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How can I calculate intermolecular forces of attraction?

Answer 1

The energy formulas for each interaction are given here.

London Dispersion Force

#V = −3/4(α^2I)/r^6#

where #α# is the polarizability, #r# is the distance, and #I# is the first ionization energy. The negative sign indicates the attractive interaction.

Dipole-Dipole Exchange

#V = −(2/3)(μ_A^2μ_B^2)/((4πϵ_0)^2r^6)1/(k_BT)#

where #mu_i# are the dipole moments, #epsilon# is the permittivity of the medium. #k_B# is Boltzmann's constant, and #T# is the Kelvin temperature.

Dipole-Ion interaction

#V = −(qμ)/((4πϵ_0)r^2)#

where #q# is the charge on the ion.

AN EXAMPLE

Calculate the dipole-dipole interaction energy at 298 K between two HF molecules. Assume that the positive and negative ends are separated by 400 pm. ϵ₀ = 8.854 × 10⁻¹² C²N⁻¹m⁻²; µ = 1.92 D; #k_B# = 1.381 × 10⁻²³ J•K⁻¹

Resolution

µ = 1.92 D × #(3.336 × 10⁻³⁰" C·m")/(1" D")# = 6.41 × 10⁻³⁰ C•m

#V = −(2/3)((μ_A^2μ_B^2)/(4πϵ_0)^2r^6)1/(k_BT)#

#V = −(2/3)((6.41 × 10^-30" C·m")^4)/((4π × 8.854 × 10^-12" C²N⁻¹m⁻²")^2(400 × 10⁻¹⁰" m")^6) × 1/(1.381 × 10⁻²³ J·K⁻¹ × 298" K")# = 5.37 × 10⁻²¹ J

In terms of molecules,

#V# = 5.37 × 10⁻²¹ J × 6.022 × 10²³ mol⁻¹ = 3240 J/mol = 3.24 kJ/mol

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Answer 2

Luna Chen

Intermolecular forces of attraction can be calculated using various methods, including computational simulations, empirical equations such as the Lennard-Jones potential, or experimental techniques such as spectroscopy or calorimetry. The specific method depends on factors such as the nature of the molecules involved and the desired level of accuracy in the calculation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.