Unit 8: Chlor-Alkali and Heavy Chemicals: Membrane Cells & Heavy Acids
Exhaustive electrochemical and process engineering treatise on the chlor-alkali industry: primary brine precipitation, secondary chelating ion-exchange resin purification, membrane cell electrochemistry (Nafion perfluorosulfonate membranes, DSA anodes, nickel gas-diffusion cathodes), cell voltage decomposition (overpotentials and ohmic drops), caustic concentration, chlorine liquefaction, and industrial sulfuric acid manufacture via the DCDA contact process.
Β§8.1 Brine Chemistry & Ultra-Pure Purification: Primary Treatment & Chelating Resins
The raw feedstock for the chlor-alkali industry is saturated aqueous sodium chloride ($\text{NaCl}$) brine ($300 - 320\text{ g/L NaCl}$) sourced from solution-mined underground salt deposits or solar marine salt pans.
Impurity Hazards in Modern Membrane Cells
Modern perfluorinated cation-exchange membranes (e.g., DuPont Nafion, Asahi Kasei Aciplex) are irreversibly poisoned by multivalent alkaline-earth cations ($\text{Ca}^{2+}, \text{Mg}^{2+}, \text{Ba}^{2+}, \text{Sr}^{2+}$). Inside the membrane, migrating divalent cations encounter hydroxide ions ($\text{OH}^-$) diffusing from the catholyte:
Insoluble precipitates crystallize inside the microscopic hydrophilic ion clusters ($2 - 4\text{ nm}$), rupturing polymer chains, causing blistering, and escalating electrical cell voltage. Consequently, total hardness ($[\text{Ca}^{2+}] + [\text{Mg}^{2+}]$) must be reduced below $20\text{ ppb}$ ($0.020\text{ mg/L}$).
Two-Stage Industrial Purification Circuit
1. Primary Chemical Precipitation:
- Sodium carbonate ($\text{Na}_2\text{CO}_3$) precipitates calcium:
- Sodium hydroxide ($\text{NaOH}$) precipitates magnesium and iron:
- Barium chloride ($\text{BaCl}_2$) precipitates sulfate:
The effluent is treated with polyelectrolyte flocculants, clarified in rake settlers, and polished through anthracite/sand filters, reducing hardness to $1 - 5\text{ ppm}$.
2. Secondary Purification via Chelating Ion-Exchange Resins:
The polished brine passes through packed columns of macroporous polystyrene resins functionalized with iminodiacetic acid or aminomethylphosphonic acid groups:
The chelating resin exhibits an affinity for divalent alkaline earths over sodium ions exceeding $10,000 : 1$, consistently discharging ultra-pure brine containing $< 10\text{ ppb total hardness}$.
Β§8.2 Chlor-Alkali Technologies: Mercury, Diaphragm & Modern Cation-Exchange Membrane Cells
The industrial electrolysis of aqueous sodium chloride has undergone three major technological transitions:
Comparison of Electrolytic Technologies
| Feature | Mercury Cell (Castner-Kellner) | Diaphragm Cell | Modern Membrane Cell | |---|---|---|---| | Anode Reaction | $2\text{Cl}^- \to \text{Cl}_2 + 2e^-$ | $2\text{Cl}^- \to \text{Cl}_2 + 2e^-$ | $2\text{Cl}^- \to \text{Cl}_2 + 2e^-$ | | Cathode Reaction | $\text{Na}^+ + \text{Hg} + e^- \to \text{Na(Hg)}$ amalgam | $2\text{H}_2\text{O} + 2e^- \to \text{H}_2 + 2\text{OH}^-$ | $2\text{H}_2\text{O} + 2e^- \to \text{H}_2 + 2\text{OH}^-$ | | Caustic Purity | Pure $50\%\text{ NaOH}$ directly (from decomposer) | Dilute $12\%\text{ NaOH} + 15\%\text{ NaCl}$ (requires huge evaporation) | Pure $32 - 35\%\text{ NaOH}$ ($< 30\text{ ppm NaCl}$) | | Electrical Energy | $3,100 - 3,400\text{ kWh/t NaOH}$ | $2,700 - 3,000\text{ kWh/t NaOH}$ | $2,100 - 2,400\text{ kWh/t NaOH}$ | | Environmental Hazard | Severe toxic mercury bioaccumulation (Minamata) | Carcinogenic asbestos fiber emission | Completely environmentally benign |
