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Number of Extraction Stages by Kremser Equation Formula

GoNumber of Ideal Equilibrium Extraction Stages Formula

GoNumber of Stages for Extraction Factor equal to 1 Formula

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The Number of Equilibrium Extraction Stages is the number of Ideal Equilibrium stages required for Liquid-Liquid Extraction. Check FAQs

N = \frac{\log 10 ((\frac{z C - (\frac{y s}{K Solute})}{(\frac{x C - y s}{K Solute})}) \cdot (1 - (\frac{1}{ε})) + (\frac{1}{ε}))}{\log 10 (ε)}

N - Number of Equilibrium Extraction Stages?z_C - Mass Fraction of Solute in the Feed?y_s - Mass Fraction of Solute in the Solvent?K_Solute - Distribution Coefficient of Solute?x_C - Mass Fraction of Solute in the Raffinate?ε - Extraction Factor?

Number of Extraction Stages by Kremser Equation Example

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Here is how the Number of Extraction Stages by Kremser Equation equation looks like with Values.

Here is how the Number of Extraction Stages by Kremser Equation equation looks like with Units.

Here is how the Number of Extraction Stages by Kremser Equation equation looks like.

2.6502 = \frac{\log 10 ((\frac{0.5 - (\frac{0.05}{2.6})}{(\frac{0.1394 - 0.05}{2.6})}) \cdot (1 - (\frac{1}{2.2})) + (\frac{1}{2.2}))}{\log 10 (2.2)}

2.6502 = \frac{\log 10 ((\frac{0.5 - (\frac{0.05}{2.6})}{(\frac{0.1394 - 0.05}{2.6})}) \cdot (1 - (\frac{1}{2.2})) + (\frac{1}{2.2}))}{\log 10 (2.2)}

2.6502 = \frac{\log 10 ((\frac{0.5 - (\frac{0.05}{2.6})}{(\frac{0.1394 - 0.05}{2.6})}) \cdot (1 - (\frac{1}{2.2})) + (\frac{1}{2.2}))}{\log 10 (2.2)}

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Number of Extraction Stages by Kremser Equation Solution

Follow our step by step solution on how to calculate Number of Extraction Stages by Kremser Equation?

FIRST Step Consider the formula

N = \frac{\log 10 ((\frac{z C - (\frac{y s}{K Solute})}{(\frac{x C - y s}{K Solute})}) \cdot (1 - (\frac{1}{ε})) + (\frac{1}{ε}))}{\log 10 (ε)}

Next Step Substitute values of Variables

∴

N = \frac{\log 10 ((\frac{0.5 - (\frac{0.05}{2.6})}{(\frac{0.1394 - 0.05}{2.6})}) \cdot (1 - (\frac{1}{2.2})) + (\frac{1}{2.2}))}{\log 10 (2.2)}

Next Step Prepare to Evaluate

∴

N = \frac{\log 10 ((\frac{0.5 - (\frac{0.05}{2.6})}{(\frac{0.1394 - 0.05}{2.6})}) \cdot (1 - (\frac{1}{2.2})) + (\frac{1}{2.2}))}{\log 10 (2.2)}

Next Step Evaluate

∴

N = 2.65015450169299

LAST Step Rounding Answer

∴

N = 2.6502

Number of Extraction Stages by Kremser Equation Formula Elements

Variables

Functions

Number of Equilibrium Extraction Stages

The Number of Equilibrium Extraction Stages is the number of Ideal Equilibrium stages required for Liquid-Liquid Extraction.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Equilibrium Extraction Stages

Mass Fraction of Solute in the Feed

The Mass Fraction of Solute in the Feed is the mass fraction of the solute in the Feed to the Liquid-Liquid Extraction operation.

Symbol: z_C

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Mass Fraction of Solute in the Feed

Mass Fraction of Solute in the Solvent

The Mass Fraction of Solute in the Solvent is the mass ratio of the solute in the inlet solvent to the solvent mass in Liquid-Liquid Extraction operation.

Symbol: y_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mass Fraction of Solute in the Solvent

Distribution Coefficient of Solute

The distribution coefficient of solute is defined as the concentration of solute in the extract phase divided by the concentration of solute in the raffinate phase.

Symbol: K_Solute

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Distribution Coefficient of Solute

Mass Fraction of Solute in the Raffinate

The Mass Fraction of Solute in the Raffinate Phase is the mass fraction of the solute in the raffinate phase after separation of the ternary mixture.

Symbol: x_C

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Mass Fraction of Solute in the Raffinate

Extraction Factor

The Extraction Factor is defined as the ratio of the slope of equilibrium line to the slope of operating line.

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Extraction Factor

log10

The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function.

