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

Concentration Formula:

\[ C = C_S \times \left(1 - e^{\left(\frac{-K_L \times A \times t}{V_{Leaching}}\right)}\right) \]

Concentration of Saturated Solution (C_S):

kg/m³

Mass Transfer Coefficient (K_L):

mol/(s·m²)

Area of Leaching (A):

m²

Time of Batch Leaching (t):

seconds

Volume of Leaching Solution (V_Leaching):

m³

Concentration at Time t (C): kg/m³

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1. What is Concentration of Solute in Bulk Solution at Time t?

Definition: This calculator determines the concentration of solute in the bulk solution at a specific time during batch leaching.

Purpose: It helps chemical engineers and process technicians understand the progress of leaching operations over time.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C = C_S \times \left(1 - e^{\left(\frac{-K_L \times A \times t}{V_{Leaching}}\right)}\right) \]

Where:

\( C \) — Concentration at time t (kg/m³)
\( C_S \) — Saturated solution concentration (kg/m³)
\( K_L \) — Mass transfer coefficient (mol/(s·m²))
\( A \) — Area of leaching (m²)
\( t \) — Time of batch leaching (seconds)
\( V_{Leaching} \) — Volume of leaching solution (m³)

Explanation: The formula models the exponential approach to saturation concentration over time.

3. Importance of This Calculation

Details: Understanding concentration profiles helps optimize leaching time, predict process completion, and design efficient systems.

4. Using the Calculator

Tips: Enter all parameters with correct units. Default values are provided for reference.

5. Frequently Asked Questions (FAQ)

Q1: What affects the mass transfer coefficient (K_L)?
A: Temperature, solvent properties, solute properties, and agitation intensity all influence K_L.

Q2: How do I determine the saturated concentration (C_S)?
A: C_S is typically determined experimentally for the specific solute-solvent system.

Q3: What if my leaching area changes over time?
A: For systems with changing area, the calculation becomes more complex and may require numerical methods.

Q4: How accurate is this model?
A: This provides a first-order approximation. Real systems may deviate due to factors like particle size distribution.

Q5: What's a typical range for K_L?
A: K_L values typically range from 0.001 to 0.1 mol/(s·m²) depending on the system.