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Energies of interaction

  1. Feb 24, 2015 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant 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)

    3. 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
     
  2. jcsd
  3. Feb 25, 2015 #2

    DrClaude

    User Avatar

    Staff: Mentor

    You definitely need to put units in there.
     
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