The equilibrium constant for the reaction, `Ag_2O(s) hArr2Ag(s) +1/2 O_2 ` (g) is given by

Options

A. `K=([2Ag][1/2O_2])/([Ag_2O])`
B. `K=([Ag]^2[O_2]^(1/2))/([Ag_2O])`
C. `K=([Ag][O_2])/([Ag_2O])`
D. none of the above

Answer

To find the equilibrium constant for the reaction:

\[ \text{Ag}_2\text{O}(s) \rightleftharpoons 2\text{Ag}(s) + \frac{1}{2} \text{O}_2(g) \]

we follow these steps:

### Step 1: Identify the products and reactants
In the given reaction, we have:
- Reactant: \(\text{Ag}_2\text{O}(s)\) (solid)
- Products: \(2\text{Ag}(s)\) (solid) and \(\frac{1}{2}\text{O}_2(g)\) (gas)

### Step 2: Write the expression for the equilibrium constant (K)
The equilibrium constant \(K\) is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their respective coefficients in the balanced equation.

### Step 3: Consider only gaseous species
Since the equilibrium constant expression only includes gases and aqueous species, we will not include solids in our expression. Thus, we only consider \(\text{O}_2(g)\).

### Step 4: Write the equilibrium constant expression
From the reaction, the equilibrium constant \(K\) can be expressed as:

\[ K = \frac{[\text{Products}]}{[\text{Reactants}]} \]

Since the only gaseous product is \(\text{O}_2\) and its coefficient is \(\frac{1}{2}\), we write:

\[ K = [\text{O}_2]^{\frac{1}{2}} \]

### Step 5: Finalize the equilibrium constant expression
Since there are no gaseous reactants, the concentration of the reactants does not appear in the expression. Therefore, the final expression for the equilibrium constant for the reaction is:

\[ K = [\text{O}_2]^{\frac{1}{2}} \]

### Conclusion
The equilibrium constant for the reaction \(\text{Ag}_2\text{O}(s) \rightleftharpoons 2\text{Ag}(s) + \frac{1}{2}\text{O}_2(g)\) is:

\[ K = [\text{O}_2]^{\frac{1}{2}} \]