Why Kp and Kc not defined for this reaction!?

Dear student
The equilibrium constant expression is the ratio of the concentrations of a reaction at equilibrium.  When dealing with partial pressures, Kp is used, whereas when dealing with concentrations (molarity), Kc is employed as the equilibrium constant.
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A system whose reactants, products, or both are in more than one phase is a heterogeneous equilibrium, such as the reaction of a gas with a solid or liquid.

The equilibrium constant expression is actually a ratio of activities.  The activity of each substance in the reaction is often approximated using a ratio of the molarity of a substance compared to the standard state of that substance. Tecause the molar concentrations of pure liquids and solids normally do not vary greatly with temperature, the ratio of the molarity to the standard state for substances that are liquids or solids always has a value of 1.
 

The given reaction is

HCl (g)  ⇌  H⁺ (aq)    +    Cl^-   (aq)

 The equilibrium constant expression for this reaction is as follows:

K_c  = $\frac{\left[1\right] \left[1\right]}{\left[HCl\right]}$ = $\frac{1}{\left[HCl\right]}$

The equilibrium constant for this reaction can also be written in terms of the partial pressures of the gases:

K_p =  $\frac{\left(1\right)}{(P_{HCl} )} =\frac{{\displaystyle 1}}{{\displaystyle (P_{HCl} )}}$

Hence the equilibrium constants can not be found for this reaction because it is a heterogeneous reaction

Regards