Question

Calculate the value of the equilibrium constant, K c , for the reaction AgCl ( s ) + Cl − ( aq ) − ⇀ ↽ − AgCl − 2 ( aq ) K c = ? The solubility product constant, K sp , for AgCl is 1.77 × 10 − 10 and the overall formation constant, K f ( β 2 ), for AgCl − 2 is 1.8 × 10 5 .

Answer 1

Answer:

The equilibrium constant is  Kc $=1.9116*10^{-5}$  

Explanation:

      The equation for the formation of $AgCl_2^-$ can also be defined as  

                  $Ag^+(aq) + 2Cl^-(aq) -----> AgCl^-_2(aq)$

Now the formation constant is mathematically represented as

            $Kf =\frac{concentration \ of \ formation \ionic\ product }{concentration \ of \ formation \ionic \ reactant }$     for the formation of $AgCl_2^-$

Substituting parameters

                $Kf = \frac{[AgCl_2^-]}{[Ag^+ ] * [2Cl^-]}$

Now the value of  $Kf = 1.8*10^5$

    The solubility product is mathematically represented as

                    $Ksp = The \ product \ of \ the concentration \ of \ the \ reactant$

For $AgCl$

                   $Ksp = [Ag^+] [Cl ^-]$

The value is given as $Ksp = 1.77*10^{-10}$

The equation given to us in this question is

              $AgCl ( s ) + Cl ^- ( aq ) -----> AgCl ^-_ 2 ( aq )$

The equilibrium constant is mathematically represented as

                  $Kc =\frac{concentration \ of \ ionic \ product }{concentration \ of \ ionic \ reactant }$

For the above equation

                  $Kc = \frac{[AgCl^-_2]}{[Cl^-]}$

Now

        $Ksp \cdot Kf = \frac{[AgCl_2^-]}{[Ag^+ ] * [2Cl^-]}[Ag^+] [Cl ^-]$

                         $=\frac{[AgCl^-_2]}{[Cl^-]}$

                         $= Kc$

Substituting values

Therefore $Kc = 1.77*10^{-10} * 1.08*10^{5}$

                     Kc $=1.9116*10^{-5}$