1. Ag+ (aq) + 2NH3(aq) = [Ag(NH3)2]+ (aq) K = 1.7 x 107 II. AgCl(s) Ag+ (aq) + Cl(aq) K 1.6 x 10-10 1 What is the K value for the reaction below? AgCl(s) + 2NH3(aq) = Coefficient (green) || [Ag (NH3)2]+ (aq) + Cl- (aq) K = [?] x 10?] Exponent (yellow) Enter

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### Chemical Equilibrium Problem

Below are two equilibrium reactions and their respective equilibrium constants (K):

I. \( \text{Ag}^+(aq) + 2\text{NH}_3(aq) \iff [\text{Ag(NH}_3\text{)}_2]^+(aq) \)
\[ K = 1.7 \times 10^7 \]

II. \( \text{AgCl}(s) \iff \text{Ag}^+(aq) + \text{Cl}^-(aq) \)
\[ K = 1.6 \times 10^{-10} \]

Now, let's consider the following reaction:

\[ \text{AgCl}(s) + 2\text{NH}_3(aq) \iff [\text{Ag(NH}_3\text{)}_2]^+(aq) + \text{Cl}^-(aq) \]

### Question
What is the equilibrium constant \( K \) for the above reaction?

### Calculation
To determine the equilibrium constant for the reaction, we need to combine the given reactions and their equilibrium constants. The equilibrium constant for the overall reaction can be found by multiplying the equilibrium constants of the individual steps.

1. **Combine the reactions:**
   
   - Reaction I involves the formation of \( [\text{Ag(NH}_3\text{)}_2]^+ \) from \( \text{Ag}^+ \) and \( \text{NH}_3 \).
   - Reaction II involves the dissociation of \( \text{AgCl} \) into \( \text{Ag}^+ \) and \( \text{Cl}^- \).

2. **Use the given equilibrium constants:**
   
   \[
    K_{\text{overall}} = K_{\text{reaction I}} \times K_{\text{reaction II}}
   \]

   \[
    K_{\text{overall}} = (1.7 \times 10^7) \times (1.6 \times 10^{-10})
   \]

3. **Solve for \( K \):**

   \[
    K_{\text{overall}} = (1.7 \times 1.6) \times 10^{7 + (-10)}
   \]
   \[
    K_{\text{overall}} = 2.72 \times 10^{-3}
   \]
Transcribed Image Text:### Chemical Equilibrium Problem Below are two equilibrium reactions and their respective equilibrium constants (K): I. \( \text{Ag}^+(aq) + 2\text{NH}_3(aq) \iff [\text{Ag(NH}_3\text{)}_2]^+(aq) \) \[ K = 1.7 \times 10^7 \] II. \( \text{AgCl}(s) \iff \text{Ag}^+(aq) + \text{Cl}^-(aq) \) \[ K = 1.6 \times 10^{-10} \] Now, let's consider the following reaction: \[ \text{AgCl}(s) + 2\text{NH}_3(aq) \iff [\text{Ag(NH}_3\text{)}_2]^+(aq) + \text{Cl}^-(aq) \] ### Question What is the equilibrium constant \( K \) for the above reaction? ### Calculation To determine the equilibrium constant for the reaction, we need to combine the given reactions and their equilibrium constants. The equilibrium constant for the overall reaction can be found by multiplying the equilibrium constants of the individual steps. 1. **Combine the reactions:** - Reaction I involves the formation of \( [\text{Ag(NH}_3\text{)}_2]^+ \) from \( \text{Ag}^+ \) and \( \text{NH}_3 \). - Reaction II involves the dissociation of \( \text{AgCl} \) into \( \text{Ag}^+ \) and \( \text{Cl}^- \). 2. **Use the given equilibrium constants:** \[ K_{\text{overall}} = K_{\text{reaction I}} \times K_{\text{reaction II}} \] \[ K_{\text{overall}} = (1.7 \times 10^7) \times (1.6 \times 10^{-10}) \] 3. **Solve for \( K \):** \[ K_{\text{overall}} = (1.7 \times 1.6) \times 10^{7 + (-10)} \] \[ K_{\text{overall}} = 2.72 \times 10^{-3} \]
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