Geometric Mean of Equilibrium Line Slope Calculator

✖The Feed Point Slope of Equilibrium Curve is the slope of the equilibrium curve line at the feed point i.e. the distribution factor of the solute based on feed concentrations.ⓘ Feed Point Slope of Equilibrium Curve [m_F]			+10% -10%
✖The Raffinate Point Slope of Equilibrium Curve is the slope of the equilibrium curve line at the raffinate point i.e. the distribution factor of the solute based on raffinate concentration.ⓘ Raffinate Point Slope of Equilibrium Curve [m_R]			+10% -10%

✖The Mean Slope of Equilibrium Curve is the geometric mean slope of the equilibrium curve line i.e. the distribution factor of the solute.ⓘ Geometric Mean of Equilibrium Line Slope [m]

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Formula

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Geometric Mean of Equilibrium Line Slope

Formula

`"m" = sqrt("m"_{"F"}*"m"_{"R"})`

Example

`"3.722"=sqrt("3.721"*"3.723")`

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Geometric Mean of Equilibrium Line Slope Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Slope of Equilibrium Curve = sqrt(Feed Point Slope of Equilibrium Curve*Raffinate Point Slope of Equilibrium Curve)
m = sqrt(m_F*m_R)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Mean Slope of Equilibrium Curve - The Mean Slope of Equilibrium Curve is the geometric mean slope of the equilibrium curve line i.e. the distribution factor of the solute.
Feed Point Slope of Equilibrium Curve - The Feed Point Slope of Equilibrium Curve is the slope of the equilibrium curve line at the feed point i.e. the distribution factor of the solute based on feed concentrations.
Raffinate Point Slope of Equilibrium Curve - The Raffinate Point Slope of Equilibrium Curve is the slope of the equilibrium curve line at the raffinate point i.e. the distribution factor of the solute based on raffinate concentration.

STEP 1: Convert Input(s) to Base Unit

Feed Point Slope of Equilibrium Curve: 3.721 --> No Conversion Required
Raffinate Point Slope of Equilibrium Curve: 3.723 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m = sqrt(m_F*m_R) --> sqrt(3.721*3.723)

Evaluating ... ...

m = 3.72199986566362

STEP 3: Convert Result to Output's Unit

3.72199986566362 --> No Conversion Required

FINAL ANSWER

3.72199986566362 ≈ 3.722 <-- Mean Slope of Equilibrium Curve

(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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< 6 Kremser's Equation for Liquid-Liquid Extraction Calculators

Number of Extraction Stages by Kremser Equation

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

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 based on Raffinate Point Slope

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

Extraction Factor at Feed Point Slope of Equilibrium Curve

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

Extraction Factor at Mean Slope of Equilibrium Curve

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

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

< 23 Important Formulas in Liquid-Liquid Extraction Calculators

Number of Extraction Stages by Kremser Equation

Number of Ideal Equilibrium Extraction Stages

Go 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))

Raffinate Phase Solute Concentration for N Number of Ideal Stage Extraction

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

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)

Number of Stages for Extraction Factor equal to 1

Raffinate Phase Solute Concentration for Single Ideal Stage Extraction

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

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)))

Recovery of Solute in Liquid-Liquid Extraction

Go Recovery of Solute in Liquid-Liquid Extraction = 1-((Mass Fraction of Solute in the Raffinate*Raffinate Phase Flowrate in LLE)/(Mass Fraction of Solute in the Feed*Feed Flowrate in Liquid-Liquid Extraction))

Selectvity of Solute based on Activity Coefficients

Go Selectivity = (Activity Coefficient of Solute in Raffinate/Activity Coefficient of Solute in Extract)/(Activity Coefficient of Carrier Liq in Raffinate/Activity Coefficient of Carrier Liquid in Extract)

Selectvity of Solute based on Mole Fractions

Go Selectivity = (Mass Fraction of Solute in the Extract/Mass Fraction of Carrier Liquid in the Extract)/(Mass Fraction of Solute in the Raffinate/Mass Fraction of Carrier Liquid in the Raffinate)

Mass Ratio of Solvent in Raffinate Phase

Go Mass Ratio of Solvent in Raffinate Phase = Mass Fraction of Solvent in the Raffinate/(Mass Fraction of Carrier Liquid in the Raffinate+Mass Fraction of Solute in the Raffinate)