``` MODERN MEMBRANE ELECTROLYSIS CELL Depleted Brine (200 g/L) Water / Dilute NaOH (30%) β² β² β β ββββββ΄βββββββββββββββββββββββ ββββββββ΄βββββββββββββββββββββ β ANODE COMPARTMENT β β CATHODE COMPARTMENT β β β β β Saturated ββ> [ DSA Ti Mesh Anode]β β[ Nickel Mesh Cathode ] <ββ Dilute Brine β 2 Clβ» ββ> Clβ + 2eβ» β β 2 HβO + 2eβ» ββ> Hβ + 2OHβ» β NaOH Feed (300 g/L) β β β β β β β β Clβ Gas ββ> β NaβΊ β <ββ Hβ Gas β β β ββββββ>β β ββββββββββββββ¬βββββββββββββββ ββββββββββββββββ¬βββββββββββββ β Nafion Perfluorinated β β Cation-Exchange Membrane βΌ β (Sulfonate / Carboxylate Layers) Pure Product NaOH (32-35%) ```
Membrane Architecture (Bilayer Design)
Modern membranes consist of a reinforced perfluorosulfonic acid (PFSA) backing layer facing the anode (low electrical resistance) coupled to an ultra-thin carboxylate polymer layer facing the cathode. The high fixed charge density of carboxylate groups ($\text{-COO}^-$) creates extreme Donnan exclusion against back-migrating hydroxide ions ($\text{OH}^-$), maintaining caustic current efficiencies above $95 - 97\%$ at $35\text{ wt}\%\text{ NaOH}$.
Β§8.3 Membrane Cell Electrochemistry: Cell Potential, Overpotentials & Ohmic Drops
The overall electrochemical decomposition of aqueous sodium chloride:
Thermochemically, $\Delta G^\circ = +422.3\text{ kJ/mol}$. The reversible thermodynamic cell potential ($E_{\text{rev}}^\circ$) under standard conditions ($298\text{ K}$, $1\text{ bar}$):
Cell Voltage Breakdown ($U_{\text{cell}}$)
The actual operational cell voltage required to drive electrolysis at commercial current densities ($j = 4.0 - 7.0\text{ kA/m}^2$) is significantly higher, expressed by the additive polarization sum:
1. Reversible Potential under Operating Conditions ($90^\circ\text{C}$):
2. Anodic Overpotential ($\eta_{\text{anode}}$):
Chlorine evolution on modern Dimensionally Stable Anodes (DSA: titanium substrate coated with mixed metal oxides $\text{RuO}_2-\text{TiO}_2-\text{IrO}_2$). Catalytic activation lowers overpotential to $\eta_{\text{anode}} \approx 0.05 - 0.08\text{ V}$ via the Butler-Volmer relation:
3. Cathodic Overpotential ($\eta_{\text{cathode}}$):
Hydrogen evolution on activated nickel cathodes coated with ruthenium or Raney nickel. $\eta_{\text{cathode}} \approx 0.08 - 0.12\text{ V}$.
4. Ohmic Voltage Drop Across Membrane ($I \cdot R_{\text{membrane}}$):
Resistance of $\text{Na}^+$ transport across the membrane: $\Delta U_{\text{mem}} \approx 0.35 - 0.50\text{ V}$.
5. Ohmic Drops in Electrolytes and Structural Hardware:
Bubble void fraction (gas dispersion of $\text{Cl}_2$ and $\text{H}_2$) elevates solution resistance by the Bruggeman relation:
Zero-gap cell configurations (where flexible mesh electrodes compress directly against the membrane) compress inter-electrode electrolyte drops to $< 0.10\text{ V}$. Total industrial operational cell voltage sits between $2.95\text{ V}$ and $3.15\text{ V}$ at $6.0\text{ kA/m}^2$.
