Question

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 \({{\rm{I}}_3}^ - .\)

Short answer

The complete chemical equation, the total ionic equation, and the net ionic equation for the reaction is composed of the ions \({K^ + }\) and \({I_3}^ - \) as\(\frac{{\left[ {K{I_3}} \right]}}{{[KI] \cdot \left[ {{I_2}} \right]}} = \frac{{\left[ {{K^ + }} \right] \cdot \left[ {I_3^ - } \right]}}{{\left[ {{K^ + }} \right] \cdot \left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}} = \frac{{\left[ {I_3^ - } \right]}}{{\left[ {{I^ - }} \right] \cdot \left[ {{I_2}} \right]}}\)

Step-by-step solution

Total ionic equation versus the net ionic equation

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

Expression for the chemical equations

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

• \({\rm{K}}{{\rm{l}}_3}\)is composed of the ions\({{\rm{K}}^ + }\)and\({\rm{I}}_3^ - \)

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 complete chemical equation \({\rm{KI}}({\rm{aq}}) + {{\rm{I}}_2}({\rm{aq}})\rightleftharpoons{\rm{K}}{{\rm{I}}_3}({\rm{aq}})\)

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 total ionic equation \({{\rm{K}}^ + }({\rm{aq}}) + {{\rm{I}}^ - }({\rm{aq}}) + {{\rm{I}}_2}({\rm{aq}})\rightleftharpoons {{\rm{K}}^ + }({\rm{aq}}) + {\rm{I}}_3^ - ({\rm{aq}})\)

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 net ionic equation \({{\rm{I}}^ - }({\rm{aq}}) + {{\rm{I}}_2}({\rm{aq}})\rightleftharpoons {\rm{I}}_3^ - ({\rm{aq}})\)

The reaction quotient

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

Therefore,

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