Van der Waals Interaction Energy between Two Spherical Bodies Calculator

↳

⤿

Van der Waals Force

Berthelot and Modified Berthelot Model of Real Gas

Clausius Model of Real Gas

Peng Robinson Model of Real Gas

Redlich Kwong Model of Real Gas

Saturation Vapour Pressure

Specific Heat Capacity

Wohl Model of Real Gas

⤿

Hamaker Coefficient

Number Density

✖Hamaker coefficient A can be defined for a Van der Waals body–body interaction.ⓘ Hamaker Coefficient [A]			+10% -10%
✖Radius of Spherical Body 1 represented as R1.ⓘ Radius of Spherical Body 1 [R₁]			+10% -10%
✖Radius of Spherical Body 2 represented as R1.ⓘ Radius of Spherical Body 2 [R₂]			+10% -10%
✖Center-to-center Distance is a concept for distances, also called on-center spacing, z = R1 + R2 + r.ⓘ Center-to-center Distance [z]			+10% -10%

✖Van der Waals interaction energy include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces.ⓘ Van der Waals Interaction Energy between Two Spherical Bodies [U_VWaals]

⎘ Copy

👎

Formula

✖

Van der Waals Interaction Energy between Two Spherical Bodies

Formula

`"U"_{"VWaals"} = (-("A"/6))*(((2*"R"_{"1"}*"R"_{"2"})/(("z"^2)-(("R"_{"1"}+"R"_{"2"})^2)))+((2*"R"_{"1"}*"R"_{"2"})/(("z"^2)-(("R"_{"1"}-"R"_{"2"})^2)))+ln((("z"^2)-(("R"_{"1"}+"R"_{"2"})^2))/(("z"^2)-(("R"_{"1"}-"R"_{"2"})^2))))`

Example

`"-0.618579J"=(-("100J"/6))*(((2*"12A"*"15A")/((("40A")^2)-(("12A"+"15A")^2)))+((2*"12A"*"15A")/((("40A")^2)-(("12A"-"15A")^2)))+ln(((("40A")^2)-(("12A"+"15A")^2))/((("40A")^2)-(("12A"-"15A")^2))))`

Calculator

LaTeX

Reset

👍

Download Real Gas Formula PDF

Van der Waals Interaction Energy between Two Spherical Bodies Solution

STEP 0: Pre-Calculation Summary

Formula Used

Van der Waals interaction energy = (-(Hamaker Coefficient/6))*(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2))))
U_VWaals = (-(A/6))*(((2*R₁*R₂)/((z^2)-((R₁+R₂)^2)))+((2*R₁*R₂)/((z^2)-((R₁-R₂)^2)))+ln(((z^2)-((R₁+R₂)^2))/((z^2)-((R₁-R₂)^2))))
This formula uses 1 Functions, 5 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Van der Waals interaction energy - (Measured in Joule) - Van der Waals interaction energy include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces.
Hamaker Coefficient - (Measured in Joule) - Hamaker coefficient A can be defined for a Van der Waals body–body interaction.
Radius of Spherical Body 1 - (Measured in Meter) - Radius of Spherical Body 1 represented as R1.
Radius of Spherical Body 2 - (Measured in Meter) - Radius of Spherical Body 2 represented as R1.
Center-to-center Distance - (Measured in Meter) - Center-to-center Distance is a concept for distances, also called on-center spacing, z = R1 + R2 + r.

STEP 1: Convert Input(s) to Base Unit

Hamaker Coefficient: 100 Joule --> 100 Joule No Conversion Required
Radius of Spherical Body 1: 12 Angstrom --> 1.2E-09 Meter (Check conversion here)
Radius of Spherical Body 2: 15 Angstrom --> 1.5E-09 Meter (Check conversion here)
Center-to-center Distance: 40 Angstrom --> 4E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U_VWaals = (-(A/6))*(((2*R₁*R₂)/((z^2)-((R₁+R₂)^2)))+((2*R₁*R₂)/((z^2)-((R₁-R₂)^2)))+ln(((z^2)-((R₁+R₂)^2))/((z^2)-((R₁-R₂)^2)))) --> (-(100/6))*(((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09+1.5E-09)^2)))+((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09-1.5E-09)^2)))+ln(((4E-09^2)-((1.2E-09+1.5E-09)^2))/((4E-09^2)-((1.2E-09-1.5E-09)^2))))

Evaluating ... ...

