## Fraction of Solute Remaining based on Beta Value Solution

STEP 0: Pre-Calculation Summary
Formula Used
Fraction of Solute Remaining in Solid = (1/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching))
θN = (1/((1+β)^N))
This formula uses 3 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.
Solvent Decanted per Solvent Remaining in Solid - The Solvent Decanted per Solvent Remaining in Solid is the ratio of the solvent mass decanted per unit solvent remaining in the insoluble solid.
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
Solvent Decanted per Solvent Remaining in Solid: 3 --> 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+β)^N)) --> (1/((1+3)^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 100+ more calculators!
Verified by Prerana Bakli
National Institute of Technology (NIT), Meghalaya
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## < 10+ Washing Calculators

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

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

Formula
"N" = (ln(1/"θ"_{"N"})/ln(1+"β"))

Example
"4.982892"=(ln(1/"0.001")/ln(1+"3"))

Calculator
LaTeX
Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+Solvent Decanted per Solvent Remaining in Solid))
Fraction of Solute remaining based on Solvent Decanted

## Fraction of Solute remaining based on Solvent Decanted

Formula
"θ"_{"N"} = (1/((1+ ("b"/"a"))^"N"))

Example
"0.000977"=(1/((1+ ("30kg"/"10kg"))^"5"))

Calculator
LaTeX
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

## Beta Value based on Number of Stages and Fraction of Solute

Formula
"β" = ((1/"θ"_{"N"})^(1/"N"))-1

Example
"2.981072"=((1/"0.001")^(1/"5"))-1

Calculator
LaTeX
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 based on Beta Value

Formula
"θ"_{"N"} = (1/((1+"β")^"N"))

Example
"0.000977"=(1/((1+"3")^"5"))

Calculator
LaTeX
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 before Washing

Formula
"S" = "S"_{"N"}/"θ"_{"N"}

Example
"10kg"="0.01kg"/"0.001"

Calculator
LaTeX
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 as ratio of Solute

Formula
"θ"_{"N"} = "S"_{"N"}/"S"

Example
"0.1"="0.01kg"/"0.1kg"

Calculator
LaTeX
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

Formula
"S"_{"N"} = "θ"_{"N"}*"S"

Example
"0.0001kg"="0.001"*"0.1kg"

Calculator
LaTeX
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

Formula
"b" = "a"*"β"

Example
"30kg"="10kg"*"3"

Calculator
LaTeX
Amount of Solvent Decanted = Amount of Solvent Remaining*Solvent Decanted per Solvent Remaining in Solid
Beta Value based on ratio of Solvent

## Beta Value based on ratio of Solvent

Formula
"β" = "b"/"a"

Example
"3"="30kg"/"10kg"

Calculator
LaTeX
Solvent Decanted per Solvent Remaining in Solid = Amount of Solvent Decanted/Amount of Solvent Remaining
Amount of Solvent Remaining

## Amount of Solvent Remaining

Formula
"a" = "b"/"β"

Example
"10kg"="30kg"/"3"

Calculator
LaTeX
Amount of Solvent Remaining = Amount of Solvent Decanted/Solvent Decanted per Solvent Remaining in Solid

## Fraction of Solute Remaining based on Beta Value Formula

Fraction of Solute Remaining in Solid = (1/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching))
θN = (1/((1+β)^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 Beta Value?

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

How to calculate Fraction of Solute Remaining based on Beta Value using this online calculator? To use this online calculator for Fraction of Solute Remaining based on Beta Value, enter Solvent Decanted per Solvent Remaining in Solid (β) & Number of Washings in Batch Leaching (N) and hit the calculate button. Here is how the Fraction of Solute Remaining based on Beta Value calculation can be explained with given input values -> 0.000977 = (1/((1+3)^5)).

### FAQ

What is Fraction of Solute Remaining based on Beta Value?
The Fraction of Solute remaining based on Beta Value formula is defined as the fraction of the solute in solids after washing to that originally present in the solids as a function of Beta Value and Number of Stages and is represented as θN = (1/((1+β)^N)) or Fraction of Solute Remaining in Solid = (1/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching)). The Solvent Decanted per Solvent Remaining in Solid is the ratio of the solvent mass decanted per unit solvent remaining in the insoluble solid & 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 Beta Value?
The Fraction of Solute remaining based on Beta Value formula is defined as the fraction of the solute in solids after washing to that originally present in the solids as a function of Beta Value and Number of Stages is calculated using Fraction of Solute Remaining in Solid = (1/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching)). To calculate Fraction of Solute Remaining based on Beta Value, you need Solvent Decanted per Solvent Remaining in Solid (β) & Number of Washings in Batch Leaching (N). With our tool, you need to enter the respective value for Solvent Decanted per Solvent Remaining in Solid & 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 Solvent Decanted per Solvent Remaining in Solid & 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 = Weight of Solute remaining in Solid after Washing/Original Weight of Solute in Solid
• Fraction of Solute Remaining in Solid = (1/((1+ (Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching))
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