Concentration of Saturated Solution in Contact with Solid Solution

STEP 0: Pre-Calculation Summary
Formula Used
Concentration of Saturated Solution with Solute = Concentration of Solute in Bulk Solution at Time/(1-exp((-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/Volume of Leaching Solution))
CS = C/(1-exp((-KL*A*t)/V))
This formula uses 1 Constants, 1 Functions, 6 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
exp - Exponential function, exp(Number)
Variables Used
Concentration of Saturated Solution with Solute - (Measured in Kilogram per Cubic Meter) - The Concentration of Saturated Solution with Solute is the concentration of the saturated solution in contact with the solute particles for batch leaching process.
Concentration of Solute in Bulk Solution at Time - (Measured in Kilogram per Cubic Meter) - The Concentration of Solute in Bulk Solution at Time (t) is the solute concentration in bulk of solution at time (t) of the batch leaching process.
Mass Transfer Coefficient for Batch Leaching - (Measured in Mole per Second Square Meter) - The Mass Transfer Coefficient for Batch Leaching is the coefficient that accounts for driving force for mass transfer in the liquid phase.
Area of Leaching - (Measured in Square Meter) - The Area of Leaching is the are of contact available for leaching mass transfer, i.e. the surface area of the solids in contact with the solvent liquid.
Time of Batch Leaching - (Measured in Second) - The Time of Batch Leaching is the time the solid and the solvent is kept into contact (mixed together) in Batch Leaching Operation.
Volume of Leaching Solution - (Measured in Cubic Meter) - The Volume of Leaching Solution is the volume of complete solution i.e. solute plus solvent for Leaching.
STEP 1: Convert Input(s) to Base Unit
Concentration of Solute in Bulk Solution at Time: 25 Kilogram per Cubic Meter --> 25 Kilogram per Cubic Meter No Conversion Required
Mass Transfer Coefficient for Batch Leaching: 0.0147 Mole per Second Square Meter --> 0.0147 Mole per Second Square Meter No Conversion Required
Area of Leaching: 0.1 Square Meter --> 0.1 Square Meter No Conversion Required
Time of Batch Leaching: 600 Second --> 600 Second No Conversion Required
Volume of Leaching Solution: 2.5 Cubic Meter --> 2.5 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
CS = C/(1-exp((-KL*A*t)/V)) --> 25/(1-exp((-0.0147*0.1*600)/2.5))
Evaluating ... ...
CS = 84.0951577780497
STEP 3: Convert Result to Output's Unit
84.0951577780497 Kilogram per Cubic Meter --> No Conversion Required
FINAL ANSWER
84.0951577780497 Kilogram per Cubic Meter <-- Concentration of Saturated Solution with Solute
(Calculation completed in 00.031 seconds)

Credits

Created by Vaibhav Mishra
DJ Sanghvi College of Engineering (DJSCE), Mumbai
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6 Leaching Calculators

Mass Transfer Coefficient for Batch Leaching

Mass Transfer Coefficient for Batch Leaching

Formula
`"K"_{"L"} = (-"V"/("A"*"t"))*ln((("C"_{"S"}-"C")/"C"_{"S"}))`

Example
`"0.02464mol/s*m²"=(-"2.5m³"/("0.1m²"*"600s"))*ln((("56kg/m³"-"25kg/m³")/"56kg/m³"))`

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

Area of Contact for Batch Leaching Operation

Formula
`"A" = (-"V"/("K"_{"L"}*"t"))*ln((("C"_{"S"}-"C")/"C"_{"S"}))`

Example
`"0.16762m²"=(-"2.5m³"/("0.0147mol/s*m²"*"600s"))*ln((("56kg/m³"-"25kg/m³")/"56kg/m³"))`

Calculator
LaTeX
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)/Concentration of Saturated Solution with Solute))
Time of Batch Leaching Operation

Time of Batch Leaching Operation

Formula
`"t" = (-"V"/("A"*"K"_{"L"}))*ln((("C"_{"S"}-"C")/"C"_{"S"}))`

Example
`"1005.722s"=(-"2.5m³"/("0.1m²"*"0.0147mol/s*m²"))*ln((("56kg/m³"-"25kg/m³")/"56kg/m³"))`

Calculator
LaTeX
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)/Concentration of Saturated Solution with Solute))
Volume of Leaching Solution

