## Q. 13.3

Writing Equilibrium Equations for Solution Reactions

Methyl tert-butyl ether (MTBE), a substance once used as a gasoline additive but now being phased out because of safety concerns, can be synthesized by heating methanol and tert-butyl alcohol with a catalytic amount of sulfuric acid:

$\begin{gathered}\mathrm{CH}_3 \mathrm{OH}(\text { soln })+\mathrm{C}_4 \mathrm{H}_9 \mathrm{OH}(\text { soln }) \underset{\text { catalyst }}{\stackrel{\mathrm{H}^{+}}{\rightleftharpoons}} \mathrm{C}_4 \mathrm{H}_9 \mathrm{OCH}_3(\text { soln })+\mathrm{H}_2 \mathrm{O}(\text { soln }) \\\text { Methanol } \quad \text { tert-Butyl alcohol } \quad \text { Methyl tert-butyl ether }\end{gathered}$

In this equation, soln denotes a largely organic solution that also contains water. Write the equilibrium-constant expression for the reaction.

STRATEGY

The rules for writing the equilibrium-constant expression apply to reactions in liquid solutions as well as to gas-phase reactions (reactions in gaseous mixtures). Put the concentrations of the products in the numerator and the concentrations of the reactants in the denominator. No exponents are needed because all the coefficients in the balanced chemical equation equal 1.

## Verified Solution

$K_{\mathrm{c}}=\frac{\left[\mathrm{C}_4 \mathrm{H}_9 \mathrm{OCH}_3\right]\left[\mathrm{H}_2 \mathrm{O}\right] \ \leftarrow \ Products}{\left[\mathrm{CH}_3 \mathrm{OH}\right]\left[\mathrm{C}_4 \mathrm{H}_9 \mathrm{OH}\right] \ \leftarrow \ Reactants }$