Complete Electrochemical Parameters of Modern Chlor-Alkali Membrane Cells
| Electrochemical Parameter | Symbol | Industrial Operating Range | Reference Target Value | |---|---|---|---| | Current Density | $j$ | $4.0 - 7.0\text{ kA/m}^2$ | $6.0\text{ kA/m}^2$ | | Operating Temperature | $T$ | $85 - 92^\circ\text{C}$ | $88^\circ\text{C}$ | | Anolyte NaCl Concentration | $[\text{NaCl}]_{\text{ano}}$ | $190 - 220\text{ g/L}$ | $205\text{ g/L}$ | | Catholyte NaOH Concentration| $[\text{NaOH}]_{\text{cat}}$ | $32.0 - 35.0\text{ wt}\%$ | $33.5\text{ wt}\%$ | | Current Efficiency (NaOH) | $\eta_{\text{NaOH}}$ | $95.5 - 97.5\%$ | $96.5\%$ | | Operating Cell Voltage | $U_{\text{cell}}$ | $2.95 - 3.15\text{ V}$ | $3.02\text{ V}$ | | Specific Power Consumption | $w_{\text{spec}}$ | $2,050 - 2,250\text{ kWh/t NaOH}$ | $2,120\text{ kWh/t NaOH}$ | | Membrane Service Life | $\tau_{\text{mem}}$ | $3 - 5\text{ years}$ | $4\text{ years}$ | | Anode Coating Service Life | $\tau_{\text{anode}}$ | $8 - 12\text{ years}$ | $10\text{ years}$ |
Β§8.4 Caustic Soda Processing: Multi-Effect Evaporative Concentration & Flaking
The aqueous sodium hydroxide discharged from modern membrane cells has a concentration of $32 - 35\text{ wt}\%\text{ NaOH}$. Standard global merchant commerce requires $50.0\text{ wt}\%\text{ NaOH}$ liquid caustic soda or $99\%\text{ NaOH}$ anhydrous solid pearls/flakes.
1. Multi-Effect Falling-Film Evaporation ($32\% \to 50\%\text{ NaOH}$)
Concentrating caustic soda requires specialized metallurgy (pure nickel $\text{Ni } 200$ or high-nickel alloys) to resist caustic stress-corrosion cracking and embrittlement at elevated temperatures ($> 120^\circ\text{C}$):
- Modern plants employ triple- or quadruple-effect falling film evaporators operating under forward or counter-current feed.
- Boiling Point Elevation (BPE): Saturated caustic solutions exhibit extreme boiling point elevation. While water boils at $100^\circ\text{C}$ at $1\text{ atm}$, a $50\text{ wt}\%\text{ NaOH}$ solution boils at $143^\circ\text{C}$ ($\text{BPE} = 43\text{ K}$). At $73\text{ wt}\%\text{ NaOH}$, the boiling point climbs to $190^\circ\text{C}$. This massive BPE significantly compresses the effective logarithmic mean temperature difference ($\Delta T_{\text{eff}}$) available across successive evaporator effects.
2. Solid Anhydrous Caustic Production ($50\% \to 99\%\text{ NaOH}$)
To produce solid flake or pearl caustic:
- The $50\text{ wt}\%$ caustic is concentrated in a falling film evaporator heated by molten heat transfer salts (eutectic mixture of $53\%\text{ KNO}_3 + 40\%\text{ NaNO}_2 + 7\%\text{ NaNO}_3$) operating at $380 - 400^\circ\text{C}$ under vacuum.
- Molten anhydrous caustic leaves at $320 - 340^\circ\text{C}$ ($< 0.5\%\text{ moisture}$).
- Flaking: The molten liquid is fed onto water-cooled rotating nickel flaker drums, solidifying instantaneously into a crystalline sheet that is sheared off by doctor blades.
- Prilling: Alternatively, molten caustic is sprayed down a counter-current air prilling tower, crystallizing into spherical beads (pearls).
