# 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

### Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

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