Question

Question:The amino acid alanine has two isomers, \(\alpha - alanine\;\)and \(\beta - alanine\;\). When equal masses of these two compounds are dissolved in equal amounts of a solvent, the solution of \(\alpha - alanine\;\)freezes at the lowest temperature. Which form, \(\alpha - alanine\;\)or\(\beta - alanine\;\) has the larger equilibrium constant for ionization \(\left( {HX \rightleftharpoons {H^ + } + {X^ - }} \right)?\)

Short answer

\(\alpha {\rm{ - alanine\;}}\)solution has the larger equilibrium constant for ionization

Step-by-step solution

Define Equilibrium

Definition of equilibrium constant: A number that expresses the relationship between the amounts of products and reactants present at equilibrium in a reversible chemical reaction at a given temperature

Solution of two compounds

The we have two solutions. Solution of \(\alpha {\rm{ - alanine\;}}\)we have two solutions. Solution of \(\alpha {\rm{ - alanine\;}}\) and solution of\(\beta {\rm{ - alanine\;}}\) (equal masses of these two compounds in equal amounts of a solvent)

\(\alpha {\rm{ - alanine\;}}\)freezes at the lower temperature.

Let us find, which solution has the larger equilibrium constant for ionization

The Equilibrium constant

\[\begin{aligned}{{}{}}{{\text{HX}} \rightleftharpoons {{\text{H}}^ + } + {{\text{X}}^ - }} \\ {{K_c} =\frac{{\left[ {{H^ + }} \right] \cdot \left[ {{X^ - }} \right]}}{{[HX]}}} \end{aligned}\]

The larger equilibrium constant of Ionization

The Freezing point of depression - lowering the temperature of the freezing point of a solvent caused by adding ionic solute.

Since, \(\alpha {\rm{ - alanine\;}}\)- alanine solution has lower freezing point, it contains more ions\(\left( {{{\rm{H}}^ + }{\rm{and\;}}{{\rm{X}}^ - }} \right)\)hence, the equilibrium constant will be larger.

\(\alpha {\rm{ - alanine\;}}\)solution has the larger equilibrium constant for ionization