Volume of Leaching Solution

Formula
`"V" = (-"K"_{"L"}*"A"*"t")/ln((("C"_{"S"}-"C")/"C"_{"S"}))`

Example
`"1.491466m³"=(-"0.0147mol/s*m²"*"0.1m²"*"600s")/ln((("56kg/m³"-"25kg/m³")/"56kg/m³"))`

Calculator
LaTeX
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)/Concentration of Saturated Solution with Solute))
Concentration of Saturated Solution in Contact with Solid

Concentration of Saturated Solution in Contact with Solid

Formula
`"C"_{"S"} = "C"/(1-exp((-"K"_{"L"}*"A"*"t")/"V"))`

Example
`"84.09516kg/m³"="25kg/m³"/(1-exp((-"0.0147mol/s*m²"*"0.1m²"*"600s")/"2.5m³"))`

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

Concentration of Solute in Bulk Solution at Time t

Formula
`"C" = "C"_{"S"}*(1-exp((-"K"_{"L"}*"A"*"t")/"V"))`

Example
`"16.64781kg/m³"="56kg/m³"*(1-exp((-"0.0147mol/s*m²"*"0.1m²"*"600s")/"2.5m³"))`

Calculator
LaTeX
Go Concentration of Solute in Bulk Solution at Time = 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))

Concentration of Saturated Solution in Contact with Solid Formula

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

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 Concentration of Saturated Solution in Contact with Solid?

Concentration of Saturated Solution in Contact with Solid calculator uses Concentration of Saturated Solution with Solute = Concentration of Solute in Bulk Solution at Time/(1-exp((-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/Volume of Leaching Solution)) to calculate the Concentration of Saturated Solution with Solute, The Concentration of Saturated Solution in Contact with Solid formula is defined as the concentration of the solute in the saturated leaching solution in contact with the solid calculated as a function of the concentration of solute in bulk solution at time t. Concentration of Saturated Solution with Solute is denoted by CS symbol.

How to calculate Concentration of Saturated Solution in Contact with Solid using this online calculator? To use this online calculator for Concentration of Saturated Solution in Contact with Solid, enter Concentration of Solute in Bulk Solution at Time (C), Mass Transfer Coefficient for Batch Leaching (KL), Area of Leaching (A), Time of Batch Leaching (t) & Volume of Leaching Solution (V) and hit the calculate button. Here is how the Concentration of Saturated Solution in Contact with Solid calculation can be explained with given input values -> 84.09516 = 25/(1-exp((-0.0147*0.1*600)/2.5)).

FAQ

What is Concentration of Saturated Solution in Contact with Solid?
The Concentration of Saturated Solution in Contact with Solid formula is defined as the concentration of the solute in the saturated leaching solution in contact with the solid calculated as a function of the concentration of solute in bulk solution at time t and is represented as CS = C/(1-exp((-KL*A*t)/V)) or Concentration of Saturated Solution with Solute = Concentration of Solute in Bulk Solution at Time/(1-exp((-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/Volume of Leaching Solution)). The Concentration of Solute in Bulk Solution at Time (t) is the solute concentration in bulk of solution at time (t) of the batch leaching process, The Mass Transfer Coefficient for Batch Leaching is the coefficient that accounts for driving force for mass transfer in the liquid phase, The Area of Leaching is the are of contact available for leaching mass transfer, i.e. the surface area of the solids in contact with the solvent liquid, The Time of Batch Leaching is the time the solid and the solvent is kept into contact (mixed together) in Batch Leaching Operation & The Volume of Leaching Solution is the volume of complete solution i.e. solute plus solvent for Leaching.
How to calculate Concentration of Saturated Solution in Contact with Solid?
The Concentration of Saturated Solution in Contact with Solid formula is defined as the concentration of the solute in the saturated leaching solution in contact with the solid calculated as a function of the concentration of solute in bulk solution at time t is calculated using Concentration of Saturated Solution with Solute = Concentration of Solute in Bulk Solution at Time/(1-exp((-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/Volume of Leaching Solution)). To calculate Concentration of Saturated Solution in Contact with Solid, you need Concentration of Solute in Bulk Solution at Time (C), Mass Transfer Coefficient for Batch Leaching (KL), Area of Leaching (A), Time of Batch Leaching (t) & Volume of Leaching Solution (V). With our tool, you need to enter the respective value for Concentration of Solute in Bulk Solution at Time, Mass Transfer Coefficient for Batch Leaching, Area of Leaching, Time of Batch Leaching & Volume of Leaching Solution 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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