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Number of Ideal Equilibrium Extraction Stages Formula

GoNumber of Extraction Stages by Kremser Equation 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}{X N})}{\log 10 ((\frac{K Solute \cdot E'}{F'}) + 1)}

N - Number of Equilibrium Extraction Stages?z_C - Mass Fraction of Solute in the Feed?X_N - N Stages Mass Fraction of Solute in Raffinate?K_Solute - Distribution Coefficient of Solute?E' - Solute Free Extract Phase Flowrate in LLE?F' - Solute Free Feed Flowrate in Extraction?

Number of Ideal Equilibrium Extraction Stages Example

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Here is how the Number of Ideal Equilibrium Extraction Stages equation looks like with Values.

Here is how the Number of Ideal Equilibrium Extraction Stages equation looks like with Units.

Here is how the Number of Ideal Equilibrium Extraction Stages equation looks like.

2.9988 = \frac{\log 10 (\frac{0.5}{0.0334})}{\log 10 ((\frac{2.6 \cdot 62}{110}) + 1)}

2.9988 = \frac{\log 10 (\frac{0.5}{0.0334})}{\log 10 ((\frac{2.6 \cdot 62kg/s}{110kg/s}) + 1)}

2.9988 = \frac{\log 10 (\frac{0.5}{0.0334})}{\log 10 ((\frac{2.6 \cdot 62}{110}) + 1)}

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Number of Ideal Equilibrium Extraction Stages

Number of Ideal Equilibrium Extraction Stages Solution

Follow our step by step solution on how to calculate Number of Ideal Equilibrium Extraction Stages?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

N = \frac{\log 10 (\frac{0.5}{0.0334})}{\log 10 ((\frac{2.6 \cdot 62kg/s}{110kg/s}) + 1)}

Next Step Prepare to Evaluate

∴

N = \frac{\log 10 (\frac{0.5}{0.0334})}{\log 10 ((\frac{2.6 \cdot 62}{110}) + 1)}

Next Step Evaluate

∴

N = 2.99880717998376

LAST Step Rounding Answer

∴

N = 2.9988

Number of Ideal Equilibrium Extraction Stages 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.

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.

N Stages Mass Fraction of Solute in Raffinate

The N Stages Mass Fraction of Solute in Raffinate Phase is the mass fraction of the solute in the raffinate phase on solute free basis after N Number of LLE Stages.

Symbol: X_N

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

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.

Solute Free Extract Phase Flowrate in LLE

The Solute Free Extract Phase Flowrate in LLE is the flowrate of the extracting solvent after separation in liquid-liquid extraction operation.

Symbol: E'

Measurement: Mass Flow RateUnit: kg/s

Note: Value should be greater than 0.

Solute Free Feed Flowrate in Extraction

The Solute Free Feed Flowrate in Extraction is the flowrate of the carrier liquid to the liquid-liquid extraction operation for separation.

Symbol: F'

Measurement: Mass Flow RateUnit: kg/s

Note: Value should be greater than 0.

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)

Credits

Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

Vaibhav Mishra has created this Formula and 300+ more formulas!

Verified by Prerana Bakli

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

Prerana Bakli has verified this Formula and 1600+ more formulas!

Other Formulas to find Number of Equilibrium Extraction Stages

Go Number of Extraction Stages by Kremser Equation

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)}

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 Equilibrium Stage Calculations for Immiscible (Pure) Solvent and Carrier Liquid 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 Ideal Equilibrium Extraction Stages?

Number of Ideal Equilibrium Extraction Stages evaluator uses 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)) to evaluate the Number of Equilibrium Extraction Stages, The Number of Ideal Equilibrium Extraction Stages formula is defined as the number of equilibrium extraction stages required to achieve the extraction of raffinate mass fraction from the given feed mass fraction. Number of Equilibrium Extraction Stages is denoted by N symbol.

How to evaluate Number of Ideal Equilibrium Extraction Stages using this online evaluator? To use this online evaluator for Number of Ideal Equilibrium Extraction Stages, enter Mass Fraction of Solute in the Feed (z_C), N Stages Mass Fraction of Solute in Raffinate (X_N), Distribution Coefficient of Solute (K_Solute), Solute Free Extract Phase Flowrate in LLE (E') & Solute Free Feed Flowrate in Extraction (F') and hit the calculate button.

FAQs on Number of Ideal Equilibrium Extraction Stages

What is the formula to find Number of Ideal Equilibrium Extraction Stages?

The formula of Number of Ideal Equilibrium Extraction Stages is expressed as 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)). Here is an example- 2.998807 = (log10(0.5/0.0334))/(log10(((2.6*62)/110)+1)).

How to calculate Number of Ideal Equilibrium Extraction Stages?

With Mass Fraction of Solute in the Feed (z_C), N Stages Mass Fraction of Solute in Raffinate (X_N), Distribution Coefficient of Solute (K_Solute), Solute Free Extract Phase Flowrate in LLE (E') & Solute Free Feed Flowrate in Extraction (F') we can find Number of Ideal Equilibrium Extraction Stages using the formula - 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)). 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-(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))
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 Ideal Equilibrium Extraction Stages Formula

​GoNumber of Extraction Stages by Kremser Equation Formula

​GoNumber of Stages for Extraction Factor equal to 1 Formula

Number of Ideal Equilibrium Extraction Stages Example

Number of Ideal Equilibrium Extraction Stages Solution

Number of Ideal Equilibrium Extraction Stages Formula Elements

Credits

Other Formulas to find Number of Equilibrium Extraction Stages

Other formulas in Equilibrium Stage Calculations for Immiscible (Pure) Solvent and Carrier Liquid category

How to Evaluate Number of Ideal Equilibrium Extraction Stages?

FAQs on Number of Ideal Equilibrium Extraction Stages

Variable Name

GoNumber of Extraction Stages by Kremser Equation Formula

GoNumber of Stages for Extraction Factor equal to 1 Formula