## 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))
θN = (1/((1+ (b/a))^N))
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 Kilogram --> 10 Kilogram No Conversion Required
Number of Washings in Batch Leaching: 5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θN = (1/((1+ (b/a))^N)) --> (1/((1+ (30/10))^5))
Evaluating ... ...
θN = 0.0009765625
STEP 3: Convert Result to Output's Unit
0.0009765625 --> No Conversion Required
0.0009765625 <-- Fraction of Solute Remaining in Solid
(Calculation completed in 00.000 seconds)
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## Credits

Created by Vaibhav Mishra
DJ Sanghvi College of Engineering (DJSCE), Mumbai
Vaibhav Mishra has created this Calculator and 200+ more calculators!
Verified by Prerana Bakli
National Institute of Technology (NIT), Meghalaya
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## < 21 Washing Calculators

Number of Stages based on Original Weight of Solute
Number of Washings in Batch Leaching = (ln(Original Weight of Solute in Solid/Weight of Solute remaining in Solid after Washing)/ln(1+Solvent Decanted per Solvent Remaining in Solid))
Solvent Remaining based on Original Weight of Solute and Number of Stages
Amount of Solvent Remaining = Amount of Solvent Decanted/(((Weight of Solute remaining in Solid after Washing/Original Weight of Solute in Solid)^(1/Number of Washings in Batch Leaching))-1)
Solvent Decanted based on Original Weight of Solute and Number of Stages
Amount of Solvent Decanted = Amount of Solvent Remaining*(((Original Weight of Solute in Solid/Weight of Solute remaining in Solid after Washing)^(1/Number of Washings in Batch Leaching))-1)
Original Weight of Solute based on Number of Stages and Amount of Solvent Decanted
Original Weight of Solute in Solid = Weight of Solute remaining in Solid after Washing*((1+(Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching)
Weight of Solute remaining based on Number of Stages and Amount of Solvent Decanted
Weight of Solute remaining in Solid after Washing = Original Weight of Solute in Solid/((1+Amount of Solvent Decanted/Amount of Solvent Remaining)^Number of Washings in Batch Leaching)
Number of Stages based on Solvent Decanted
Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+(Amount of Solvent Decanted/Amount of Solvent Remaining)))
Beta Value based on Original Weight of Solute
Solvent Decanted per Solvent Remaining in Solid = ((1/(Weight of Solute remaining in Solid after Washing/Original Weight of Solute in Solid))^(1/Number of Washings in Batch Leaching))-1
Weight of Solute remaining based on Number of Stages and Beta Value
Weight of Solute remaining in Solid after Washing = Original Weight of Solute in Solid/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching)
Original Weight of Solute based on Number of Stages and Beta Value
Original Weight of Solute in Solid = Weight of Solute remaining in Solid after Washing*((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching)
Number of Stages for Leaching based on Fraction Solute Retained and Beta Value
Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+Solvent Decanted per Solvent Remaining in Solid))
Solvent Remaining based on Fraction of Solute remaining and Number of Stages
Amount of Solvent Remaining = Amount of Solvent Decanted/(((1/Fraction of Solute Remaining in Solid)^(1/Number of Washings in Batch Leaching))-1)
Solvent Decanted based on Fraction of Solute remaining and Number of Stages
Amount of Solvent Decanted = Amount of Solvent Remaining*(((1/Fraction of Solute Remaining in Solid)^(1/Number of Washings in Batch Leaching))-1)
Fraction of Solute remaining based on Solvent Decanted
Fraction of Solute Remaining in Solid = (1/((1+ (Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching))
Beta Value based on Number of Stages and Fraction of Solute
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
Fraction of Solute Remaining in Solid = (1/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching))
Original Weight of Solute in Solid before Washing
Original Weight of Solute in Solid = Weight of Solute remaining in Solid after Washing/Fraction of Solute Remaining in Solid
Fraction of Solute as ratio of Solute
Fraction of Solute Remaining in Solid = Weight of Solute remaining in Solid after Washing/Original Weight of Solute in Solid
Weight of Solute remaining in Solid
Weight of Solute remaining in Solid after Washing = Fraction of Solute Remaining in Solid*Original Weight of Solute in Solid
Amount of Solvent Decanted
Amount of Solvent Decanted = Amount of Solvent Remaining*Solvent Decanted per Solvent Remaining in Solid
Beta Value based on ratio of Solvent
Solvent Decanted per Solvent Remaining in Solid = Amount of Solvent Decanted/Amount of Solvent Remaining
Amount of Solvent Remaining
Amount of Solvent Remaining = Amount of Solvent Decanted/Solvent Decanted per Solvent Remaining in Solid

## 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))
θN = (1/((1+ (b/a))^N))

## 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 θN 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) 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 -> 0.000977 = (1/((1+ (30/10))^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 θN = (1/((1+ (b/a))^N)) 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). 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 2 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 Let Others Know