Calculating Ion-Ion and Ion-Dipole Interaction Energies in Aqueous Solutions

[burns96]

Homework Statement

Neglecting hydrogen-bonding, calculate the interaction energy between
(i) H₃O⁺ and H₂O and
(ii) H₃O⁺ and H₃O⁺,
if each pair is separated by 0.3 nm and assuming that the aqueous solvent can be treated as a medium with constant relative permittivity. Using your result, comment on the likelihood of ideal behaviour by H₃O⁺ at high molality

Homework Equations

Ion-dipole interaction
V=−qμ/(4πϵ₀)r²
r is the distance of separation.
q is the charge of the ion ( only the magnitude of the charge is shown here.)
μ is the permanent dipole moment of the polar molecule.

Ion-ion interaction
U(r)= (q1q2)/(4*π*E0)*(1/r)

The Attempt at a Solution

V=−qμ/(4πϵ₀)r²
r is the distance of separation so 0.3nm
q is the charge of the ion so 1 here
μ is the permanent dipole moment of the polar molecule 6.2 x 10^-30 C m
So if I can treat it as having constant relative permittivity then I just need the permittivity of a vacuum.
so
(-1 x 6.2 x 10^-30)/(4π8.85 x 10^-12x(0.3x10^-9)²
And I got 0.619 from this which doesn't sound right?

U(r)= (q1q2)/(4*π*E0)*(1/r)
(1x1)/(4π8.85 x 10^-12x(0.3x10^-9) x (1/0.3x10^-9)
=2.70 x 10¹⁸ which sounds ridiculous

 

[DrClaude]

You definitely need to put units in there.