Β§8.5 Chlorine Gas Engineering: Cooling, Sulfuric Acid Drying, Compression & Liquefaction
Moist, saturated chlorine gas ($\text{Cl}_2$) discharged from the membrane cell anodes at $85 - 90^\circ\text{C}$ is saturated with water vapor and is intensely corrosive to all conventional structural metals:
``` CHLORINE GAS PROCESSING TRAIN Wet Hot Cl2 Gas (~85Β°C) from Cells β βΌ ββββββββββββββββ β DIRECT WATER β (Chilled water spray cools Cl2 to 12-15Β°C; β COOLER β condenses >80% of water vapor without hydrate formation) ββββββββ¬ββββββββ βΌ Cooled Wet Cl2 ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β SULFURIC ACID DRYING TOWERS (3-Stage Counter-Current) β <ββ Fresh 98% H2SO4 β Stage 1 (78% H2SO4) ββ> Stage 2 (92%) ββ> Stage 3 (96-98%)β ββ> Spent Dilute H2SO4 ββββββββββββββββββββββββββββ¬ββββββββββββββββββββββββββββββ βΌ Bone-Dry Cl2 Gas (Moisture < 5 ppm) ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β CHLORINE COMPRESSOR (Liquid Ring or Centrifugal) β ββ> Pressurizes to 8-12 bar ββββββββββββββββββββββββββββ¬ββββββββββββββββββββββββββββββ βΌ ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β LIQUEFACTION CONDENSER (Refrigerated Freon/Ammonia) β ββ> Pure Liquid Chlorine (-15Β°C) ββββββββββββββββββββββββββββ¬ββββββββββββββββββββββββββββββ βΌ ββββββββββββββββ β STORAGE TANK β ββ> Bulk Pressurized Railcars / Pipeline Distribution ββββββββββββββββ ```
1. Direct Gas Cooling & Hydrate Prevention
The gas is cooled to $12 - 15^\circ\text{C}$ in packed titanium or polyvinylidene fluoride (PVDF) direct-contact cooling towers using chilled water. Cooling must strictly remain above $9.8^\circ\text{C}$ at atmospheric pressure to prevent crystallization of solid yellow chlorine hydrate ($\text{Cl}_2\cdot 7.3\text{H}_2\text{O}$), which clogs tower packing and transfer pipelines.
2. Multi-Stage Sulfuric Acid Drying
Water must be removed to $< 5\text{ ppm}$ moisture:
- When moisture $< 20\text{ ppm}$, chlorine is non-corrosive to ordinary carbon steel, allowing inexpensive steel pipes, valves, and railcars to be used safely.
- Drying is conducted in three packed towers flowing concentrated sulfuric acid ($\text{H}_2\text{SO}_4$) counter-currently. Fresh $98\text{ wt}\%\text{ H}_2\text{SO}_4$ enters the third stage, cascading to the first stage where spent acid exits at $75 - 78\text{ wt}\%$.
3. Compression & Liquefaction
Bone-dry chlorine is compressed using liquid-ring compressors (employing concentrated sulfuric acid as the sealing fluid) or multi-stage centrifugal compressors to $8 - 12\text{ bar}$. The pressurized gas enters shell-and-tube condensers chilled by refrigerant (ammonia or R-134a) to $-10^\circ\text{C}$ to $-25^\circ\text{C}$, condensing into clear amber liquid chlorine ($\rho = 1.41\text{ g/cm}^3$). Non-condensable inert gases ($\text{H}_2, \text{N}_2, \text{O}_2$) are purged ("sniff gas") to a sodium hydroxide scrubber.
Β§8.6 Hydrochloric Acid & Sodium Hypochlorite Synthesis Engineering
Byproduct chlorine and hydrogen from the chlor-alkali cell room are converted on-site into essential industrial chemicals:
1. Hydrochloric Acid ($\text{HCl}$) Synthesis
Pure gaseous hydrogen and chlorine are reacted in a specialized water-cooled silica or impregnated graphite combustion chamber:
- Combustion Control: To ensure complete consumption of chlorine (which is intensely toxic and corrosive), hydrogen is fed at a $5 - 10\%$ stoichiometric excess. The flame temperature exceeds $2000 - 2500^\circ\text{C}$.
