Number of Stages for Extraction Factor equal to 1 Calculator

Number of Equilibrium Extraction Stages Formula:

\[ N = \frac{z_C - \left(\frac{y_s}{K_{Solute}}\right)}{x_C - \left(\frac{y_s}{K_{Solute}}\right)} - 1 \]

Mass Fraction of Solute in the Feed:

Mass Fraction of Solute in the Solvent:

Distribution Coefficient of Solute:

Mass Fraction of Solute in the Raffinate:

Number of Equilibrium Extraction Stages:

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1. What is Number of Stages for Extraction Factor equal to 1?

Definition: This calculator determines the number of equilibrium stages required in liquid-liquid extraction when the extraction factor equals 1.

Purpose: It helps chemical engineers design extraction processes by calculating the ideal number of stages needed for separation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N = \frac{z_C - \left(\frac{y_s}{K_{Solute}}\right)}{x_C - \left(\frac{y_s}{K_{Solute}}\right)} - 1 \]

Where:

\( N \) — Number of equilibrium extraction stages
\( z_C \) — Mass fraction of solute in the feed
\( y_s \) — Mass fraction of solute in the solvent
\( K_{Solute} \) — Distribution coefficient of solute
\( x_C \) — Mass fraction of solute in the raffinate

Explanation: The formula calculates the stages needed when the extraction factor (E = K*S/F) equals 1, meaning the solvent flow rate times distribution coefficient equals the feed flow rate.

3. Importance of Stage Calculation

Details: Accurate stage calculation ensures efficient separation, optimal solvent usage, and proper equipment sizing in extraction processes.

4. Using the Calculator

Tips: Enter all mass fractions (0-1 range) and the distribution coefficient (>0). The raffinate mass fraction should be less than the feed mass fraction.

5. Frequently Asked Questions (FAQ)

Q1: What does extraction factor = 1 mean?
A: It means the solvent flow rate times distribution coefficient equals the feed flow rate (E = K*S/F = 1).

Q2: What's a typical distribution coefficient range?
A: It varies widely (0.1-10) depending on the solute-solvent system and conditions like temperature.

Q3: Can this be used for countercurrent extraction?
A: Yes, this formula applies to countercurrent extraction when E=1.

Q4: What if my result is negative?
A: Check your inputs - likely the raffinate concentration is higher than possible for the given feed and distribution coefficient.

Q5: How does temperature affect the calculation?
A: Temperature affects the distribution coefficient (K), which should be measured at your operating temperature.