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

✖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 Saturated Solution with Solute [C_S]			+10% -10%
✖The Mass Transfer Coefficient for Batch Leaching is the coefficient that accounts for driving force for mass transfer in the liquid phase.ⓘ Mass Transfer Coefficient for Batch Leaching [K_L]			+10% -10%
✖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.ⓘ Area of Leaching [A]			+10% -10%
✖The Time of Batch Leaching is the time the solid and the solvent is kept into contact (mixed together) in Batch Leaching Operation.ⓘ Time of Batch Leaching [t]			+10% -10%
✖The Volume of Leaching Solution is the volume of complete solution i.e. solute plus solvent for Leaching.ⓘ Volume of Leaching Solution [V_Leaching]			+10% -10%

✖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 Solute in Bulk Solution at Time t for Batch Leaching [C]

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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 = C_S*(1-exp((-K_L*A*t)/V_Leaching))
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 = C_S*(1-exp((-K_L*A*t)/V_Leaching)) --> 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)

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Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< Operation Calculators

Time of Batch Leaching Operation

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 t)/Concentration of Saturated Solution with Solute))

Volume of Leaching Solution in Batch Leaching

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 t)/Concentration of Saturated Solution with Solute))

Concentration of Saturated Solution in Contact with Solid in Batch Leaching

LaTeX 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

LaTeX 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))

< Important Formulas in Solid Liquid Extraction Calculators

Area of Contact for Batch Leaching Operation

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 t)/Concentration of Saturated Solution with Solute))

Time of Batch Leaching Operation

Volume of Leaching Solution in Batch Leaching

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

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

LaTeX Go

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 (C_S), Mass Transfer Coefficient for Batch Leaching (K_L), Area of Leaching (A), Time of Batch Leaching (t) & Volume of Leaching Solution (V_Leaching) 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 = C_S*(1-exp((-K_L*A*t)/V_Leaching)) 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 (C_S), Mass Transfer Coefficient for Batch Leaching (K_L), Area of Leaching (A), Time of Batch Leaching (t) & Volume of Leaching Solution (V_Leaching). 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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