Overall Excess Free Energy for Spherical Crystalline Body Calculator

✖Crystal Radius refers to the size of individual crystal grains or particles that form during the crystallization process.ⓘ Crystal Radius [r_crystal]			+10% -10%
✖Interfacial Tension, also known as surface tension, is a property of the interface between two immiscible substances, such as a liquid and a gas or two different liquids.ⓘ Interfacial Tension [σ]			+10% -10%
✖Free Energy Change Per Volume refers to the change in Gibbs free energy (ΔG) associated with the formation of a unit volume of a crystalline solid from a solution.ⓘ Free Energy Change Per Volume [ΔG_v]			+10% -10%

✖Overall Excess Energy refers to the total energy difference between the initial state of a system and the final state of the system when the crystallization process occurs.ⓘ Overall Excess Free Energy for Spherical Crystalline Body [ΔG]

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Overall Excess Free Energy for Spherical Crystalline Body

Formula

`"ΔG" = 4*pi*("r"_{"crystal"}^2)*"σ"+(4*pi/3)*("r"_{"crystal"}^3)*"ΔG"_{"v"}`

Example

`"9.4E^-12J"=4*pi*(("3.2μm")^2)*"0.0728N/m"+(4*pi/3)*(("3.2μm")^3)*"-0.048J"`

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Overall Excess Free Energy for Spherical Crystalline Body Solution

STEP 0: Pre-Calculation Summary

Formula Used

Overall Excess Energy = 4*pi*(Crystal Radius^2)*Interfacial Tension+(4*pi/3)*(Crystal Radius^3)*Free Energy Change Per Volume
ΔG = 4*pi*(r_crystal^2)*σ+(4*pi/3)*(r_crystal^3)*ΔG_v
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Overall Excess Energy - (Measured in Joule) - Overall Excess Energy refers to the total energy difference between the initial state of a system and the final state of the system when the crystallization process occurs.
Crystal Radius - (Measured in Meter) - Crystal Radius refers to the size of individual crystal grains or particles that form during the crystallization process.
Interfacial Tension - (Measured in Newton per Meter) - Interfacial Tension, also known as surface tension, is a property of the interface between two immiscible substances, such as a liquid and a gas or two different liquids.
Free Energy Change Per Volume - (Measured in Joule) - Free Energy Change Per Volume refers to the change in Gibbs free energy (ΔG) associated with the formation of a unit volume of a crystalline solid from a solution.

STEP 1: Convert Input(s) to Base Unit

Crystal Radius: 3.2 Micrometer --> 3.2E-06 Meter (Check conversion here)
Interfacial Tension: 0.0728 Newton per Meter --> 0.0728 Newton per Meter No Conversion Required
Free Energy Change Per Volume: -0.048 Joule --> -0.048 Joule No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔG = 4*pi*(r_crystal^2)*σ+(4*pi/3)*(r_crystal^3)*ΔG_v --> 4*pi*(3.2E-06^2)*0.0728+(4*pi/3)*(3.2E-06^3)*(-0.048)

Evaluating ... ...

ΔG = 9.36787084623024E-12

STEP 3: Convert Result to Output's Unit

9.36787084623024E-12 Joule --> No Conversion Required

FINAL ANSWER

9.36787084623024E-12 ≈ 9.4E-12 Joule <-- Overall Excess Energy

(Calculation completed in 00.020 seconds)

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Created by Rishi Vadodaria

Malviya National Institute Of Technology (MNIT JAIPUR ), JAIPUR

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DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< 24 Crystallization Calculators

Supersaturation based on activities of Species A and B

Go Supersaturation Ratio = ((Activity of Specie A^Stochiometric Value for A)*((Activity of Specie B^Stochiometric Value for B))/Solubility Product for Activity)^(1/(Stochiometric Value for A+Stochiometric Value for B))

Supersaturation based on Concentration of Species A and B along with Solubility Product

