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

✖Number of Particles refers to the total count or quantity of individual particles, typically molecules or ions, that come together to form a crystal in a crystallization process.ⓘ Number of Particles [N_T]			+10% -10%
✖Supersaturation Volume refers to the volume of a solution that contains a concentration of solute that exceeds its thermodynamic solubility limit at a given temperature and pressure.ⓘ Supersaturation Volume [ΔV]			+10% -10%
✖Supersaturation Time refers to the amount of time that a solution remains in a supersaturated state before the nucleation of crystals begins.ⓘ Supersaturation Time [Δt]			+10% -10%

✖Nucleation rate refers to the rate at which tiny crystal nuclei form in a supercooled or supersaturated solution.ⓘ Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation [B]

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

Formula

`"B" = "N"_{"T"}/("ΔV"*"Δt")`

Example

`"5.870513"="2100"/("5.42m³"*"66s")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Nucleation Rate = Number of Particles/(Supersaturation Volume*Supersaturation Time)
B = N_T/(ΔV*Δt)
This formula uses 4 Variables

Variables Used

Nucleation Rate - Nucleation rate refers to the rate at which tiny crystal nuclei form in a supercooled or supersaturated solution.
Number of Particles - Number of Particles refers to the total count or quantity of individual particles, typically molecules or ions, that come together to form a crystal in a crystallization process.
Supersaturation Volume - (Measured in Cubic Meter) - Supersaturation Volume refers to the volume of a solution that contains a concentration of solute that exceeds its thermodynamic solubility limit at a given temperature and pressure.
Supersaturation Time - (Measured in Second) - Supersaturation Time refers to the amount of time that a solution remains in a supersaturated state before the nucleation of crystals begins.

STEP 1: Convert Input(s) to Base Unit

Number of Particles: 2100 --> No Conversion Required
Supersaturation Volume: 5.42 Cubic Meter --> 5.42 Cubic Meter No Conversion Required
Supersaturation Time: 66 Second --> 66 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

B = N_T/(ΔV*Δt) --> 2100/(5.42*66)

Evaluating ... ...

B = 5.87051325058705

STEP 3: Convert Result to Output's Unit

5.87051325058705 --> No Conversion Required

FINAL ANSWER

5.87051325058705 ≈ 5.870513 <-- Nucleation Rate

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Crystallization » Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation

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Created by Rishi Vadodaria

Malviya National Institute Of Technology (MNIT JAIPUR ), JAIPUR

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Verified by Vaibhav Mishra

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

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

Nucleation Rate = Number of Particles/(Supersaturation Volume*Supersaturation Time)
B = N_T/(ΔV*Δt)

What is Nucleation Rate in Crystallization?

In the context of crystallization, the nucleation rate specifically refers to the rate at which tiny crystal nuclei form in a supercooled or supersaturated solution, leading to the growth of larger crystals. Crystallization is the process by which atoms, ions, or molecules arrange themselves into a highly ordered, three-dimensional structure known as a crystal lattice. Nucleation is the initial step in this process.

What is Volume of Supersaturation in Crystallization?

It's the volume of the solution in which the solute is dissolved to a greater extent than it would be in a saturated solution at the same conditions.

Supersaturation is a crucial concept in crystallization because it sets the stage for nucleation, which is the initial formation of crystal nuclei from the supersaturated solution. When the supersaturation level is high, the solution becomes more prone to nucleation, and crystals are more likely to form.

How to Calculate Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation?

Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation calculator uses Nucleation Rate = Number of Particles/(Supersaturation Volume*Supersaturation Time) to calculate the Nucleation Rate, The Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation formula is defined as the rate at which clusters of atoms, ions, or molecules come together and arrange themselves in a structured manner, forming the initial building blocks or nuclei for the growth of larger crystals. Nucleation Rate is denoted by B symbol.

How to calculate Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation using this online calculator? To use this online calculator for Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation, enter Number of Particles (N_T), Supersaturation Volume (ΔV) & Supersaturation Time (Δt) and hit the calculate button. Here is how the Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation calculation can be explained with given input values -> 5.870513 = 2100/(5.42*66).

FAQ

What is Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation?

The Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation formula is defined as the rate at which clusters of atoms, ions, or molecules come together and arrange themselves in a structured manner, forming the initial building blocks or nuclei for the growth of larger crystals and is represented as B = N_T/(ΔV*Δt) or Nucleation Rate = Number of Particles/(Supersaturation Volume*Supersaturation Time). Number of Particles refers to the total count or quantity of individual particles, typically molecules or ions, that come together to form a crystal in a crystallization process, Supersaturation Volume refers to the volume of a solution that contains a concentration of solute that exceeds its thermodynamic solubility limit at a given temperature and pressure & Supersaturation Time refers to the amount of time that a solution remains in a supersaturated state before the nucleation of crystals begins.

How to calculate Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation?

The Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation formula is defined as the rate at which clusters of atoms, ions, or molecules come together and arrange themselves in a structured manner, forming the initial building blocks or nuclei for the growth of larger crystals is calculated using Nucleation Rate = Number of Particles/(Supersaturation Volume*Supersaturation Time). To calculate Nucleation Rate for given Number of Particles and Volume of Constant Supersaturation, you need Number of Particles (N_T), Supersaturation Volume (ΔV) & Supersaturation Time (Δt). With our tool, you need to enter the respective value for Number of Particles, Supersaturation Volume & Supersaturation Time 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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