For the reaction
`Cu(s)+2Ag^(o+)(aq)rarr Cu^(2+)(aq)+2Ag(s)`
Fill in the blanks in the following table for the three solution at equilibrium.
`{:("Solution",[Cu^(2+)(aq)],[Ag^(o+)(aq)],K L^(-1)),(,mol L^(-1),mol L^(-1),mol L^(-1)),(1.,(a),1.0xx10^(-9),2.0xx10^(15)),(2.,2.0xx10^(-7),1.0xx10^(-11),(b)),(3.,2.0xx10^(-2),(c),2.0xx10^(15)):}`

Explanation

To solve the problem, we need to fill in the blanks for the concentrations of \( Cu^{2+}(aq) \), \( Ag^{+}(aq) \), and the equilibrium constant \( K_c \) for the given reaction:

\[ Cu(s) + 2Ag^+(aq) \rightleftharpoons Cu^{2+}(aq) + 2Ag(s) \]

### Step-by-Step Solution:

1. **Write the expression for the equilibrium constant \( K_c \)**:
The equilibrium constant for the reaction can be expressed as:
\[ K_c = \frac{[Cu^{2+}]}{[Ag^+]^2} \]
Here, the concentration of solids (like \( Cu(s) \) and \( Ag(s) \)) is not included in the expression.

2. **Determine \( a \) for the first solution**:
Given:
- \( K_c = 2.0 \times 10^{15} \)
- \( [Ag^+] = 1.0 \times 10^{-9} \, mol \, L^{-1} \)

Plugging in the values into the \( K_c \) expression:
\[ 2.0 \times 10^{15} = \frac{[Cu^{2+}]}{(1.0 \times 10^{-9})^2} \]
Rearranging gives:
\[ [Cu^{2+}] = 2.0 \times 10^{15} \times (1.0 \times 10^{-9})^2 \]
\[ [Cu^{2+}] = 2.0 \times 10^{15} \times 1.0 \times 10^{-18} = 2.0 \times 10^{-3} \, mol \, L^{-1} \]
Thus, \( a = 2.0 \times 10^{-3} \, mol \, L^{-1} \).

3. **Determine \( b \) for the second solution**:
Given:
- \( [Cu^{2+}] = 2.0 \times 10^{-7} \, mol \, L^{-1} \)
- \( [Ag^+] = 1.0 \times 10^{-11} \, mol \, L^{-1} \)

Using the \( K_c \) expression:
\[ K_c = \frac{[Cu^{2+}]}{[Ag^+]^2} = \frac{2.0 \times 10^{-7}}{(1.0 \times 10^{-11})^2} \]
\[ K_c = \frac{2.0 \times 10^{-7}}{1.0 \times 10^{-22}} = 2.0 \times 10^{15} \]
Thus, \( b = 2.0 \times 10^{15} \).

4. **Determine \( c \) for the third solution**:
Given:
- \( [Cu^{2+}] = 2.0 \times 10^{-2} \, mol \, L^{-1} \)

Using the \( K_c \) expression:
\[ K_c = 2.0 \times 10^{15} = \frac{2.0 \times 10^{-2}}{[Ag^+]^2} \]
Rearranging gives:
\[ [Ag^+]^2 = \frac{2.0 \times 10^{-2}}{2.0 \times 10^{15}} = 1.0 \times 10^{-17} \]
Taking the square root:
\[ [Ag^+] = \sqrt{1.0 \times 10^{-17}} = 3.16 \times 10^{-9} \, mol \, L^{-1} \]
Thus, \( c = 3.16 \times 10^{-9} \, mol \, L^{-1} \).

### Final Answers:
- \( a = 2.0 \times 10^{-3} \, mol \, L^{-1} \)
- \( b = 2.0 \times 10^{15} \)
- \( c = 3.16 \times 10^{-9} \, mol \, L^{-1} \)