What is the equilibrium constant for the reaction between benzylamine and${}^{\mathbf{HCI}}$?

• A chemical reaction's equilibrium constant is the value of its reaction quotient at chemical equilibrium, a state attained by a dynamic chemical system after a sufficient amount of time has passed in which its composition has no measurable tendency to change further.

• The equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture for a given set of reaction conditions.

• ${\mathbf{K}}_{\mathbf{c}}\mathbf{=}{\mathbf{K}}^{\mathbf{\text{'}}}\mathbf{/}\mathbf{T}\frac{{\left[R\right]}^{\mathbf{\rho }}{\left[S\right]}^{\mathbf{\sigma }}\mathbf{.}\mathbf{.}}{{\left[A\right]}^{\mathbf{\infty }}{\left[B\right]}^{\mathbf{\beta }}\mathbf{.}\mathbf{.}\mathbf{.}}$

The reaction between benzylamine and${}^{\mathbf{HCI}}$is a reaction of a weak base$\left({}^{{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{5}}{\mathbf{NH}}_{\mathbf{2}}}\right)$and a strong acid

$\mathbf{HCI}\mathbf{+}{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{5}}{\mathbf{NH}}_{\mathbf{2}}\mathbf{+}{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{5}}{\mathbf{NH}}_{\mathbf{3}}^{\mathbf{+}}\mathbf{+}{\mathbf{Cl}}^{\mathbf{-}}$

It is a reverse reaction of the conjugate acidlocalid="1654839015124" $\left({}^{{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{5}}{\mathbf{NH}}^{\mathbf{+}}}\right)$reaction, so to get the equilibirum constant for the reaction in the task, we need to inverse the${}^{{\mathbf{K}}_{\mathbf{a}}}$value. The${}^{{\mathbf{K}}_{\mathbf{a}}}$ value can be found in the appendix${}^{\mathbf{G}}$

$$\begin{gathered} \mathit{K}\mathbf{=}\frac{\mathbf{1}}{{}^{{\mathbf{K}}_{\mathbf{a}}}} \\ \mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{1}}{\mathbf{4}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}} \\ \mathbf{}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}} \end{gathered}$$

The equilibrium constant for the reaction between benzylamine and HCL is${}^{\mathbf{2}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}}$.