U_VWaals = -0.618579303089315

STEP 3: Convert Result to Output's Unit

-0.618579303089315 Joule --> No Conversion Required

FINAL ANSWER

-0.618579303089315 ≈ -0.618579 Joule <-- Van der Waals interaction energy

(Calculation completed in 00.004 seconds)

You are here -

Home » Chemistry » Kinetic Theory of Gases » Real Gas » Van der Waals Force » Van der Waals Interaction Energy between Two Spherical Bodies

Credits

Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

Prerana Bakli has created this Calculator and 800+ more calculators!

Verified by Prashant Singh

K J Somaiya College of science (K J Somaiya), Mumbai

Prashant Singh has verified this Calculator and 500+ more calculators!

< 21 Van der Waals Force Calculators

Van der Waals Interaction Energy between Two Spherical Bodies

Go Van der Waals interaction energy = (-(Hamaker Coefficient/6))*(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2))))

Distance between Surfaces given Van Der Waals Force between Two Spheres

Go Distance Between Surfaces = sqrt((Hamaker Coefficient*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Radius of Spherical Body 1+Radius of Spherical Body 2)*6*Potential Energy))

Van der Waals Force between Two Spheres

Go Van der Waals force = (Hamaker Coefficient*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Radius of Spherical Body 1+Radius of Spherical Body 2)*6*(Distance Between Surfaces^2))

Distance between Surfaces given Potential Energy in Limit of Close-Approach

Go Distance Between Surfaces = (-Hamaker Coefficient*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Radius of Spherical Body 1+Radius of Spherical Body 2)*6*Potential Energy)

Potential Energy in Limit of Closest-Approach

Go Potential Energy = (-Hamaker Coefficient*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Radius of Spherical Body 1+Radius of Spherical Body 2)*6*Distance Between Surfaces)

Radius of Spherical Body 1 given Van der Waals Force between Two Spheres

Go Radius of Spherical Body 1 = 1/((Hamaker Coefficient/(Van der Waals force*6*(Distance Between Surfaces^2)))-(1/Radius of Spherical Body 2))

Radius of Spherical Body 2 given Van Der Waals Force between Two Spheres

Go Radius of Spherical Body 2 = 1/((Hamaker Coefficient/(Van der Waals force*6*(Distance Between Surfaces^2)))-(1/Radius of Spherical Body 1))

Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach

Go Radius of Spherical Body 1 = 1/((-Hamaker Coefficient/(Potential Energy*6*Distance Between Surfaces))-(1/Radius of Spherical Body 2))

Radius of Spherical Body 2 given Potential Energy in Limit of Closest-Approach

Go Radius of Spherical Body 2 = 1/((-Hamaker Coefficient/(Potential Energy*6*Distance Between Surfaces))-(1/Radius of Spherical Body 1))

Coefficient in Particle-Particle Pair Interaction

Go Coefficient of Particle–Particle Pair Interaction = Hamaker Coefficient/((pi^2)*Number Density of particle 1*Number Density of particle 2)

Radius of Spherical Body 1 given Center-to-Center Distance

Go Radius of Spherical Body 1 = Center-to-center Distance-Distance Between Surfaces-Radius of Spherical Body 2

Radius of Spherical Body 2 given Center-to-Center Distance

Go Radius of Spherical Body 2 = Center-to-center Distance-Distance Between Surfaces-Radius of Spherical Body 1

Distance between Surfaces given Center-to-Center Distance

Go Distance Between Surfaces = Center-to-center Distance-Radius of Spherical Body 1-Radius of Spherical Body 2

Center-to-Center Distance

Go Center-to-center Distance = Radius of Spherical Body 1+Radius of Spherical Body 2+Distance Between Surfaces

Distance between Surfaces given Van Der Waals Pair Potential

Go Distance Between Surfaces = ((0-Coefficient of Particle–Particle Pair Interaction)/Van der Waals pair potential)^(1/6)

Coefficient in Particle-Particle Pair Interaction given Van der Waals Pair Potential

Go Coefficient of Particle–Particle Pair Interaction = (-1*Van der Waals pair potential)*(Distance Between Surfaces^6)

