Show that the complete chemical equation, the total ionic equation, and the net ionic equation for the reaction represented by the equation \({\rm{KI}}(aq) + {{\rm{I}}_2}(aq) \rightleftharpoons {\rm{K}}{{\rm{I}}_3}(aq)\) give the same expression for the reaction quotient. \({\rm{K}}{{\rm{I}}_3}\)is composed of the ions \({{\rm{K}}^ + }\) and \({{\rm{I}}_3}^ - .\)

A net ionic equation depicts simply the chemical species participating in a reaction, but a complete ionic equation includes spectator ions as well.

The reaction \({\rm{KI}}({\rm{aq}}) + {{\rm{I}}_2}({\rm{aq}}) \rightleftharpoons {\rm{K}}{{\rm{I}}_3}({\rm{aq}})\)

Let us show that the reaction quotients for the total ionic equation, the net ionic equation, and the full chemical equation all have the same expression.

The reaction quotient

\(\begin{array}{}{Q_c} = \frac{{\left[ {K{I_3}} \right]}}{{[KI] \cdot \left[ {{I_2}} \right]}}\\ = \frac{{\left[ {{K^ + }} \right] \cdot \left[ {I_3^ - } \right]}}{{\left[ {{K^ + }} \right] \cdot \left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}}\\ = \frac{{\left[ {I_3^ - } \right]}}{{\left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}}\end{array}\)

The reaction quotient

\(\begin{array}{c}{Q_c} = \frac{{\left[ {{K^ + }} \right] \cdot \left[ {I_3^ - } \right]}}{{\left[ {{K^ + }} \right] \cdot \left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}}\\ = \frac{{\left[ {I_3^ - } \right]}}{{\left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}}\end{array}\)

The reaction quotient

\({Q_c} = \frac{{\left[ {I_3^ - } \right]}}{{\left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}}\)

Therefore,

\(\begin{array}{c}{Q_c} = \frac{{\left[ {K{I_3}} \right]}}{{[KI] \cdot \left[ {{I_2}} \right]}}\\ = \frac{{\left[ {{K^ + }} \right] \cdot \left[ {I_3^ - } \right]}}{{\left[ {{K^ + }} \right] \cdot \left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}}\\ = \frac{{\left[ {I_3^ - } \right]}}{{\left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}}\end{array}\)