- Adiabatic Absorption: The exiting hot anhydrous $\text{HCl}$ gas enters an isothermal or adiabatic falling-film graphite absorption tower where it dissolves violently in demineralized water:
The maximum concentration at atmospheric pressure is governed by the negative azeotrope ($20.22\text{ wt}\%\text{ HCl}$ at $108.6^\circ\text{C}$), but refrigerated commercial absorbers produce concentrated $33 - 36\text{ wt}\%\text{ Technical Grade HCl}$.
2. Sodium Hypochlorite ($\text{NaOCl}$) Bleach Manufacture
Produced by scrubbing dilute or tail-gas chlorine with refrigerated aqueous sodium hydroxide:
- Temperature & Decomposition Control: The reaction is conducted below $30 - 35^\circ\text{C}$. Above $40^\circ\text{C}$, hypochlorite decomposes rapidly into toxic and inactive chlorate:
- Free Alkali Stabilization: Excess sodium hydroxide ($0.5 - 1.0\text{ wt}\%\text{ free NaOH}$) is maintained to keep the $\text{pH} > 11.5$, preventing decomposition into hypochlorous acid ($\text{HOCl}$) and toxic chlorine gas.
Β§8.7 Sulfuric Acid Manufacture: The Modern Double Contact Double Absorption (DCDA) Process
Sulfuric acid ($\text{H}_2\text{SO}_4$, $M = 98.08\text{ g/mol}$) is the world's most widely consumed heavy industrial chemical. Modern production utilizes the Double Contact Double Absorption (DCDA) catalytic contact process:
1. Sulfur Combustion & Gas Conditioning
Molten bright sulfur ($135 - 145^\circ\text{C}$) is atomized with dry air in a refractory burner:
The resulting process gas ($10 - 11.5\text{ vol}\%\text{ SO}_2$, $9.5 - 11\text{ vol}\%\text{ O}_2$) is cooled from $1050^\circ\text{C}$ to $420^\circ\text{C}$ in a waste heat boiler, generating high-pressure steam ($40 - 60\text{ bar}$).
2. Catalytic Oxidation Kinetics ($SO_2 \to SO_3$)
The reversible oxidation is conducted over a cesium-promoted vanadium pentoxide catalyst supported on silica ($\text{V}_2\text{O}_5-\text{K}_2\text{SO}_4/\text{SiO}_2$):
The equilibrium constant is given by:
Because the reaction is strongly exothermic, thermodynamic equilibrium conversion decreases with increasing temperature, while reaction kinetics freeze below $400^\circ\text{C}$. The converter is structured into four sequential adiabatic catalyst beds with inter-bed cooling:
- Bed 1 ($420 \to 600^\circ\text{C}$): Rapid kinetic conversion reaches $60 - 65\%$.
- Bed 2 ($440 \to 510^\circ\text{C}$): Cumulative conversion reaches $85\%$.
- Bed 3 ($430 \to 455^\circ\text{C}$): Conversion reaches $93 - 95\%$.
3. The DCDA Innovation (Interpass Absorption)
In a single absorption plant, Le Chatelier's principle restricts overall conversion to $\le 97.5\%$, discharging thousands of ppm of harmful $\text{SO}_2$ into the atmosphere. In the DCDA configuration:
- Process gas leaving Bed 3 is cooled and passed through an Intermediate Absorption Tower (IPAT) where $> 99.9\%$ of generated $\text{SO}_3$ is absorbed into circulating $98.5\%\text{ H}_2\text{SO}_4$.
- The $\text{SO}_3$-depleted gas is reheated to $420^\circ\text{C}$ in gas-gas heat exchangers and fed to Bed 4.
- Removing $\text{SO}_3$ drives the thermodynamic equilibrium of the remaining gas overwhelmingly forward, raising overall conversion to $> 99.85\%$, cutting stack emissions to $< 100\text{ ppm SO}_2$.