Mass Ratio of Solute in Raffinate Phase

Go Mass Ratio of Solute in Raffinate Phase = Mass Fraction of Solute in the Raffinate/(Mass Fraction of Carrier Liquid in the Raffinate+Mass Fraction of Solute in the Raffinate)

Mass Ratio of Solvent in Extract Phase

Go Mass Ratio of Solvent in Extract Phase = Mass Fraction of Solvent in the Extract/(Mass Fraction of Carrier Liquid in the Extract+Mass Fraction of Solute in the Extract)

Mass Ratio of Solute in Extract Phase

Go Mass Ratio of Solute in Extract Phase = Mass Fraction of Solute in the Extract/(Mass Fraction of Carrier Liquid in the Extract+Mass Fraction of Solute in the Extract)

Extraction Factor based on Raffinate Point Slope

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

Extraction Factor at Feed Point Slope of Equilibrium Curve

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

Extraction Factor at Mean Slope of Equilibrium Curve

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

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

Distribution Coefficient of Carrier Liquid from Activity Coefficients

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

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

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

Distribution Coefficient of Solute from Mass Fractions

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

Selectivity of Solute based on Distribution Coefficients

Go Selectivity = Distribution Coefficient of Solute/Distribution Coefficient of Carrier Liquid

Geometric Mean of Equilibrium Line Slope Formula

Mean Slope of Equilibrium Curve = sqrt(Feed Point Slope of Equilibrium Curve*Raffinate Point Slope of Equilibrium Curve)
m = sqrt(m_F*m_R)

What is Geometric Mean of Equilibrium Line Slope?

The equilibrium curve is a plot of the solute composition in extract phase to that in the raffinate phase. If this relation between the solute concentration is linear, the slope value stays constant. But for equilibrium curves, where the line is not straight, the values vary and in this scenario, an average is used for calculation of number of stages. This average is the geometric average of the slope at the feed point and the raffinate point.

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 Geometric Mean of Equilibrium Line Slope?

Geometric Mean of Equilibrium Line Slope calculator uses Mean Slope of Equilibrium Curve = sqrt(Feed Point Slope of Equilibrium Curve*Raffinate Point Slope of Equilibrium Curve) to calculate the Mean Slope of Equilibrium Curve, The Geometric Mean of Equilibrium Line Slope formula is defined as the mean value of the slope of equilibrium line, applicable for cases where equilibrium line is not straight. Mean Slope of Equilibrium Curve is denoted by m symbol.

How to calculate Geometric Mean of Equilibrium Line Slope using this online calculator? To use this online calculator for Geometric Mean of Equilibrium Line Slope, enter Feed Point Slope of Equilibrium Curve (m_F) & Raffinate Point Slope of Equilibrium Curve (m_R) and hit the calculate button. Here is how the Geometric Mean of Equilibrium Line Slope calculation can be explained with given input values -> 3.722 = sqrt(3.721*3.723).

FAQ

What is Geometric Mean of Equilibrium Line Slope?

The Geometric Mean of Equilibrium Line Slope formula is defined as the mean value of the slope of equilibrium line, applicable for cases where equilibrium line is not straight and is represented as m = sqrt(m_F*m_R) or Mean Slope of Equilibrium Curve = sqrt(Feed Point Slope of Equilibrium Curve*Raffinate Point Slope of Equilibrium Curve). The Feed Point Slope of Equilibrium Curve is the slope of the equilibrium curve line at the feed point i.e. the distribution factor of the solute based on feed concentrations & The Raffinate Point Slope of Equilibrium Curve is the slope of the equilibrium curve line at the raffinate point i.e. the distribution factor of the solute based on raffinate concentration.

How to calculate Geometric Mean of Equilibrium Line Slope?

The Geometric Mean of Equilibrium Line Slope formula is defined as the mean value of the slope of equilibrium line, applicable for cases where equilibrium line is not straight is calculated using Mean Slope of Equilibrium Curve = sqrt(Feed Point Slope of Equilibrium Curve*Raffinate Point Slope of Equilibrium Curve). To calculate Geometric Mean of Equilibrium Line Slope, you need Feed Point Slope of Equilibrium Curve (m_F) & Raffinate Point Slope of Equilibrium Curve (m_R). With our tool, you need to enter the respective value for Feed Point Slope of Equilibrium Curve & Raffinate Point Slope of Equilibrium Curve 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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