Complete and balance the following reaction: Ca(OH)_{2(aq)} + HC_2H_3O_{2(aq)} \to _____. Also,...

The reaction between calcium hydroxide, {eq}\rm Ca(OH)_2 {/eq}, and acetic acid, {eq}\rm HC_2H_3O_2 {/eq}, is an example of a double displacement reaction. In this reaction, the calcium ions, {eq}\rm Ca^{2+} {/eq}, abstract the acetate ions,{eq}\rm C_2H_3O_2^- {/eq} forming calcium acetate, {eq}\rm Ca(C_2H_3O_2)_2 {/eq}, while hydrogen ions, {eq}\rm H^+ {/eq}, pair up with hydroxide ions, {eq}\rm ^-OH {/eq}, to form water, {eq}\rm H_2O {/eq}:

{eq}\rm Ca(OH)_2(aq) + HC_2H_3O_2(aq) \to Ca(C_2H_3O_2)_2(aq) + H_2O(l) {/eq}

To balance this equation, we look at the number of ions on both sides. There is only 1 acetate ion on the reactant side and 2 on the product side. Thus, we add a coefficient of 2 before acetic acid to balance acetate:

{eq}\rm Ca(OH)_2(aq) + 2HC_2H_3O_2(aq) \to Ca(C_2H_3O_2)_2(aq) + H_2O(l) {/eq}

The addition of 2 before acetic acid increased the number of hydrogen ions to 2 on the reactant side. In water, there is only 1 hydrogen ion. Hence, to balance hydrogen ions, we introduce a coefficient of 2 before water giving us the balanced chemical equation below:

{eq}\rm Ca(OH)_2(aq) + 2HC_2H_3O_2(aq) \to Ca(C_2H_3O_2)_2(aq) + 2H_2O(l) {/eq}

To get the complete ionic equations, we split into ions all the compounds with the label (aq) which is short for aqueous and which suggests that the compounds form ions in water:

{eq}\rm Ca^{2+}(aq) + 2^-OH(aq) + 2H^+(aq) + 2C_2H_3O_2^-(aq) \to Ca^{2+}(aq) + 2C_2H_3O_2^-(aq) + 2H_2O(l) {/eq}

To determine the net ionic equation, we eliminate the ions appearing on both sides of the equation which are calcium ion and acetate ions:

{eq}\rm 2^-OH(aq) + 2H^+(aq) \to 2H_2O(l) {/eq}

We can simplify the net ionic equation by removing the coefficients 2:

{eq}\rm ^-OH(aq) + H^+(aq) \to H_2O(l) {/eq}