aqueous or gaseous state contribute to the equilibrium constant. The concentrations of solids do not appear in the expression because their activities are considered to be 1.

Thus, we can simplify our expression for \( K_c \):

\[ K_c = \frac{[K_2SO_4]}{[K_2CO_3]} \]

### Step 4: Write the dissociation of the aqueous species

We can further analyze the aqueous species. The dissociation of \( K_2CO_3 \) in water can be represented as:

\[ K_2CO_3 \rightleftharpoons 2K^+ + CO_3^{2-} \]

And for \( K_2SO_4 \):

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

### Step 5: Relate the concentrations of the ions

At equilibrium, the concentrations of the ions can be related back to the original compounds. However, since we are looking for \( K_c \) in terms of the original compounds, we can directly use the concentrations of \( K_2SO_4 \) and \( K_2CO_3 \).

### Final Expression for \( K_c \)

Thus, the final expression for the equilibrium constant \( K_c \) for the reaction is:

\[ K_c = \frac{[K_2SO_4]}{[K_2CO_3]} \]

### Conclusion

The equilibrium constant \( K_c \) for the reaction is determined by the concentrations of the aqueous species only, and the solids do not contribute to the equilibrium constant.

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