`Ag^(+) + NH_3 iff [Ag(NH_3)]^+ , k_1 = 1.6 xx 10^3`
`[Ag(NH_3)]^(+) + NH_3 iff [Ag(NH_3)_2]^+ , k_2 = 6.8 xx 10^3` the. The formation constant of `[Ag(NH_3)_2]^+` is

Options

A. `1.088 xx 10^6`
B. `6.08 xx 10^3`
C. `1.088 xx 10^7`
D. `1.6 xx 10^3`

Explanation

To find the formation constant of \([Ag(NH_3)_2]^+\), we can use the given equilibrium constants \(K_1\) and \(K_2\).

### Step-by-Step Solution:

1. **Write the reactions and their corresponding equilibrium constants:**
- The first reaction is:
\[ Ag^+ + NH_3 \iff [Ag(NH_3)]^+, \quad K_1 = 1.6 \times 10^3 \]
- The second reaction is:
\[ [Ag(NH_3)]^+ + NH_3 \iff [Ag(NH_3)_2]^+, \quad K_2 = 6.8 \times 10^3 \]

2. **Determine the overall reaction for the formation of \([Ag(NH_3)_2]^+\):**
- The overall reaction can be expressed as:
\[ Ag^+ + 2NH_3 \iff [Ag(NH_3)_2]^+ \]

3. **Combine the equilibrium constants:**
- The formation constant \(K_f\) for the overall reaction can be obtained by multiplying the two constants:
\[ K_f = K_1 \times K_2 \]
- Substitute the values of \(K_1\) and \(K_2\):
\[ K_f = (1.6 \times 10^3) \times (6.8 \times 10^3) \]

4. **Calculate \(K_f\):**
- Perform the multiplication:
\[ K_f = 1.6 \times 6.8 \times 10^{3+3} = 10.88 \times 10^6 \]
- This can be simplified to:
\[ K_f = 1.088 \times 10^7 \]

5. **Final Answer:**
- The formation constant of \([Ag(NH_3)_2]^+\) is:
\[ K_f = 1.088 \times 10^7 \]