Go Supersaturation Ratio = ((Concentration of Specie A^Stochiometric Value for A)*((Concentration of specie B^Stochiometric Value for B))/Solubility Product)^(1/(Stochiometric Value for A+Stochiometric Value for B))

Solubility Product given Activity Coefficient and Mole Fraction of Species A and B

Go Solubility Product for Activity = ((Activity Coefficient of A*Mole Fraction A)^Stochiometric Value for A)*((Activity Coefficient of B*Mole Fraction B)^Stochiometric Value for B)

Overall Excess Free Energy for Spherical Crystalline Body

Go Overall Excess Energy = 4*pi*(Crystal Radius^2)*Interfacial Tension+(4*pi/3)*(Crystal Radius^3)*Free Energy Change Per Volume

Reaction Rate Constant in Crystallization given Mass Flux Density and Order of Reaction

Go Reaction Rate Constant = Mass Density of Crystal Surface/((Interfacial Concentration-Equilibrium Saturation Value)^Order of Integration Reaction)

Mass Flux Density given Reaction Rate Constant and Order of Integration Reaction

Go Mass Density of Crystal Surface = Reaction Rate Constant*(Interfacial Concentration-Equilibrium Saturation Value)^Order of Integration Reaction

Solubility Product given Activities of Species A and B

Go Solubility Product for Activity = (Activity of Specie A^Stochiometric Value for A)*(Activity of Specie B^Stochiometric Value for B)

Solubility Product given Concentration of Species A and B

Go Solubility Product = ((Concentration of Specie A)^Stochiometric Value for A)*(Concentration of specie B)^Stochiometric Value for B

Mass Flux Density given Mass Transfer Coefficient and Concentration Gradient

Go Mass Density of Crystal Surface = Mass Transfer Coefficient*(Bulk Solution Concentration-Interface Concentration)

Mass Transfer Coefficient given Mass Flux Density and Concentration Gradient

Go Mass Transfer Coefficient = Mass Density of Crystal Surface/(Bulk Solution Concentration-Interface Concentration)

Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation

Go Nucleation Rate = Number of Particles/(Supersaturation Volume*Supersaturation Time)

Number of Particles given Nucleation Rate and Supersaturation Volume and Time

Go Number of Particles = Nucleation Rate*(Supersaturation Volume*Supersaturation Time)

Supersaturation Volume given Nucleation Rate and Supersaturation Time

Go Supersaturation Volume = Number of Particles/(Nucleation Rate*Supersaturation Time)

Supersaturation Time given Nucleation Rate and Supersaturation Volume

Go Supersaturation Time = Number of Particles/(Nucleation Rate*Supersaturation Volume)

Supersaturation Ratio given Partial Pressure for Ideal Gas Condition

Go Supersaturation Ratio = Partial Pressure at Solution Concentration/Partial Pressure at Saturation Concentration

Kinetic Driving Force in Crystallization given Chemical Potential of Fluid and Crystal

Go Kinetic Driving Force = Chemical Potential of Fluid-Chemical Potential of Crystal

Relative Supersaturation given Degree of Saturation and Equilibrium Saturation Value

Go Relative Supersaturation = Degree of Supersaturation/Equilibrium Saturation Value

Equilibrium Saturation Value given Relative Supersaturation and Degree of Saturation

Go Equilibrium Saturation Value = Degree of Supersaturation/Relative Supersaturation

Degree of Supersaturation given Solution Concentration and Equilibrium Saturation Value

Go Degree of Supersaturation = Solution Concentration-Equilibrium Saturation Value

Solution Concentration given Degree of Supersaturation and Equilibrium Saturation Value

Go Solution Concentration = Degree of Supersaturation+Equilibrium Saturation Value

Equilibrium Saturation Value given Solution Concentration and Degree of Saturation

Go Equilibrium Saturation Value = Solution Concentration-Degree of Supersaturation

Supersaturation Ratio given Solution Concentration and Equilibrium Saturation Value

