Number of Extraction Stages by Kremser Equation 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 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.ⓘ Mass Fraction of Solute in the Solvent [y_s]			+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 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.ⓘ Mass Fraction of Solute in the Raffinate [x_C]			+10% -10%
✖The Extraction Factor is defined as the ratio of the slope of equilibrium line to the slope of operating line.ⓘ Extraction Factor [ε]			+10% -10%

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

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Liquid Liquid Extraction Formula PDF PDF Image

Number of Extraction Stages by Kremser Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
N = (log10(((z_C-(y_s/K_Solute))/(((x_C-y_s)/K_Solute)))*(1-(1/ε))+(1/ε)))/(log10(ε))
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.
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.
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.
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.
Extraction Factor - The Extraction Factor is defined as the ratio of the slope of equilibrium line to the slope of operating line.

STEP 1: Convert Input(s) to Base Unit

Mass Fraction of Solute in the Feed: 0.5 --> No Conversion Required
Mass Fraction of Solute in the Solvent: 0.05 --> No Conversion Required
Distribution Coefficient of Solute: 2.6 --> No Conversion Required
Mass Fraction of Solute in the Raffinate: 0.1394 --> No Conversion Required
Extraction Factor: 2.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = (log10(((z_C-(y_s/K_Solute))/(((x_C-y_s)/K_Solute)))*(1-(1/ε))+(1/ε)))/(log10(ε)) --> (log10(((0.5-(0.05/2.6))/(((0.1394-0.05)/2.6)))*(1-(1/2.2))+(1/2.2)))/(log10(2.2))

Evaluating ... ...

N = 2.65015450169299

STEP 3: Convert Result to Output's Unit

2.65015450169299 --> No Conversion Required

FINAL ANSWER

2.65015450169299 ≈ 2.650155 <-- Number of Equilibrium Extraction Stages

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Chemical Engineering » Mass Transfer Operations » Liquid Liquid Extraction » Kremser's Equation for Liquid Liquid Extraction » Number of Extraction Stages by Kremser Equation

Credits

Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

Vaibhav Mishra has created this Calculator and 300+ more calculators!

Verified by Prerana Bakli

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

Prerana Bakli has verified this Calculator and 1600+ more calculators!

< Kremser's Equation for Liquid Liquid Extraction Calculators

Number of Extraction Stages by Kremser Equation

LaTeX Go 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 Stages for Extraction Factor equal to 1

LaTeX Go 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

Extraction Factor at Mean Slope of Equilibrium Curve

LaTeX Go Extraction Factor = Mean Slope of Equilibrium Curve*Solute Free Solvent Flowrate in Extraction/Solute Free Feed Flowrate in Extraction

Geometric Mean of Equilibrium Line Slope

LaTeX Go Mean Slope of Equilibrium Curve = sqrt(Feed Point Slope of Equilibrium Curve*Raffinate Point Slope of Equilibrium Curve)

< 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 Extraction Stages by Kremser Equation Formula

LaTeX Go

What is the Kremser - Souders - Brown Equation?

In unit operation design calculations, it is useful to find out the quality of separation for a given number of stages. It is also useful to find the required number of stages if the product recovery is specified. The development was first given by Kremser in 1930, and by Souders and Brown in 1932. The resulting equations are referred to as the KSB or Kremser equations. These equation were originally developed for gas absorption operation in a plate column, however, it is applicable to other mass transfer operations as well (for example, counter current adsorption).

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 Extraction Stages by Kremser Equation?

Number of Extraction Stages by Kremser Equation calculator 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 calculate 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 calculate Number of Extraction Stages by Kremser Equation using this online calculator? To use this online calculator 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. Here is how the Number of Extraction Stages by Kremser Equation calculation can be explained with given input values -> 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)).

FAQ

What is Number of Extraction Stages by Kremser Equation?

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 and is represented as N = (log10(((z_C-(y_s/K_Solute))/(((x_C-y_s)/K_Solute)))*(1-(1/ε))+(1/ε)))/(log10(ε)) or 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)). 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 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, 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 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 & The Extraction Factor is defined as the ratio of the slope of equilibrium line to the slope of operating line.

How to calculate Number of Extraction Stages by Kremser Equation?

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 is calculated using 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 calculate Number of Extraction Stages by Kremser Equation, you need 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). With our tool, you need to enter the respective value for 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 & Extraction Factor 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, Mass Fraction of Solute in the Solvent, Distribution Coefficient of Solute, Mass Fraction of Solute in the Raffinate & Extraction Factor. We can use 3 other way(s) to calculate the same, which is/are as follows -

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
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

Home

FREE PDFs

🔍 Search