Van Der Waals Pair Potential

Go Van der Waals pair potential = (0-Coefficient of Particle–Particle Pair Interaction)/(Distance Between Surfaces^6)

Molar Mass given Number and Mass Density

Go Molar Mass = ([Avaga-no]*Mass Density)/Number Density

Mass Density given Number density

Go Mass Density = (Number Density*Molar Mass)/[Avaga-no]

Concentration given Number Density

Go Molar Concentration = Number Density/[Avaga-no]

Mass of Single Atom

Go Atomic Mass = Molecular Weight/[Avaga-no]

Van der Waals Interaction Energy between Two Spherical Bodies Formula

What are main characteristics of Van der Waals forces?

1) They are weaker than normal covalent and ionic bonds.
2) Van der Waals forces are additive and cannot be saturated.
3) They have no directional characteristic.
4) They are all short-range forces and hence only interactions between the nearest particles need to be considered (instead of all the particles). Van der Waals attraction is greater if the molecules are closer.
5) Van der Waals forces are independent of temperature except for dipole – dipole interactions.

How to Calculate Van der Waals Interaction Energy between Two Spherical Bodies?

Van der Waals Interaction Energy between Two Spherical Bodies calculator uses Van der Waals interaction energy = (-(Hamaker Coefficient/6))*(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))) to calculate the Van der Waals interaction energy, The Van der Waals interaction energy between two spherical bodies of radii R1 and R2 and with smooth surfaces was approximated in 1937 by Hamaker (using London's famous 1937 equation for the dispersion interaction energy between atoms/molecules as the starting point). Van der Waals interaction energy is denoted by U_VWaals symbol.

How to calculate Van der Waals Interaction Energy between Two Spherical Bodies using this online calculator? To use this online calculator for Van der Waals Interaction Energy between Two Spherical Bodies, enter Hamaker Coefficient (A), Radius of Spherical Body 1 (R₁), Radius of Spherical Body 2 (R₂) & Center-to-center Distance (z) and hit the calculate button. Here is how the Van der Waals Interaction Energy between Two Spherical Bodies calculation can be explained with given input values -> -0.618579 = (-(100/6))*(((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09+1.5E-09)^2)))+((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09-1.5E-09)^2)))+ln(((4E-09^2)-((1.2E-09+1.5E-09)^2))/((4E-09^2)-((1.2E-09-1.5E-09)^2)))).

FAQ

What is Van der Waals Interaction Energy between Two Spherical Bodies?

The Van der Waals interaction energy between two spherical bodies of radii R1 and R2 and with smooth surfaces was approximated in 1937 by Hamaker (using London's famous 1937 equation for the dispersion interaction energy between atoms/molecules as the starting point) and is represented as U_VWaals = (-(A/6))*(((2*R₁*R₂)/((z^2)-((R₁+R₂)^2)))+((2*R₁*R₂)/((z^2)-((R₁-R₂)^2)))+ln(((z^2)-((R₁+R₂)^2))/((z^2)-((R₁-R₂)^2)))) or Van der Waals interaction energy = (-(Hamaker Coefficient/6))*(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))). Hamaker coefficient A can be defined for a Van der Waals body–body interaction, Radius of Spherical Body 1 represented as R1, Radius of Spherical Body 2 represented as R1 & Center-to-center Distance is a concept for distances, also called on-center spacing, z = R1 + R2 + r.

How to calculate Van der Waals Interaction Energy between Two Spherical Bodies?

The Van der Waals interaction energy between two spherical bodies of radii R1 and R2 and with smooth surfaces was approximated in 1937 by Hamaker (using London's famous 1937 equation for the dispersion interaction energy between atoms/molecules as the starting point) is calculated using Van der Waals interaction energy = (-(Hamaker Coefficient/6))*(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))). To calculate Van der Waals Interaction Energy between Two Spherical Bodies, you need Hamaker Coefficient (A), Radius of Spherical Body 1 (R₁), Radius of Spherical Body 2 (R₂) & Center-to-center Distance (z). With our tool, you need to enter the respective value for Hamaker Coefficient, Radius of Spherical Body 1, Radius of Spherical Body 2 & Center-to-center Distance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search