# 11.2: Interactions between Ion and Molecules with a Permanent Dipole

## Ion-Dipole Interactions

Ion-Dipole Forces are involved in solutions where an ionic compound can be dissolved into a molecular solvent with polar covalent bonds, like that of the solution of table salt (NaCl) into water. For example, the sodium ion/water cluster interaction is approximately 50 KJ/mol.

$Na^+ ↔ (H_2O)_n \tag{1}$

Figure 2a: Ion-Dipole interaction. Note the oxygen end of dipole is closer to the sodium than the hydrogen end, and so the net interaction is attractive.

The name "Ion dipole forces" describes what they are, which simply speaking, are the result of the Coulombic electrostatic interactions between an ion and the charged ends of a dipole. Here the term "Intermolecular Force" is a misnomer, even though it is commonly used, as these are the forces between ions with molecules possessing a dipole moment (unequal sharing of valence electrons). To gain an understanding we can start by looking at the Coulombic potential between two ions (eq. 2).

$V= \dfrac{q_1q_2}{(4\pi\epsilon_0) r} \tag{2}$

(ion-ion potential)

• $$r$$ is the distance of separation (note that the potential goes to zero when they are separated by infinity)
• $$q$$ is the charge of the ions

Note, in eq. (2) this potential can be either attractive (opposite charges) or repulsive (like charges), and that a negative potential leads to an attractive bonding type interaction. That is, the potential reaches zero when the distance between them (r) approaches infinity, and so a bond has a negative potential, in that in accordance with the first law of thermodynamics, you add energy to break a bond, and the broken bond has zero energy (review potential well diagrams).

So what is the difference between Ion-Ion and Ion-Dipole interactions?

$V= \dfrac{q_1\mu_2}{(4\pi\epsilon_0) r} \tag{2}$

$V=-\dfrac{\mid q_1\mid\mu_2}{(4\pi\epsilon_0) r^2} \tag{3}$

(ion-dipole potential)

• r is the distance of separation.
• q is the charge of the ion ( only the magnitude of the charge is shown here.)
• $$\mu$$ is the permanent dipole moment of the polar molecule.

There are several differences between ion-ion (eq.2) and ion-dipole (eq.3) types of interactions. First, is that the dipole has both a positive and negative end, leading to two interactions, one being attractive and the other repulsive. In the case of the sodium cation, the negative oxygen end of the dipole is attractive, and the positive hydrogen end is repulsive. This means the dipole aligns as in figure 11.2a, with the oxygen distance to the sodium being smaller than the hydrogen end of the dipole, and thus the attractive interaction is greater than the repulsive. As μ is positive, we use the absolute value sign around the charge, and place a minus sign in front of the equation, to indicate that the net ion-dipole interaction is a lowering of the system’s energy (attractive).

The second thing to note is that the potential drops off quicker, as Eq. 3 is an inverse square relationship to the radius (1/r2), while eq. 2 is a linear inverse relations ship (1/r). This means the ion-dipole are a shorter range interaction and diminish more rapidly the father the polar molecule is from the ion. This is logical, because the relative distance of the two dipoles from the ion become less significant the farther away they are. For example, if a cation had a radius of 200pm and the distance between the centers of positive and negative charges in a polar molecule molecule were also 200 pm, and they were touching each other, the radius for the negative end would be 100 pm, while the positive would be 300 pm, that is, the attractive interaction is 3 times closer than the repulsive. Now, if we moved them to a separation of 500 pm, the distances become 600 and 800, or only 3/4ths as close. That is, as you move the polar molecule away from the charge the repulsive and attractive interactions not only diminish, but also converge to more similar values,

Two are Repulsive:

• Positive Ion - Positive Dipole Repulsions (between cation and positive end of dipole)
• Negative Ion - Negative Dipole Repulsions (between anion and negative end of dipole)

Two are Attractive:

• Positive Ion - Negative Dipole Attractions (between the positive ion and the negative end of the dipole)
• Negative Ion - Positive Dipole Attractions (between the negative ion and the positive end of the dipole).

In visualizing these types of interactions one also needs to be realize that there are attractions between the ions with each other, and between the polar molecules with each other.

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