- The gas exits Bed 4 through a Final Absorption Tower (FAT), producing concentrated $98.5\text{ wt}\%\text{ H}_2\text{SO}_4$ and Oleum ($20 - 65\%\text{ free SO}_3$).
Β§8.8 Oxygen-Depolarized Cathodes (ODC), Green Hydrogen & Zero-Emission Chlor-Alkali
The chlor-alkali sector consumes massive electrical energy ($> 2,200\text{ kWh/metric ton NaOH}$). The development of Oxygen-Depolarized Cathode (ODC) technology and hydrogen valorization represents a paradigm shift toward decarbonized heavy chemicals:
1. Oxygen-Depolarized Cathode (ODC) Electrochemistry
In conventional membrane cells, hydrogen gas is evolved at the cathode by water reduction:
In an ODC cell, gaseous pure oxygen ($\text{O}_2$) is introduced through a porous gas-diffusion cathode coated with silver or platinum catalysts, depolarizing the cathode reaction into oxygen reduction:
- Thermodynamic Voltage Reduction:
The cathode standard potential shifts positively by $\Delta E^\circ = 0.401 - (-0.828) = +1.229\text{ V}$.
- Cell Operating Voltage Drop:
Operational cell voltage plummets from $\sim 3.00\text{ V}$ to $2.00 - 2.10\text{ V}$ at $4 - 5\text{ kA/m}^2$.
- Energy Conservation:
Electrical energy consumption drops from $2,200\text{ kWh/t NaOH}$ to $1,500 - 1,600\text{ kWh/t NaOH}$, achieving an extraordinary $30\%$ reduction in grid power consumption.
2. High-Purity Green Hydrogen Valorization
For conventional membrane plants that continue to produce byproduct hydrogen:
- Chlor-alkali hydrogen is ultra-pure ($> 99.999\%$ after moisture condensation and trace oxygen catalytic deoxidation).
- Rather than combusting hydrogen for low-grade process steam, modern complexes feed this chemical-grade hydrogen into fuel-cell vehicles, direct ammonia synthesis, or green methanol plants, capturing immense clean-energy carbon credits.
University Honors Industrial Case Study: Wet Chlorine Crevice Corrosion in Titanium Exchangers
Titanium is the universal metal of choice for handling wet chlorine gas because a stable, self-healing rutile passive oxide film ($\text{TiO}_2$) forms instantaneously in the presence of trace moisture ($> 0.5\text{ wt}\%\text{ H}_2\text{O}$):
- The Dry Chlorine Fire Hazard: In bone-dry chlorine gas ($< 20\text{ ppm H}_2\text{O}$), the protective oxide film cannot self-repair. If mechanical scratching exposes virgin titanium metal, a violent, auto-igniting exothermic chlorination fire erupts:
The titanium metal burns vigorously in dry chlorine at room temperature, releasing dense white clouds of boiling $\text{TiCl}_4$.
- Crevice Corrosion: In gasket joints of plate heat exchangers where brine flow stagnates and temperature exceeds $75^\circ\text{C}$, localized acid buildup ($\text{pH} < 1$) breaks down passivity. Modern chlor-alkali exchangers specify palladium-stabilized titanium (ASTM Grade 7, $\text{Ti}-0.15\%\text{Pd}$) to prevent crevice initiation.
A chlor-alkali plant operates an electrolyzer circuit containing $120$ membrane cells connected in electrical series.
- Operational direct current is $I = 15,000\text{ A}$ ($15.0\text{ kA}$).
- Current efficiency for sodium hydroxide ($\text{NaOH}$, $40.00\text{ g/mol}$) is $\eta_{\text{NaOH}} = 96.0\%$.
- Current efficiency for chlorine gas ($\text{Cl}_2$, $70.90\text{ g/mol}$) is $\eta_{\text{Cl}_2} = 94.5\%$.
- Current efficiency for hydrogen gas ($\text{H}_2$, $2.016\text{ g/mol}$) is $\eta_{\text{H}_2} = 99.0\%$.
Faraday's constant is $F = 96,485\text{ C/mol}$.
- Calculate the daily production rate of pure $100\%\text{ NaOH}$ in metric tons per day.
