Certainly! Let’s break down the solution step-by-step for the **recovery of toluene from a wastewater stream** using **liquid-liquid extraction (LLE)** followed by **distillation**. We’ll also address how an **increase in temperature** affects both units. --- ## **Step 1: Problem Overview and Feed Composition** **Feed to Extraction Unit (by weight):** - Toluene: **15 wt%** - Water: **75 wt%** - Acetic Acid: **10 wt%** **Objective:** 1. Recover toluene from the aqueous mixture using LLE. 2. Purify the extracted toluene by distillation for reuse. 3. Evaluate the effect of a temperature increase (malfunction) on both steps. --- ## **Step 2: Liquid-Liquid Extraction (LLE)** ### **a. Principle** - **LLE** separates compounds based on their solubility in two immiscible liquids (typically aqueous and organic phase). - **Toluene** is much more soluble in organic solvents (like itself or similar) than in water. - **Acetic acid** is somewhat soluble in both phases; water is highly soluble in water phase. ### **b. Choosing Extraction Solvent** - Often, an organic solvent immiscible with water is used (sometimes pure toluene is used to “wash” more toluene out, or another solvent like hexane or DCM). - Here, let’s assume we use **pure toluene** to extract more toluene from aqueous phase (or another suitable organic solvent). ### **c. Extraction Equilibrium (Distribution Coefficient)** Let: - \( K_{\text{tol}} = \frac{[\text{Toluene}]_{\text{org}}}{[\text{Toluene}]_{\text{aq}}} \) *(distribution coefficient for toluene)* - \( K_{\text{aa}} = \frac{[\text{Acetic Acid}]_{\text{org}}}{[\text{Acetic Acid}]_{\text{aq}}} \) Suppose (from data, typically at 25–50°C): - \( K_{\text{tol}} \gg 1 \) (toluene strongly prefers organic phase) - \( K_{\text{aa}} \sim 0.1-0.2 \) (acetic acid prefers aqueous, but some transfers) - Water remains in the aqueous phase. **Assume:** - For calculation, let’s use \( K_{\text{tol}} = 10 \) (toluene:organic/aqueous) - \( K_{\text{aa}} = 0.15 \) (acetic acid:organic/aqueous) --- ### **d. Material Balance and Extraction** Let’s assume **100 kg feed** for simplicity: - Toluene: 15 kg - Water: 75 kg - Acetic Acid: 10 kg Let’s use **pure toluene** as the extracting solvent, 15 kg (equal mass to toluene in feed). **Let**: - \( F \) = feed (100 kg) - \( S \) = solvent (15 kg; all toluene) - \( x_{\text{tol,aq}} \) = final toluene in aqueous phase - \( x_{\text{tol,org}} \) = final toluene in organic phase **Toluene mass balance:** \[ \text{Total toluene} = (\text{in aqueous phase}) + (\text{in organic phase}) \] \[ 15 = x_{\text{tol,aq}} + x_{\text{tol,org}} \] **Distribution equilibrium:** \[ K_{\text{tol}} = \frac{\frac{x_{\text{tol,org}}}{\text{mass of org phase}}}{\frac{x_{\text{tol,aq}}}{\text{mass of aq phase}}} \] - Organic phase mass: \( S + x_{\text{tol,org}} \approx S \) (if toluene only) - Aqueous phase mass: \( 100 - 15 = 85 \) kg But for simplicity, use \( S = 15 \) kg, aqueous = 85 kg. So: \[ K_{\text{tol}} = \frac{x_{\text{tol,org}}/15}{x_{\text{tol,aq}}/85} \implies x_{\text{tol,org}} = K_{\text{tol}} \cdot x_{\text{tol,aq}} \cdot \frac{15}{85} \] But also: \[ x_{\text{tol,org}} + x_{\text{tol,aq}} = 15 \] Substitute: \[ x_{\text{tol,org}} = 15 - x_{\text{tol,aq}} \] So: \[ 15 - x_{\text{tol,aq}} = K_{\text{tol}} \cdot x_{\text{tol,aq}} \cdot \frac{15}{85} \] \[ 15 - x_{\text{tol,aq}} = \frac{150}{85} x_{\text{tol,aq}} \] \[ 15 = x_{\text{tol,aq}} \left(1 + \frac{150}{85}\right) \] \[ 1 + \frac{150}{85} = 1 + 1.765 = 2.765 \] \[ x_{\text{tol,aq}} = \frac{15}{2.765} = 5.43 \text{ kg} \] \[ x_{\text{tol,org}} = 15 - 5.43 = 9.57 \text{ kg} \] **So, after extraction:** - Aqueous phase: **5.43 kg toluene** - Organic phase: **9.57 kg toluene + 15 kg toluene solvent = 24.57 kg total** (mostly toluene) **Acetic acid:** \[ K_{\text{aa}} = 0.15 \] \[ x_{\text{aa,org}} = K_{\text{aa}} \cdot x_{\text{aa,aq}} \cdot \frac{15}{85} \] \[ x_{\text{aa,org}} + x_{\text{aa,aq}} = 