Go Supersaturation Ratio = Solution Concentration/Equilibrium Saturation Value

Suspension Density given Solid Density and Volumetric Holdup

Go Suspension Density = Solid Density*Volumetric Holdup

Relative Supersaturation for given Supersaturation Ratio

Go Relative Supersaturation = Supersaturation Ratio-1

Overall Excess Free Energy for Spherical Crystalline Body Formula

Overall Excess Energy = 4*pi*(Crystal Radius^2)*Interfacial Tension+(4*pi/3)*(Crystal Radius^3)*Free Energy Change Per Volume
ΔG = 4*pi*(r_crystal^2)*σ+(4*pi/3)*(r_crystal^3)*ΔG_v

What is the Significance of Excess Free Energy in Crystallization?

The crystallization process involves the formation of ordered, three-dimensional arrangements of atoms or molecules from a disordered or supersaturated solution.

The overall excess energy can be thought of as the energy barrier that must be overcome for the crystallization process to occur. When this energy barrier is surpassed, the solute particles start to aggregate and form stable crystal structures, resulting in the release of heat.

How to Calculate Overall Excess Free Energy for Spherical Crystalline Body?

Overall Excess Free Energy for Spherical Crystalline Body calculator uses Overall Excess Energy = 4*pi*(Crystal Radius^2)*Interfacial Tension+(4*pi/3)*(Crystal Radius^3)*Free Energy Change Per Volume to calculate the Overall Excess Energy, The Overall Excess Free Energy for Spherical Crystalline Body formula is defined as the total energy difference between the initial state of a system (typically a solution) and the final state of the system (a crystalline solid) when the crystallization process occurs. Overall Excess Energy is denoted by ΔG symbol.

How to calculate Overall Excess Free Energy for Spherical Crystalline Body using this online calculator? To use this online calculator for Overall Excess Free Energy for Spherical Crystalline Body, enter Crystal Radius (r_crystal), Interfacial Tension (σ) & Free Energy Change Per Volume (ΔG_v) and hit the calculate button. Here is how the Overall Excess Free Energy for Spherical Crystalline Body calculation can be explained with given input values -> 9.4E-12 = 4*pi*(3.2E-06^2)*0.0728+(4*pi/3)*(3.2E-06^3)*(-0.048).

FAQ

What is Overall Excess Free Energy for Spherical Crystalline Body?

The Overall Excess Free Energy for Spherical Crystalline Body formula is defined as the total energy difference between the initial state of a system (typically a solution) and the final state of the system (a crystalline solid) when the crystallization process occurs and is represented as ΔG = 4*pi*(r_crystal^2)*σ+(4*pi/3)*(r_crystal^3)*ΔG_v or Overall Excess Energy = 4*pi*(Crystal Radius^2)*Interfacial Tension+(4*pi/3)*(Crystal Radius^3)*Free Energy Change Per Volume. Crystal Radius refers to the size of individual crystal grains or particles that form during the crystallization process, Interfacial Tension, also known as surface tension, is a property of the interface between two immiscible substances, such as a liquid and a gas or two different liquids & Free Energy Change Per Volume refers to the change in Gibbs free energy (ΔG) associated with the formation of a unit volume of a crystalline solid from a solution.

How to calculate Overall Excess Free Energy for Spherical Crystalline Body?

The Overall Excess Free Energy for Spherical Crystalline Body formula is defined as the total energy difference between the initial state of a system (typically a solution) and the final state of the system (a crystalline solid) when the crystallization process occurs is calculated using Overall Excess Energy = 4*pi*(Crystal Radius^2)*Interfacial Tension+(4*pi/3)*(Crystal Radius^3)*Free Energy Change Per Volume. To calculate Overall Excess Free Energy for Spherical Crystalline Body, you need Crystal Radius (r_crystal), Interfacial Tension (σ) & Free Energy Change Per Volume (ΔG_v). With our tool, you need to enter the respective value for Crystal Radius, Interfacial Tension & Free Energy Change Per Volume and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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