- Determine the hourly mass and STP volumetric flow rate of chlorine gas ($\text{Cl}_2$) in $\text{kg/h}$ and $\text{Nm}^3\text{/h}$ ($22.414\text{ Nm}^3\text{/kmol}$).
- Calculate the hourly mass and STP volumetric flow rate of hydrogen gas in $\text{kg/h}$ and $\text{Nm}^3\text{/h}$.
Step 1: Daily $\text{NaOH}$ Production Rate
Since all $N = 120$ cells are in series, the same current $I$ passes through each cell. Total charge passed across the entire circuit per day ($t = 24\text{ h} = 86,400\text{ s}$):
Moles of electrons transferred per day:
Since $1\text{ mol } e^-$ produces $1\text{ mol NaOH}$:
Mass of pure $\text{NaOH}$:
Step 2: Chlorine Production Rates
Total charge passed per hour:
Moles of electrons per hour:
Chlorine generation requires $2\text{ mol } e^-$ per mole of $\text{Cl}_2$:
Mass of chlorine per hour:
Volumetric flow rate at STP:
Step 3: Hydrogen Production Rates
Hydrogen generation requires $2\text{ mol } e^-$ per mole of $\text{H}_2$:
Mass of hydrogen:
Volumetric flow rate at STP:
The plant produces $61.9\text{ t/day}$ NaOH, $2.25\text{ t/h}$ ($711.3\text{ Nm}^3\text{/h}$) Cl2, and $67.0\text{ kg/h}$ ($745.2\text{ Nm}^3\text{/h}$) H2.
A membrane electrolyzer operates at a current density of $j = 6.00\text{ kA/m}^2$ ($6,000\text{ A/m}^2$) at $90^\circ\text{C}$. The components of the cell voltage are measured as:
- Reversible thermodynamic cell potential: $E_{\text{rev}} = 2.160\text{ V}$
- Anodic chlorine overpotential: $\eta_a = 0.065\text{ V}$
- Cathodic hydrogen overpotential: $|\eta_c| = 0.095\text{ V}$
- Area-specific membrane resistance: $r_{\text{mem}} = 0.060\text{ \Omega}\cdot\text{m}^2$
- Area-specific electrolyte solution resistance: $r_{\text{sol}} = 0.025\text{ \Omega}\cdot\text{m}^2$
- Structural hardware and contact resistance: $\Delta U_{\text{struct}} = 0.040\text{ V}$
Current efficiency for $\text{NaOH}$ ($40.00\text{ g/mol}$) is $\eta = 96.5\%$. Faraday's constant is $F = 96,485\text{ C/mol}$.
- Calculate the total operational cell voltage ($U_{\text{cell}}$) in volts.
- Determine the fraction of electrical voltage consumed by thermodynamic work versus irreversible overpotentials and ohmic dissipation.
- Calculate the specific direct-current electrical energy consumption per metric ton of pure $\text{NaOH}$ in $\text{kWh/t NaOH}$.
Step 1: Total Cell Voltage Calculation
Calculate the ohmic voltage drops from current density ($j = 6,000\text{ A/m}^2$):
Using consistent units with $j \cdot r_{\text{mem}} = 6.00\text{ kA/m}^2 \times 0.060\text{ V/(kA/m}^2) = 0.360\text{ V}$:
Sum all components:
The operating cell voltage is $2.870\text{ V}$.
Step 2: Energy Efficiency Distribution
Thermodynamic reversible fraction:
Irreversible dissipation fraction (overpotentials + ohmic heat):
Step 3: Specific Electrical Energy Consumption
Specific electrical energy consumption ($w_{\text{spec}}$) per metric ton ($1,000\text{ kg} = 25,000\text{ mol}$) of $\text{NaOH}$:
where $F = 96,485\text{ A}\cdot\text{s/mol}$, $M_{\text{NaOH}} = 0.04000\text{ kg/mol}$.
Recomputing:
Specific energy consumption is $1,993\text{ kWh/t NaOH}$, showcasing the high energy efficiency of modern membrane technology.
