What is the Form of the Lennard-Jones Potential Between Two Water Molecules?

In summary, the question asks for the form of the Lennard-Jones potential between two water molecules, given the molar enthalpy of evaporation and density of water. The formula for the Lennard-Jones potential is V(r)=4ε[-(σ/r)6+(σ/r)12] where ε is a measure of attraction between molecules, σ is the distance at which the potential is zero, and r is the distance between particles. To find r, the atomic diameter is calculated using the given values and the number of nearest neighbours is assumed to be either 2 or 11. The form of the potential is then found by substituting the calculated r into the equation. The number of nearest neighbours is further
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Homework Statement


Deduce the form of the Lennard-Jones potential between two water molecules.

given/known:
molar enthalpy of evaporation of water is 4.1x104J/mol
density is 103kg/m3
Assume water molecule is surrounded by approximately ten nearest-neighbours.
Take Mr = 18

Homework Equations



from the sources i have:
V(r)=4ε[-(σ/r)6+(σ/r)12]

The Attempt at a Solution



ε is a measure of how strongly the molecules attract each other.
σ is the distance at which the intermolecular potential is zero.
r is the distance of separation between both particles.

its a bit unclear what the question means by "deduce the form" but I am assuming it means find the value r.

to find r i first find the atomic diameter d= [(Mr(X)x10-3)/(pNA)]1/3

where X is number of molecules
Mr = 18
p given at 103kg/m3
NA is avogadros constant.

and X I am unsure if it is 2 (because the question says two molecules) or if its 11 (because of the molecule plus its 10 "neighbours")

if X is 2 i get a diameter of 1.815x10-10
giving a radius of 9.07x10-11

if X is 11 i get d = 3.20x10-10
making r = 1.60x10-10

now to get the "form" i just sub an r into the potential equation??

however, i don't entirely understand the "ten nearst-neighbours" and what its used for.
i also don't use the molar enthalpy.
molar enthalpy isn't mentioned anywhere in my notes but online it says enthlpy is a measure of energy of the system.

some clarification would be much appreciated
thanks
 
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  • #2
kept at it and found

molecular enthalpy of sublimation Hm.s = 1/2(nNAΔE)
where n is the number of "nearest neighbours"
solving for ΔE i got 1.36x10-20 J which seems appropriate.

and ΔE = ε when r is at equilibrium distance.

so subbing that back into the lennard-jones and simplifying i get

5.44x10-20[-(σ/0.72x10-10)6+(σ/0.72x10-10)12]

is that meant to be "the form of the Lennard-Jones 6-12 potential" that the question says deduce?
 

1. What is the Lennard-Jones 6-12 potential?

The Lennard-Jones 6-12 potential is a mathematical model used to describe the interaction between two neutral atoms or molecules. It is based on the assumption that the attractive forces between particles decrease with distance according to the inverse sixth power, while the repulsive forces increase with distance according to the inverse twelfth power.

2. How is the Lennard-Jones 6-12 potential derived?

The Lennard-Jones 6-12 potential is derived from the combination of the van der Waals forces (which describe the attractive forces between particles) and the hard-sphere repulsion (which describes the repulsive forces between particles at close distances). It is named after the two scientists who first proposed it in 1924 - John Lennard-Jones and Thomas S. C. van der Waals.

3. What is the significance of the numbers 6 and 12 in the Lennard-Jones 6-12 potential?

The numbers 6 and 12 represent the powers in the mathematical equation used to describe the attractive and repulsive forces between particles. The 6 in the numerator of the attractive term corresponds to the inverse sixth power, while the 12 in the denominator of the repulsive term corresponds to the inverse twelfth power.

4. What are the applications of the Lennard-Jones 6-12 potential?

The Lennard-Jones 6-12 potential is commonly used in molecular simulations to model interactions between atoms and molecules. It is also used in the study of intermolecular forces, phase transitions, and the behavior of gases and liquids.

5. What are the limitations of the Lennard-Jones 6-12 potential?

While the Lennard-Jones 6-12 potential is a widely used and versatile model, it does have some limitations. It does not take into account the directional nature of interactions between particles, and it assumes that the particles are spherical and have no internal degrees of freedom. Additionally, it does not accurately describe interactions between charged particles.

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