Chapter 3, Problem 35PE

Ethanol, ${\text{C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH}$, can be converted to acetic acid (the acid in vinegar), ${\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}$, by the action of sodium dichromate in aqueous sulfuric acid according to the following equation.

$\begin{array}{l}{\text{3C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH(}aq{\text{)+ 2Na}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}\left(aq\right){\text{ + 8H}}_{\text{2}}{\text{O}}_{\text{4}}\left(aq\right)\to \hfill \\ {\text{3HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\left(aq\right){\text{ + 2Cr}}_{\text{2}}{\left({\text{SO}}_{\text{4}}\right)}_3\left(aq\right){\text{ +2Na}}_{\text{2}}{\text{SO}}_{\text{4}}\left(aq\right)+11{\text{H}}_{\text{2}}\text{O}\hfill \end{array}$

In one experiment, 24.0 g of ${\text{C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH}$, 90.0 g of ${\text{Na}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$, and an excess of sulfuric acid were mixed, and 26.6 g of acetic acid $\left({\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\right)$ was isolated. Calculate the theoretical and percentage yields of ${\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}$.