Number of Ideal Equilibrium Extraction Stages Calculator

✖The Mass Fraction of Solute in the Feed is the mass fraction of the solute in the Feed to the Liquid-Liquid Extraction operation.ⓘ Mass Fraction of Solute in the Feed [z_C]			+10% -10%
✖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.ⓘ N Stages Mass Fraction of Solute in Raffinate [X_N]			+10% -10%
✖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.ⓘ Distribution Coefficient of Solute [K_Solute]			+10% -10%
✖The Solute Free Extract Phase Flowrate in LLE is the flowrate of the extracting solvent after separation in liquid-liquid extraction operation.ⓘ Solute Free Extract Phase Flowrate in LLE [E']			+10% -10%
✖The Solute Free Feed Flowrate in Extraction is the flowrate of the carrier liquid to the liquid-liquid extraction operation for separation.ⓘ Solute Free Feed Flowrate in Extraction [F']			+10% -10%

✖The Number of Equilibrium Extraction Stages is the number of Ideal Equilibrium stages required for Liquid-Liquid Extraction.ⓘ Number of Ideal Equilibrium Extraction Stages [N]

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Number of Ideal Equilibrium Extraction Stages Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
N = (log10(z_C/X_N))/(log10(((K_Solute*E')/F')+1))
This formula uses 1 Functions, 6 Variables

Functions Used

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., log10(Number)

Variables Used

Number of Equilibrium Extraction Stages - The Number of Equilibrium Extraction Stages is the number of Ideal Equilibrium stages required for Liquid-Liquid Extraction.
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.
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.
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.
Solute Free Extract Phase Flowrate in LLE - (Measured in Kilogram per Second) - The Solute Free Extract Phase Flowrate in LLE is the flowrate of the extracting solvent after separation in liquid-liquid extraction operation.
Solute Free Feed Flowrate in Extraction - (Measured in Kilogram per Second) - The Solute Free Feed Flowrate in Extraction is the flowrate of the carrier liquid to the liquid-liquid extraction operation for separation.

STEP 1: Convert Input(s) to Base Unit

Mass Fraction of Solute in the Feed: 0.5 --> No Conversion Required
N Stages Mass Fraction of Solute in Raffinate: 0.0334 --> No Conversion Required
Distribution Coefficient of Solute: 2.6 --> No Conversion Required
Solute Free Extract Phase Flowrate in LLE: 62 Kilogram per Second --> 62 Kilogram per Second No Conversion Required
Solute Free Feed Flowrate in Extraction: 110 Kilogram per Second --> 110 Kilogram per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = (log10(z_C/X_N))/(log10(((K_Solute*E')/F')+1)) --> (log10(0.5/0.0334))/(log10(((2.6*62)/110)+1))

Evaluating ... ...

N = 2.99880717998376

STEP 3: Convert Result to Output's Unit

2.99880717998376 --> No Conversion Required

FINAL ANSWER

2.99880717998376 ≈ 2.998807 <-- Number of Equilibrium Extraction Stages

(Calculation completed in 00.020 seconds)

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Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< Equilibrium Stage Calculations for Immiscible (Pure) Solvent and Carrier Liquid Calculators

Raffinate Phase Solute Concentration for N Number of Ideal Stage Extraction

LaTeX Go N Stages Mass Fraction of Solute in Raffinate = ((Solute Free Feed Flowrate in Extraction/(Solute Free Feed Flowrate in Extraction+(Solute Free Extract Phase Flowrate in LLE*Distribution Coefficient of Solute)))^Number of Equilibrium Extraction Stages)*Mass Fraction of Solute in the Feed

Feed Solute Concentration for N-number of Ideal Stage Extraction

LaTeX Go Mass Fraction of Solute in the Feed = N Stages Mass Fraction of Solute in Raffinate/((Solute Free Feed Flowrate in Extraction/(Solute Free Feed Flowrate in Extraction+(Solute Free Extract Phase Flowrate in LLE*Distribution Coefficient of Solute)))^Number of Equilibrium Extraction Stages)

Raffinate Phase Solute Concentration for Single Ideal Stage Extraction

LaTeX Go Single Stage Mass Fraction of Solute in Raffinate = (Solute Free Feed Flowrate in Extraction/(Solute Free Feed Flowrate in Extraction+(Solute Free Extract Phase Flowrate in LLE*Distribution Coefficient of Solute)))*Mass Fraction of Solute in the Feed

