Fraction of Solute remaining based on Solvent Decanted Calculator

✖The Amount of Solvent Decanted is the amount of solvent that is decanted from the solid in washing stage.ⓘ Amount of Solvent Decanted [b]			+10% -10%
✖The Amount of Solvent Remaining is the amount of solvent that is remaining in the solid in washing stage.ⓘ Amount of Solvent Remaining [a]			+10% -10%
✖The Number of Washings in Batch Leaching is the number of washings required after batch leaching operation.ⓘ Number of Washings in Batch Leaching [N_Washing]			+10% -10%

✖The Fraction of Solute Remaining in Solid is the fraction of the solute that is present in the solid after washing in ratio to the initial solute mass.ⓘ Fraction of Solute remaining based on Solvent Decanted [θ_N]

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Formula

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Fraction of Solute remaining based on Solvent Decanted

Formula

θ N = (\frac{1}{{(1 + (\frac{b}{a}))}^{N Washing}})

Example

0.001171 = (\frac{1}{{(1 + (\frac{30 kg}{10.5 kg}))}^{5}})

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Fraction of Solute remaining based on Solvent Decanted Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fraction of Solute Remaining in Solid = (1/((1+(Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching))
θ_N = (1/((1+(b/a))^N_Washing))
This formula uses 4 Variables

Variables Used

Fraction of Solute Remaining in Solid - The Fraction of Solute Remaining in Solid is the fraction of the solute that is present in the solid after washing in ratio to the initial solute mass.
Amount of Solvent Decanted - (Measured in Kilogram) - The Amount of Solvent Decanted is the amount of solvent that is decanted from the solid in washing stage.
Amount of Solvent Remaining - (Measured in Kilogram) - The Amount of Solvent Remaining is the amount of solvent that is remaining in the solid in washing stage.
Number of Washings in Batch Leaching - The Number of Washings in Batch Leaching is the number of washings required after batch leaching operation.

STEP 1: Convert Input(s) to Base Unit

Amount of Solvent Decanted: 30 Kilogram --> 30 Kilogram No Conversion Required
Amount of Solvent Remaining: 10.5 Kilogram --> 10.5 Kilogram No Conversion Required
Number of Washings in Batch Leaching: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_N = (1/((1+(b/a))^N_Washing)) --> (1/((1+(30/10.5))^5))

Evaluating ... ...

θ_N = 0.00117130872755674

STEP 3: Convert Result to Output's Unit

0.00117130872755674 --> No Conversion Required

FINAL ANSWER

0.00117130872755674 ≈ 0.001171 <-- Fraction of Solute Remaining in Solid

(Calculation completed in 00.020 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Solid Liquid Extraction » Batch Leaching » Washing » Fraction of Solute remaining based on Solvent Decanted

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Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< Washing Calculators

Number of Stages for Leaching based on Fraction Solute Retained and Beta Value

Go Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+Solvent Decanted per Solvent Remaining in Solid))

Beta Value based on Number of Stages and Fraction of Solute

Go Solvent Decanted per Solvent Remaining in Solid = ((1/Fraction of Solute Remaining in Solid)^(1/Number of Washings in Batch Leaching))-1

Fraction of Solute Remaining based on Beta Value

Go Fraction of Solute Remaining in Solid = (1/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching))

Beta Value based on Ratio of Solvent

Go Solvent Decanted per Solvent Remaining in Solid = Amount of Solvent Decanted/Amount of Solvent Remaining

< Important Formulas in Solid Liquid Extraction Calculators

Area of Contact for Batch Leaching Operation

Go Area of Leaching = (-Volume of Leaching Solution/(Mass Transfer Coefficient for Batch Leaching*Time of Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute))

Time of Batch Leaching Operation

Go Time of Batch Leaching = (-Volume of Leaching Solution/(Area of Leaching*Mass Transfer Coefficient for Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute))

Volume of Leaching Solution in Batch Leaching

Go Volume of Leaching Solution = (-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute))

Concentration of Solute in Bulk Solution at Time t for Batch Leaching

Go Concentration of Solute in Bulk Solution at Time t = Concentration of Saturated Solution with Solute*(1-exp((-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/Volume of Leaching Solution))

Fraction of Solute remaining based on Solvent Decanted Formula

Fraction of Solute Remaining in Solid = (1/((1+(Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching))
θ_N = (1/((1+(b/a))^N_Washing))

What is Batch Leaching Test?