Syntax: log10(Number)

Other Formulas to find Number of Equilibrium Extraction Stages

Go Number of Ideal Equilibrium Extraction Stages

N = \frac{\log 10 (\frac{z C}{X N})}{\log 10 ((\frac{K Solute \cdot E'}{F'}) + 1)}

Go Number of Stages for Extraction Factor equal to 1

N = (\frac{z C - (\frac{y s}{K Solute})}{x C - (\frac{y s}{K Solute})}) - 1

Other formulas in Kremser's Equation for Liquid Liquid Extraction category

Go Distribution Coefficient of Carrier Liquid from Activity Coefficients

K CarrierLiq = \frac{Υa R}{Υa E}

Go Distribution Coefficient of Carrier Liquid from Mass Fraction

K CarrierLiq = \frac{y A}{x A}

Go Distribution Coefficient of Solute from Activity Coefficient

K Solute = \frac{Υc R}{Υc E}

Go Distribution Coefficient of Solute from Mass Fractions

K Solute = \frac{y C}{x C}

How to Evaluate Number of Extraction Stages by Kremser Equation?

Number of Extraction Stages by Kremser Equation evaluator uses Number of Equilibrium Extraction Stages = (log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(((Mass Fraction of Solute in the Raffinate-Mass Fraction of Solute in the Solvent)/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor)))/(log10(Extraction Factor)) to evaluate the Number of Equilibrium Extraction Stages, The Number of Extraction Stages by Kremser Equation formula is defined as the calculation for number of stages for extraction operation according to the Kremser Souders Brown equation. Number of Equilibrium Extraction Stages is denoted by N symbol.

How to evaluate Number of Extraction Stages by Kremser Equation using this online evaluator? To use this online evaluator for Number of Extraction Stages by Kremser Equation, enter Mass Fraction of Solute in the Feed (z_C), Mass Fraction of Solute in the Solvent (y_s), Distribution Coefficient of Solute (K_Solute), Mass Fraction of Solute in the Raffinate (x_C) & Extraction Factor (ε) and hit the calculate button.

FAQs on Number of Extraction Stages by Kremser Equation

What is the formula to find Number of Extraction Stages by Kremser Equation?

The formula of Number of Extraction Stages by Kremser Equation is expressed as Number of Equilibrium Extraction Stages = (log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(((Mass Fraction of Solute in the Raffinate-Mass Fraction of Solute in the Solvent)/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor)))/(log10(Extraction Factor)). Here is an example- 2.650155 = (log10(((0.5-(0.05/2.6))/(((0.1394-0.05)/2.6)))*(1-(1/2.2))+(1/2.2)))/(log10(2.2)).

How to calculate Number of Extraction Stages by Kremser Equation?

With Mass Fraction of Solute in the Feed (z_C), Mass Fraction of Solute in the Solvent (y_s), Distribution Coefficient of Solute (K_Solute), Mass Fraction of Solute in the Raffinate (x_C) & Extraction Factor (ε) we can find Number of Extraction Stages by Kremser Equation using the formula - Number of Equilibrium Extraction Stages = (log10(((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(((Mass Fraction of Solute in the Raffinate-Mass Fraction of Solute in the Solvent)/Distribution Coefficient of Solute)))*(1-(1/Extraction Factor))+(1/Extraction Factor)))/(log10(Extraction Factor)). This formula also uses Common Logarithm (log10) function(s).

What are the other ways to Calculate Number of Equilibrium Extraction Stages?

Here are the different ways to Calculate Number of Equilibrium Extraction Stages-

Number of Equilibrium Extraction Stages=(log10(Mass Fraction of Solute in the Feed/N Stages Mass Fraction of Solute in Raffinate))/(log10(((Distribution Coefficient of Solute*Solute Free Extract Phase Flowrate in LLE)/Solute Free Feed Flowrate in Extraction)+1))
Number of Equilibrium Extraction Stages=((Mass Fraction of Solute in the Feed-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute))/(Mass Fraction of Solute in the Raffinate-(Mass Fraction of Solute in the Solvent/Distribution Coefficient of Solute)))-1

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Number of Extraction Stages by Kremser Equation Formula

​GoNumber of Ideal Equilibrium Extraction Stages Formula

​GoNumber of Stages for Extraction Factor equal to 1 Formula

Number of Extraction Stages by Kremser Equation Example

Number of Extraction Stages by Kremser Equation Solution

Number of Extraction Stages by Kremser Equation Formula Elements

Other Formulas to find Number of Equilibrium Extraction Stages

Other formulas in Kremser's Equation for Liquid Liquid Extraction category

How to Evaluate Number of Extraction Stages by Kremser Equation?

FAQs on Number of Extraction Stages by Kremser Equation

Variable Name

GoNumber of Ideal Equilibrium Extraction Stages Formula

GoNumber of Stages for Extraction Factor equal to 1 Formula