10 \] So, \[ x_{\text{aa,org}} = 0.15 \cdot x_{\text{aa,aq}} \cdot \frac{15}{85} = 0.0265 x_{\text{aa,aq}} \] \[ x_{\text{aa,org}} + x_{\text{aa,aq}} = 10 \] \[ 0.0265 x_{\text{aa,aq}} + x_{\text{aa,aq}} = 10 \] \[ 1.0265 x_{\text{aa,aq}} = 10 \] \[ x_{\text{aa,aq}} = \frac{10}{1.0265} = 9.74 \text{ kg} \] \[ x_{\text{aa,org}} = 10 - 9.74 = 0.26 \text{ kg} \] **So, after extraction:** - Aqueous phase: **9.74 kg acetic acid** - Organic phase: **0.26 kg acetic acid** --- ## **Step 3: Distillation to Purify Toluene** ### **a. Feed to Distillation** - Organic phase: **24.57 kg toluene** (almost all toluene), **0.26 kg acetic acid**. ### **b. Toluene Purification** - **Toluene boiling point:** ~110.6°C - **Acetic acid boiling point:** ~118°C - **Water boiling point:** 100°C (but not much present in organic phase) Since acetic acid is slightly higher boiling, **distillation can separate toluene as distillate** and acetic acid as bottoms. If needed, further purification can be done by **washing distillate** or using **azeotropic distillation**, but here a simple distillation should be sufficient due to the small acetic acid impurity. ### **c. Vapor Pressure Data (Rough Values, 110–120°C)** - Toluene: vapor pressure at 110°C ≈ 1 atm (boiling point) - Acetic acid: vapor pressure at 110°C ≈ less than 1 atm (does not boil yet) - Water: not much present ### **d. Distillation Outcome** - **Distillate:** High-purity toluene (can be condensed and reused) - **Bottoms:** Trace acetic acid (and any high-boiling impurities) --- ## **Step 4: Effect of Temperature Increase (Malfunction)** ### **A. On Extraction (LLE)** - **Distribution coefficients (K):** - **K for toluene** typically **decreases** with increasing temperature (toluene less soluble in organic phase, more in water). - **K for acetic acid** may **increase** (acetic acid becomes more soluble in organic phase as temperature increases). - **Result:** - **Toluene recovery decreases** (more remains in aqueous phase; less extracted). - **More acetic acid** may enter organic phase (lower purity of toluene extract). ### **B. On Distillation** - **Higher temperature:** - **Relative volatility** between toluene and acetic acid may decrease (boiling points closer). - **Separation efficiency decreases** (harder to purify toluene; more acetic acid in distillate). - **Potential issues:** - May require more stages (theoretical plates) or deeper vacuum to achieve the same purity. - Increased risk of **overheating** or **thermal degradation** if temperature exceeds safe limits. --- ## **Summary Table** | Step | Main Effect of Temperature Increase | |--------------|-----------------------------------------| | Extraction | Lower K_tol ⇒ lower toluene recovery; higher acetic acid in extract | | Distillation | Lower relative volatility ⇒ less efficient separation; lower purity toluene | --- ## **Final Answers** ### **1. Step-by-Step Recovery Process** **a. Liquid-Liquid Extraction** - Feed: 100 kg (15 kg toluene, 75 kg water, 10 kg acetic acid) - Add 15 kg pure toluene (solvent) - After extraction (assuming K_tol = 10, K_aa = 0.15): - **Aqueous phase:** 5.43 kg toluene, 9.74 kg acetic acid, 75 kg water - **Organic phase:** 24.57 kg toluene, 0.26 kg acetic acid **b. Distillation** - Feed: 24.57 kg toluene, 0.26 kg acetic acid - **Product:** High-purity toluene (distillate) ready for reuse ### **2. Effect of Temperature Increase** - **Extraction:** Lower toluene recovery, higher acetic acid contamination in toluene-rich phase. - **Distillation:** Lower separation efficiency; may reduce toluene purity unless compensated for. --- **If you have specific equilibrium or vapor pressure data, plug those values into the calculations above for more precise results.** --- **If you need a diagram or further calculations (e.g., number of stages for distillation, actual equilibrium data), please provide those details or request the next step!**