Feed Solute Concentration for Single Ideal Stage Extraction

LaTeX Go Mass Fraction of Solute in the Feed = Single Stage Mass Fraction of Solute in Raffinate/(Solute Free Feed Flowrate in Extraction/(Solute Free Feed Flowrate in Extraction+(Solute Free Extract Phase Flowrate in LLE*Distribution Coefficient of Solute)))

< Important Formulas in Liquid Liquid Extraction Calculators

Distribution Coefficient of Carrier Liquid from Activity Coefficients

LaTeX Go Distribution Coefficient of Carrier Liquid = Activity Coefficient of Carrier Liq in Raffinate/Activity Coefficient of Carrier Liquid in Extract

Distribution Coefficient of Carrier Liquid from Mass Fraction

LaTeX Go Distribution Coefficient of Carrier Liquid = Mass Fraction of Carrier Liquid in the Extract/Mass Fraction of Carrier Liquid in the Raffinate

Distribution Coefficient of Solute from Activity Coefficient

LaTeX Go Distribution Coefficient of Solute = Activity Coefficient of Solute in Raffinate/Activity Coefficient of Solute in Extract

Distribution Coefficient of Solute from Mass Fractions

LaTeX Go Distribution Coefficient of Solute = Mass Fraction of Solute in the Extract/Mass Fraction of Solute in the Raffinate

Number of Ideal Equilibrium Extraction Stages Formula

LaTeX Go

What are the Assumptions for Ideal Extraction?

1. The Solvent and the carrier liquid are immiscible (mutually non-dissolving), this leads to complete recovery of carrier liquid in raffinate phase and complete recovery of extracting solvent in extract phase. 2. The Extraction Solvent Feed to the system is Pure (i.e. has no initial solute). 3. The Extract and Raffinate streams leaving the extraction stage are in equilibrium.

What is Liquid-Liquid Extraction?

Liquid–liquid extraction (LLE), also known as solvent extraction, is a method to separate compounds or metal complexes, based on their relative solubilities in two different immiscible liquids, usually water (polar) and an organic solvent (non-polar). There is a net transfer of one or more species from one liquid into another liquid phase, generally from aqueous to organic. The transfer is driven by chemical potential, i.e. once the transfer is complete, the overall system of chemical components that make up the solutes and the solvents are in a more stable configuration (lower free energy). The solvent that is enriched in solute(s) is called extract. The feed solution that is depleted in solute(s) is called the raffinate.

How to Calculate Number of Ideal Equilibrium Extraction Stages?

Number of Ideal Equilibrium Extraction Stages calculator 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 calculate 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 calculate Number of Ideal Equilibrium Extraction Stages using this online calculator? To use this online calculator 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. Here is how the Number of Ideal Equilibrium Extraction Stages calculation can be explained with given input values -> 2.998807 = (log10(0.5/0.0334))/(log10(((2.6*62)/110)+1)).

FAQ

What is Number of Ideal 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 and is represented as N = (log10(z_C/X_N))/(log10(((K_Solute*E')/F')+1)) or 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)). The Mass Fraction of Solute in the Feed is the mass fraction of the solute in the Feed to the Liquid-Liquid Extraction operation, 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, 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, The Solute Free Extract Phase Flowrate in LLE is the flowrate of the extracting solvent after separation in liquid-liquid extraction operation & The Solute Free Feed Flowrate in Extraction is the flowrate of the carrier liquid to the liquid-liquid extraction operation for separation.

How to calculate Number of Ideal 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 is calculated using 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 calculate Number of Ideal Equilibrium Extraction Stages, you need 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'). With our tool, you need to enter the respective value for Mass Fraction of Solute in the Feed, N Stages Mass Fraction of Solute in Raffinate, Distribution Coefficient of Solute, Solute Free Extract Phase Flowrate in LLE & Solute Free Feed Flowrate in Extraction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Equilibrium Extraction Stages?

In this formula, Number of Equilibrium Extraction Stages uses Mass Fraction of Solute in the Feed, N Stages Mass Fraction of Solute in Raffinate, Distribution Coefficient of Solute, Solute Free Extract Phase Flowrate in LLE & Solute Free Feed Flowrate in Extraction. We can use 2 other way(s) to calculate the same, which is/are as follows -

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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