Question

The amino acid alanine has two isomers, \(\alpha\) -alanine and \(\beta\) -alanine. When equal masses of these two compounds are dissolved in equal mass of a solvent, the solution of \(\alpha\) -alanine freezes at relatively lower temperature. Which form, \(\alpha\) -alanine or \(\beta\) -alanine, has the larger equilibrium constant for ionization? (a) \(\alpha\) -alanine (b) \(\beta\) -alanine (c) same for both (d) unpredictable

Short answer

\(\alpha\)-alanine has the larger equilibrium constant for ionization as evidenced by its solution having a lower freezing point when equal masses are dissolved.

Step-by-step solution

- Understand Freezing Point Depression

The freezing point of a solution is lowered when a solute is dissolved in it, and this effect is known as freezing point depression. It's related to the number of particles in a solution because more particles create a larger disturbance in the solvent's solidification process. An important point to consider is that the number of particles depends on the degree of ionization in the solution. Greater ionization leads to more particles.

- Compare Freezing Points and Ionization

Given that the solution of \(\alpha\)-alanine freezes at a relatively lower temperature compared to the solution of \(\beta\)-alanine when dissolved in equal mass of a solvent, this implies that there are more solute particles disrupting the solvent's crystalline structure in the solution with \(\alpha\)-alanine.

- Link Freezing Point and Equilibrium Constant

A larger number of particles in solution usually correlates with a higher degree of ionization, which in turn suggests a larger equilibrium constant (\(K\)). This is because a higher equilibrium constant for ionization implies a greater extent of ionization, resulting in more ions present in the solution, leading to a lower freezing point.

- Determine the Isomer with a Larger Equilibrium Constant

Since the solution of \(\alpha\)-alanine has a lower freezing point, it has a higher degree of ionization, and thus \(\alpha\)-alanine must have a larger equilibrium constant for ionization than \(\beta\)-alanine.

Key concepts

Equilibrium Constant for Ionization

The equilibrium constant for ionization, represented by the symbol \(K\), is a crucial concept in chemistry that provides insight into the degree to which a substance ionizes in solution. In the context of solutions and their properties, ionization refers to the process by which molecules or atoms split into ions when dissolved in a solvent.

The value of the equilibrium constant gives us an understanding of the position of the equilibrium in the ionization reaction. A higher equilibrium constant indicates a greater proportion of the solute exists as ions in the solution. This directly affects properties such as conductivity and, as we see with alanine isomers, the freezing point depression.

In practical terms, when a compound has a higher \(K\), it means that upon dissolving, more ions will be produced. These ions disrupt the solvent's ability to form a solid crystal lattice, thus lowering the freezing point more significantly. Hence, when comparing two isomers, if one has a larger equilibrium constant for ionization, it can be concluded that this isomer ionizes to a greater extent, generating more ions in solution and therefore leading to a greater freezing point depression.

Degree of Ionization

The degree of ionization relates to the fraction of the entire amount of solute that undergoes ionization when it is dissolved in a solvent. It's usually represented by the symbol \(\text{\(\alpha\)}\), and it ranges from 0 (no ionization) to 1 (complete ionization). Understanding the degree of ionization is essential for predicting how a solute will affect the properties of a solution such as electrical conductivity, osmotic pressure, and the freezing point.

In the exercise discussing alanine isomers, observing the lower freezing point of \(\alpha\)-alanine solution implies a higher degree of ionization for that isomer. This can be interpreted to mean that a larger proportion of the \(\alpha\)-alanine molecules dissociate into ions compared to \(\beta\)-alanine. This higher degree of ionization leads to more disturbance in the solvent and lowers the freezing point more substantially.

As such, the correlation between the degree of ionization and the equilibrium constant for ionization becomes clear; the higher the degree of ionization for a given solute, the larger the equilibrium constant.

Alanine Isomers

Isomers are molecules with the same molecular formula but different structural arrangements, which often lead to different physical and chemical properties. Alanine, an amino acid, has different isomers such as \(\alpha\)-alanine and \(\beta\)-alanine.

The structural difference between these isomers affects their ability to ionize when dissolved in a solvent, which in turn influences the properties of the solutions they form. For instance, \(\alpha\)-alanine is the isomer that naturally occurs in proteins, while \(\beta\)-alanine is found in different biological contexts.

Distinguishing Characteristics of Alanine Isomers

• \(\alpha\)-Alanine has an amino group (\(-NH_2\)) and a carboxyl group (\(-COOH\)) bonded directly to the same carbon atom, forming a chiral center.
• \(\beta\)-Alanine has the amino group at the beta position relative to the carboxyl group, creating a non-chiral molecule.

These structural variations contribute to the differences in properties, such as equilibrium constant for ionization, which ultimately lead to different freezing points when these isomers are dissolved in a solvent. This distinction helps explain why the solution of \(\alpha\)-alanine freezes at a relatively lower temperature than that of \(\beta\)-alanine, mirroring the isomers' varying tendencies to ionize.