Feed Solute Concentration for N-number of Ideal Stage Extraction Calculator

✖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 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 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 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 Number of Equilibrium Extraction Stages is the number of Ideal Equilibrium stages required for Liquid-Liquid Extraction.ⓘ Number of Equilibrium Extraction Stages [N]			+10% -10%

✖The Mass Fraction of Solute in the Feed is the mass fraction of the solute in the Feed to the Liquid-Liquid Extraction operation.ⓘ Feed Solute Concentration for N-number of Ideal Stage Extraction [z_C]

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Formula

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Feed Solute Concentration for N-number of Ideal Stage Extraction

Formula

`"z"_{"C"} = "X"_{"N"}/(("F'"/("F'"+("E'"*"K"_{"Solute"})))^"N")`

Example

`"0.500538"="0.0334"/(("110kg/s"/("110kg/s"+("62kg/s"*"2.6")))^"3")`

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Feed Solute Concentration for N-number of Ideal Stage Extraction Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
z_C = X_N/((F'/(F'+(E'*K_Solute)))^N)
This formula uses 6 Variables

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

N Stages Mass Fraction of Solute in Raffinate: 0.0334 --> No Conversion Required
Solute Free Feed Flowrate in Extraction: 110 Kilogram per Second --> 110 Kilogram per Second No Conversion Required
Solute Free Extract Phase Flowrate in LLE: 62 Kilogram per Second --> 62 Kilogram per Second No Conversion Required
Distribution Coefficient of Solute: 2.6 --> No Conversion Required
Number of Equilibrium Extraction Stages: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z_C = X_N/((F'/(F'+(E'*K_Solute)))^N) --> 0.0334/((110/(110+(62*2.6)))^3)

Evaluating ... ...

z_C = 0.500538475939294

STEP 3: Convert Result to Output's Unit

0.500538475939294 --> No Conversion Required

FINAL ANSWER

0.500538475939294 ≈ 0.500538 <-- Mass Fraction of Solute in the Feed

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Liquid-Liquid Extraction » Equilibrium Stage Calculations for Immiscible (Pure) Solvent & Carrier Liquid » Feed Solute Concentration for N-number of Ideal Stage Extraction

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< 5 Equilibrium Stage Calculations for Immiscible (Pure) Solvent & Carrier Liquid Calculators

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)

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)))

< 23 Important Formulas in 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 Ideal Equilibrium Extraction Stages

Raffinate Phase Solute Concentration for N Number of Ideal Stage Extraction

Feed Solute Concentration for N-number of Ideal Stage Extraction

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

Raffinate Phase Solute Concentration for Single Ideal Stage Extraction

Feed Solute Concentration for Single Ideal Stage Extraction

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

Feed Solute Concentration for N-number of Ideal Stage Extraction Formula

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 Feed Solute Concentration for N-number of Ideal Stage Extraction?

Feed Solute Concentration for N-number of Ideal Stage Extraction calculator uses 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) to calculate the Mass Fraction of Solute in the Feed, The Feed Solute Concentration for N-number of Ideal Stage Extraction formula is defined as the mass fraction of solute in feed as the function of the raffinate mass fraction of solute coming out of the Nth number of Equilibrium Stage Extraction Process. Mass Fraction of Solute in the Feed is denoted by z_C symbol.

How to calculate Feed Solute Concentration for N-number of Ideal Stage Extraction using this online calculator? To use this online calculator for Feed Solute Concentration for N-number of Ideal Stage Extraction, enter N Stages Mass Fraction of Solute in Raffinate (X_N), Solute Free Feed Flowrate in Extraction (F'), Solute Free Extract Phase Flowrate in LLE (E'), Distribution Coefficient of Solute (K_Solute) & Number of Equilibrium Extraction Stages (N) and hit the calculate button. Here is how the Feed Solute Concentration for N-number of Ideal Stage Extraction calculation can be explained with given input values -> 0.500538 = 0.0334/((110/(110+(62*2.6)))^3).

FAQ

What is Feed Solute Concentration for N-number of Ideal Stage Extraction?

The Feed Solute Concentration for N-number of Ideal Stage Extraction formula is defined as the mass fraction of solute in feed as the function of the raffinate mass fraction of solute coming out of the Nth number of Equilibrium Stage Extraction Process and is represented as z_C = X_N/((F'/(F'+(E'*K_Solute)))^N) or 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). 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 Solute Free Feed Flowrate in Extraction is the flowrate of the carrier liquid to the liquid-liquid extraction operation for separation, The Solute Free Extract Phase Flowrate in LLE is the flowrate of the extracting solvent after separation 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 Number of Equilibrium Extraction Stages is the number of Ideal Equilibrium stages required for Liquid-Liquid Extraction.

How to calculate Feed Solute Concentration for N-number of Ideal Stage Extraction?

The Feed Solute Concentration for N-number of Ideal Stage Extraction formula is defined as the mass fraction of solute in feed as the function of the raffinate mass fraction of solute coming out of the Nth number of Equilibrium Stage Extraction Process is calculated using 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). To calculate Feed Solute Concentration for N-number of Ideal Stage Extraction, you need N Stages Mass Fraction of Solute in Raffinate (X_N), Solute Free Feed Flowrate in Extraction (F'), Solute Free Extract Phase Flowrate in LLE (E'), Distribution Coefficient of Solute (K_Solute) & Number of Equilibrium Extraction Stages (N). With our tool, you need to enter the respective value for N Stages Mass Fraction of Solute in Raffinate, Solute Free Feed Flowrate in Extraction, Solute Free Extract Phase Flowrate in LLE, Distribution Coefficient of Solute & Number of Equilibrium Extraction Stages 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 Mass Fraction of Solute in the Feed?

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

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)))
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)))

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