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

STEP 0: Pre-Calculation Summary
Formula Used
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))
C = CS*(1-exp((-KL*A*t)/VLeaching))
This formula uses 1 Functions, 6 Variables
Functions Used
exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)
Variables Used
Concentration of Solute in Bulk Solution at Time t - (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.
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.
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 Saturated Solution with Solute: 56 Kilogram per Cubic Meter --> 56 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: 0.154 Square Meter --> 0.154 Square Meter No Conversion Required
Time of Batch Leaching: 600 Second --> 600 Second No Conversion Required
Volume of Leaching Solution: 2.48 Cubic Meter --> 2.48 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
C = CS*(1-exp((-KL*A*t)/VLeaching)) --> 56*(1-exp((-0.0147*0.154*600)/2.48))
Evaluating ... ...
C = 23.616205032719
STEP 3: Convert Result to Output's Unit
23.616205032719 Kilogram per Cubic Meter --> No Conversion Required
FINAL ANSWER
23.616205032719 23.61621 Kilogram per Cubic Meter <-- Concentration of Solute in Bulk Solution at Time t
(Calculation completed in 00.004 seconds)

Credits

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

Mass Transfer Coefficient for Batch Leaching
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 t)/Concentration of Saturated Solution with Solute))
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 Saturated Solution in Contact with Solid in Batch Leaching
Go Concentration of Saturated Solution with Solute = Concentration of Solute in Bulk Solution at Time t/(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 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))

25 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))
Number of Equilibrium Leaching Stages based on Recovery of Solute
Go Number of Equilibrium Stages in Leaching = (log10(1+(Ratio of Discharge in Overflow to Underflow-1)/(1-Recovery of Solute in Leaching Column)))/(log10(Ratio of Discharge in Overflow to Underflow))-1
Number of Equilibirum Leaching Stages based on Fractional Solute Discharge
Go Number of Equilibrium Stages in Leaching = (log10(1+(Ratio of Discharge in Overflow to Underflow-1)/Fractional Solute Discharge))/(log10(Ratio of Discharge in Overflow to Underflow))-1
Number of Stages based on Original Weight of Solute
Go 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))
Solute Discharged in Underflow based on Ratio of Overflow to Underflow and Solution Discharged
Go Amount of Solute Discharge in Underflow = Amount of Solution Discharge in Underflow-((Amount of Solution Discharge in Overflow-Amount of Solute Discharge in Overflow)/Ratio of Discharge in Overflow to Underflow)
Ratio of Solvent Discharged in Underflow to Overflow
Go Ratio of Discharge in Overflow to Underflow = (Amount of Solution Discharge in Overflow-Amount of Solute Discharge in Overflow)/(Amount of Solution Discharge in Underflow-Amount of Solute Discharge in Underflow)
Solute Discharged in Overflow based on Ratio of Overflow to Underflow and Solution Discharged
Go Amount of Solute Discharge in Overflow = Amount of Solution Discharge in Overflow-Ratio of Discharge in Overflow to Underflow*(Amount of Solution Discharge in Underflow-Amount of Solute Discharge in Underflow)
Solvent Remaining based on Original Weight of Solute and Number of Stages
Go Amount of Solvent Remaining = Amount of Solvent Decanted/(((Original Weight of Solute in Solid/Weight of Solute remaining in Solid after Washing)^(1/Number of Washings in Batch Leaching))-1)
Solvent Decanted based on Original Weight of Solute and Number of Stages
Go 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
Go 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
Go 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
Go Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+(Amount of Solvent Decanted/Amount of Solvent Remaining)))
Fractional Solute Discharge based on Ratio of Overflow to Underflow
Go Fractional Solute Discharge = (Ratio of Discharge in Overflow to Underflow-1)/((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1)
Fraction of Solute remaining based on Solvent Decanted
Go Fraction of Solute Remaining in Solid = (1/((1+ (Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching))
Recovery of Solute based on Solute Underflow
Go Recovery of Solute in Leaching Column = 1-(Amount of Solute in Underflow Leaving Column/Amount of Solute in Underflow Entering Column)
Ratio of Solution Discharged in Overflow to Underflow
Go Ratio of Discharge in Overflow to Underflow = Amount of Solution Discharge in Overflow/Amount of Solution Discharge in Underflow
Ratio of Solute Discharged in Underflow to Overflow
Go Ratio of Discharge in Overflow to Underflow = Amount of Solute Discharge in Overflow/Amount of Solute Discharge in Underflow
Fraction of Solute as Ratio of Solute
Go Fraction of Solute Remaining in Solid = Weight of Solute remaining in Solid after Washing/Original Weight of Solute in Solid
Fractional Solute Discharge Ratio based on Solute Underflow
Go Fractional Solute Discharge = Amount of Solute in Underflow Leaving Column/Amount of Solute in Underflow Entering Column
Beta Value based on Ratio of Solvent
Go Solvent Decanted per Solvent Remaining in Solid = Amount of Solvent Decanted/Amount of Solvent Remaining
Fractional Solute Discharge based on Recovery of Solute
Go Fractional Solute Discharge = 1-Recovery of Solute in Leaching Column
Recovery of Solute based on Fractional Solute Discharge
Go Recovery of Solute in Leaching Column = 1-Fractional Solute Discharge

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

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))
C = CS*(1-exp((-KL*A*t)/VLeaching))

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 Solute in Bulk Solution at Time t for Batch Leaching?

Concentration of Solute in Bulk Solution at Time t for Batch Leaching calculator uses 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)) to calculate the Concentration of Solute in Bulk Solution at Time t, The Concentration of Solute in Bulk Solution at Time t for Batch Leaching formula is defined as the concentration of the solid in the bulk of leaching solution after time t has passed in batch leaching operation. Concentration of Solute in Bulk Solution at Time t is denoted by C symbol.

How to calculate Concentration of Solute in Bulk Solution at Time t for Batch Leaching using this online calculator? To use this online calculator for Concentration of Solute in Bulk Solution at Time t for Batch Leaching, enter Concentration of Saturated Solution with Solute (CS), Mass Transfer Coefficient for Batch Leaching (KL), Area of Leaching (A), Time of Batch Leaching (t) & Volume of Leaching Solution (VLeaching) and hit the calculate button. Here is how the Concentration of Solute in Bulk Solution at Time t for Batch Leaching calculation can be explained with given input values -> 23.61621 = 56*(1-exp((-0.0147*0.154*600)/2.48)).

FAQ

What is Concentration of Solute in Bulk Solution at Time t for Batch Leaching?
The Concentration of Solute in Bulk Solution at Time t for Batch Leaching formula is defined as the concentration of the solid in the bulk of leaching solution after time t has passed in batch leaching operation and is represented as C = CS*(1-exp((-KL*A*t)/VLeaching)) or 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)). The Concentration of Saturated Solution with Solute is the concentration of the saturated solution in contact with the solute particles for 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 Solute in Bulk Solution at Time t for Batch Leaching?
The Concentration of Solute in Bulk Solution at Time t for Batch Leaching formula is defined as the concentration of the solid in the bulk of leaching solution after time t has passed in batch leaching operation is calculated using 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)). To calculate Concentration of Solute in Bulk Solution at Time t for Batch Leaching, you need Concentration of Saturated Solution with Solute (CS), Mass Transfer Coefficient for Batch Leaching (KL), Area of Leaching (A), Time of Batch Leaching (t) & Volume of Leaching Solution (VLeaching). With our tool, you need to enter the respective value for Concentration of Saturated Solution with Solute, 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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