0.1M AgNO3 and 0.3M KCN are added . Find final concentration of Ag+, CN- and Ag(CN)2- if Kc is10^-21 for reaction Ag(CN)2-=Ag+ + 2CN-

To determine the final concentrations of Ag⁺, CN^-, and Ag(CN)₂^- after mixing 0.1 M AgNO₃ and 0.3 M KCN, we need to analyze the equilibrium established by the reaction:

The Reaction and Initial Concentrations

The reaction we are considering is:

Ag(CN)₂^- ⇌ Ag⁺ + 2CN^-

Initially, we have:

• Ag⁺: 0.1 M (from AgNO₃)
• CN^-: 0.3 M (from KCN)
• Ag(CN)₂^-: 0 M (no complex formed yet)

Setting Up the Equilibrium Expression

The equilibrium constant expression for the reaction is given by:

K_c = [Ag⁺][CN^-]² / [Ag(CN)_2-

Given that K_c = 10^-21, we can set up the equilibrium concentrations as follows:

Change in Concentrations

Let x be the change in concentration of Ag(CN)₂^- that forms at equilibrium. Therefore, at equilibrium, we have:

• [Ag⁺] = 0.1 - x
• [CN^-] = 0.3 - 2x
• [Ag(CN)_{2-] = x}

Substituting into the Equilibrium Expression

Now, substituting these expressions into the K_c equation gives:

10^-21 = (0.1 - x)(0.3 - 2x)² / x

Assuming x is Small

Since K_c is very small, we can assume that x is much smaller than the initial concentrations. Thus, we can approximate:

• [Ag⁺] ≈ 0.1
• [CN^-] ≈ 0.3

Now, substituting these approximations into the equation:

10^-21 ≈ (0.1)(0.3)² / x

Calculating the right side:

10^-21 ≈ (0.1)(0.09) / x

10^-21 ≈ 0.009 / x

Rearranging gives:

x ≈ 0.009 / 10^-21 = 9 × 10^-19 M

Final Concentrations

Now we can find the final concentrations:

• [Ag⁺] ≈ 0.1 M
• [CN^-] ≈ 0.3 - 2(9 × 10^-19) ≈ 0.3 M
• [Ag(CN)_{2-] = x ≈ 9 × 10^-19 M}

In summary, the final concentrations after the reaction reaches equilibrium are approximately:

• [Ag⁺] ≈ 0.1 M
• [CN^-] ≈ 0.3 M
• [Ag(CN)_{2-] ≈ 9 × 10^-19 M}

This analysis shows how the equilibrium constant influences the concentrations of the species involved in the reaction, illustrating the principles of chemical equilibrium effectively.