The Batch Leaching test estimates how readily solute particles mobilize out of the solid material if the material comes into contact with the solvent. The test involves placing a given mass of the solid sample in a container with a specific volume of a liquid solvent (leaching solution). The mixture is agitated for a specific amount of time. Afterwards, the mixture is filtered and the liquid (the leachate) is analyzed for contaminants. Batch Leaching is a two-step process, 1. Contacting solvent and solid to effect a transfer of a solute (leaching). 2. The separation of the solution from the remaining solid (washing).

What is Leaching Operation?

Leaching is a mass transfer operation in which we have a solid material which either contains components which are valuable to us or components which are considered an impurity of the solid, no matter what the case, such components are called solute. We take a liquid which is called a solvent and contact it intimately with the solid in order to extract the solute from the solid and bring it into the liquid thus effecting a separation. Leaching is a solid-liquid extraction process. The process of leaching generally concerns with processes where the solid is inert and contains soluble solute which is extracted from the inert solid with the help of chemical reaction; for example, the leaching of valuable metals from waste materials by using sulphuric acid. The process of leaching is extremely common in metallurgical industries.

How to Calculate Fraction of Solute remaining based on Solvent Decanted?

Fraction of Solute remaining based on Solvent Decanted calculator uses Fraction of Solute Remaining in Solid = (1/((1+(Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching)) to calculate the Fraction of Solute Remaining in Solid, The Fraction of Solute remaining based on Solvent Decanted formula is defined as the fraction of the solute in solids after washing to that originally present in the solids as a function of Number of Stages and Solvent Decanted after Washing. Fraction of Solute Remaining in Solid is denoted by θ_N symbol.

How to calculate Fraction of Solute remaining based on Solvent Decanted using this online calculator? To use this online calculator for Fraction of Solute remaining based on Solvent Decanted, enter Amount of Solvent Decanted (b), Amount of Solvent Remaining (a) & Number of Washings in Batch Leaching (N_Washing) and hit the calculate button. Here is how the Fraction of Solute remaining based on Solvent Decanted calculation can be explained with given input values -> 0.001171 = (1/((1+(30/10.5))^5)).

FAQ

What is Fraction of Solute remaining based on Solvent Decanted?

The Fraction of Solute remaining based on Solvent Decanted formula is defined as the fraction of the solute in solids after washing to that originally present in the solids as a function of Number of Stages and Solvent Decanted after Washing and is represented as θ_N = (1/((1+(b/a))^N_Washing)) or Fraction of Solute Remaining in Solid = (1/((1+(Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching)). The Amount of Solvent Decanted is the amount of solvent that is decanted from the solid in washing stage, The Amount of Solvent Remaining is the amount of solvent that is remaining in the solid in washing stage & The Number of Washings in Batch Leaching is the number of washings required after batch leaching operation.

How to calculate Fraction of Solute remaining based on Solvent Decanted?

The Fraction of Solute remaining based on Solvent Decanted formula is defined as the fraction of the solute in solids after washing to that originally present in the solids as a function of Number of Stages and Solvent Decanted after Washing is calculated using Fraction of Solute Remaining in Solid = (1/((1+(Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching)). To calculate Fraction of Solute remaining based on Solvent Decanted, you need Amount of Solvent Decanted (b), Amount of Solvent Remaining (a) & Number of Washings in Batch Leaching (N_Washing). With our tool, you need to enter the respective value for Amount of Solvent Decanted, Amount of Solvent Remaining & Number of Washings in Batch Leaching 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 Fraction of Solute Remaining in Solid?

In this formula, Fraction of Solute Remaining in Solid uses Amount of Solvent Decanted, Amount of Solvent Remaining & Number of Washings in Batch Leaching. We can use 3 other way(s) to calculate the same, which is/are as follows -

Fraction of Solute Remaining in Solid = (1/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching))
Fraction of Solute Remaining in Solid = Weight of Solute remaining in Solid after Washing/Original Weight of Solute in Solid
Fraction of Solute Remaining in Solid = Weight of Solute remaining in Solid after Washing/Original Weight of Solute in Solid

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