Chapter 2, Problem 1P

Suppose a chloride ion and a sodium ion are separated by a center—center distance of 5 Å. Is
the interaction energy (the energy required to pull them infinitely far apart) predicted to be larger if the medium between them is water, or if it is n-pentane? (See Table 2.5)
If Ca²⁺, Na+ and F¯ each have ionic radii ~1.16. Which ionic bond is stronger: Ca-F or Na-F? If Ca²+ is often bound on the surface of a protein by carboxylic acid functional groups. If the pK_a of a particular -COOH group is 4.2, would you predict Ca²+ to be most tightly bound at pH 8, pH 4.2, or pH 3? Explain your answer.

Table 2.5 Important properties of liquid water compared with those of n-pentane, a nonpolar,
Nonhydrogen-bonding liquid^a

Interpretation Introduction

Interpretation:

Interaction energy will be more in which of the given ion pairs must be predicted. The stronger ionic bond must be predicted among the given ionic compounds. In which of the given pH the interaction between ${\text{Ca}}^{\text{+2}}$ and $\text{COOH}$ of protein will be tight must be explained.

Concept introduction:

Ionic interaction depends on Columbic interaction which depends on the charge of ions and distance by which those ions are separated. It aslo depends on the dielectric constant of the medium and the viscosity of the medium. The ionic bond is stronger when the size of the ions is small, charge in ions is high. Lattice energy depends on Columbic interaction. The bond between ${\text{Ca}}^{\text{+2}}$ and $\text{COOH}$ will be tight if $\text{COOH}$ exists as ${\text{COO}}^{\text{-}}$. $\text{COOH}$ will be in deprotonated form when pH is greater than its ${\text{pK}}_{\text{a}}$ value.

Answer to Problem 1P

The interaction energy between sodium ion and chlorine ion will be larger in case of n-pentane.

$\text{CaF}$ will have stronger ionic bond than $\text{NaF}$. Among pH 8, pH 4.2 and pH 3, pH 8 will produce the strongest interaction between ${\text{Ca}}^{\text{+2}}$ and $\text{COOH}$ of protein.

Explanation of Solution

The interaction of ion pair will be more in case of n-pentane.

This is because the dielectric constant of n-pentane is $1.84$ which is much lesser than that of water $\left(78.3\right)$ . More is the dielectric constant of a solvent more is the decrease of the ionic interaction of two oppositely charged ions. The viscosity of water is also more than that of n-pentane.

Now, $\text{CaF}$ ionic bond will be stronger as compared to $\text{NaF}$.

This is because of Columbic interaction $\text{F = }\frac{\text{1}}{\text{K}}\text{×}\frac{{\text{q}}_{\text{1}}{\text{×q}}_{\text{2}}}{{\text{r}}^{\text{2}}}$

where ${\text{F, q}}_{\text{1}}{\text{, q}}_{\text{2}}\text{, K}$ are Columbic force, the charge of ion 1, the charge of ion 2 and dielectric constant of the medium or solvent.

As calcium ion has the double charge of sodium ion so $\text{CaF}$ will have a stronger ionic bond.

The ${\text{pK}}_{\text{a}}$ of the acid is $4.2$ . So, at a greater pH, the ${\text{Ca}}^{\text{+2}}$ will be tightly bound with the $\text{COOH}$ of protein.

This is because at pH greater than $4.2$ $\text{COOH}$ will be in a deprotonated form that is as ${\text{COO}}^{\text{-}}$ . So, the ionic interaction between ${\text{Ca}}^{\text{+2}}$ and ${\text{COO}}^{\text{-}}$ will be strongest.

So, the best pH is $8$.