# Interaction Energies and Debye Length

1. Feb 22, 2015

### burns96

1. The problem statement, all variables and given/known data
(c) (i) 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.

(ii) Using the Debye-Hückel Limiting Law, calculate the activity coefficient of H3O+ in a solution of 1 mol kg–1 HCl.

What is the Debye length of the H3O+ ion in this solution and what does this tell us about the ideality of the solution?

2. Relevant equations
Ion-dipole interaction:
V=−qμ/(4πϵ0)r2

Dipole-dipole interaction:
V=−2/3 μ12μ22/(4πϵ0)2r6 1/KBT

Dipole moment:
μ=qr

Debye length:
λD =√εTeff/n0e2
3. The attempt at a solution
Are these the right equations to use?
So for (i) I would use the first and for (ii) the second equation?
What do I use to work out the dipole moment of H3O+? I'm assuming not the 0.3nm value and the charge is 1?

For Debye length: ε = ε0(permittivity of a vacuum) x εr (relative permittivity).
Would I assume room temperature so T = 298K ?
I've got that n0 = constant volume density but not sure what that means, and e2 - are these both constants?
Sorry for all the questions, really confused.

2. Feb 27, 2015