Number of Particles given Nucleation Rate and Supersaturation Volume and Time Calculator

✖Nucleation rate refers to the rate at which tiny crystal nuclei form in a supercooled or supersaturated solution.ⓘ Nucleation Rate [B]			+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%

✖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 given Nucleation Rate and Supersaturation Volume and Time [N_T]

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Number of Particles given Nucleation Rate and Supersaturation Volume and Time

Formula

`"N"_{"T"} = "B"*("ΔV"*"Δt")`

Example

`"2100"="5.87051325058705"*("5.42m³"*"66s")`

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Number of Particles given Nucleation Rate and Supersaturation Volume and Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
Nucleation Rate - Nucleation rate refers to the rate at which tiny crystal nuclei form in a supercooled or supersaturated solution.
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

Nucleation Rate: 5.87051325058705 --> 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

N_T = B*(ΔV*Δt) --> 5.87051325058705*(5.42*66)

Evaluating ... ...

N_T = 2100

STEP 3: Convert Result to Output's Unit

2100 --> No Conversion Required

FINAL ANSWER

2100 <-- Number of Particles

(Calculation completed in 00.020 seconds)

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

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Created by Rishi Vadodaria

Malviya National Institute Of Technology (MNIT JAIPUR ), JAIPUR

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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

Number of Particles given Nucleation Rate and Supersaturation Volume and Time Formula

Number of Particles = Nucleation Rate*(Supersaturation Volume*Supersaturation Time)
N_T = B*(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 Number of Particles given Nucleation Rate and Supersaturation Volume and Time?

Number of Particles given Nucleation Rate and Supersaturation Volume and Time calculator uses Number of Particles = Nucleation Rate*(Supersaturation Volume*Supersaturation Time) to calculate the Number of Particles, The Number of Particles given Nucleation Rate and Supersaturation Volume and Time formula is defined as the formation of solid crystals from a supersaturated solution or melt. Number of Particles is denoted by N_T symbol.

How to calculate Number of Particles given Nucleation Rate and Supersaturation Volume and Time using this online calculator? To use this online calculator for Number of Particles given Nucleation Rate and Supersaturation Volume and Time, enter Nucleation Rate (B), Supersaturation Volume (ΔV) & Supersaturation Time (Δt) and hit the calculate button. Here is how the Number of Particles given Nucleation Rate and Supersaturation Volume and Time calculation can be explained with given input values -> 2100 = 5.87051325058705*(5.42*66).

FAQ

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

The Number of Particles given Nucleation Rate and Supersaturation Volume and Time formula is defined as the formation of solid crystals from a supersaturated solution or melt and is represented as N_T = B*(ΔV*Δt) or Number of Particles = Nucleation Rate*(Supersaturation Volume*Supersaturation Time). Nucleation rate refers to the rate at which tiny crystal nuclei form in a supercooled or supersaturated solution, 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 Number of Particles given Nucleation Rate and Supersaturation Volume and Time?

The Number of Particles given Nucleation Rate and Supersaturation Volume and Time formula is defined as the formation of solid crystals from a supersaturated solution or melt is calculated using Number of Particles = Nucleation Rate*(Supersaturation Volume*Supersaturation Time). To calculate Number of Particles given Nucleation Rate and Supersaturation Volume and Time, you need Nucleation Rate (B), Supersaturation Volume (ΔV) & Supersaturation Time (Δt). With our tool, you need to enter the respective value for Nucleation Rate, 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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