A secondary brine purification ion-exchange column contains $V_{\text{resin}} = 5.00\text{ m}^3$ of macroporous aminomethylphosphonic acid chelating resin.
- Total operating volumetric capacity of the resin for divalent calcium ions ($\text{Ca}^{2+}$, $40.08\text{ g/mol}$) is $q_{\text{cap}} = 1.20\text{ eq/L}$ ($0.60\text{ mol Ca}^{2+}\text{/L resin}$).
- Primary-treated feed brine flows at $\dot{V}_{\text{brine}} = 80.0\text{ m}^3\text{/h}$ and contains $3.50\text{ mg/L of Ca}^{2+}$.
- Breakthrough occurs when $85.0\%$ of the resin column's theoretical capacity is exhausted.
- Calculate the total moles of $\text{Ca}^{2+}$ that can be captured prior to breakthrough.
- Determine the operational cycle run time of the column between regenerations in hours and days.
- If effluent brine during the active cycle contains $8.0\text{ ppb of Ca}^{2+}$ ($0.008\text{ mg/L}$), calculate the percentage removal efficiency.
Step 1: Usable $\text{Ca}^{2+}$ Capacity
Resin volume:
Total theoretical calcium capacity:
Usable capacity at $85.0\%$ breakthrough threshold:
Step 2: Cycle Run Time Calculation
Mass of $\text{Ca}^{2+}$ entering per hour:
Moles of $\text{Ca}^{2+}$ entering per hour:
Cycle run time until breakthrough:
The resin operates for $365\text{ hours}$ ($15.2\text{ days}$) before requiring acidic regeneration.
Step 3: Hardness Removal Efficiency
The chelating resin achieves $99.77\%$ calcium removal, lowering hardness from $3.5\text{ ppm}$ to an ultra-pure $8\text{ ppb}$.
A chlor-alkali plant concentrates $\dot{m}_{\text{feed}} = 30.0\text{ metric tons/h}$ of cell liquor containing $33.0\text{ wt}\%\text{ NaOH}$ to merchant product containing $50.0\text{ wt}\%\text{ NaOH}$ in a triple-effect falling film evaporator.
- Live motive steam ($4.0\text{ bar}$, enthalpy of vaporization $\lambda_{\text{steam}} = 2,133\text{ kJ/kg}$) is supplied to the first effect at a rate of $4,100\text{ kg/h}$.
Assume negligible solids entrainment.
- Calculate the production rate of $50.0\text{ wt}\%\text{ NaOH}$ solution in metric tons per hour.
- Determine the total hourly water evaporation rate in metric tons per hour.
- Calculate the overall Steam Economy of the evaporator system.
Step 1: Product Rate Calculation
NaOH mass entering in feed:
Since all NaOH leaves in the $50.0\text{ wt}\%$ product:
The plant produces $19.80\text{ metric tons/h}$ of $50\%\text{ NaOH}$ solution.
Step 2: Water Evaporation Rate
Water entering in feed:
Water leaving in product:
Total water evaporated as vapor:
Step 3: Steam Economy
Motive steam supplied:
Steam economy:
The triple-effect evaporator achieves a steam economy of $2.49\text{ kg vapor / kg steam}$.
A chlorine liquefaction unit receives $\dot{m}_{\text{gas}} = 5,000\text{ kg/h}$ of bone-dry chlorine gas at $8.0\text{ bar}$ absolute and $30^\circ\text{C}$.
- Gas composition: $97.0\text{ mol}\%\text{ Cl}_2$ and $3.0\text{ mol}\%$ non-condensable inerts ($\text{O}_2, \text{N}_2, \text{H}_2$, average $M_{\text{inerts}} = 30.0\text{ g/mol}$).
- The condenser cools the stream to $-15^\circ\text{C}$ ($258.15\text{ K}$) at constant total pressure $P = 8.0\text{ bar}$.
- At $-15^\circ\text{C}$, the saturation vapor pressure of pure chlorine is $p_{\text{Cl}_2}^* = 1.35\text{ bar}$.
- Latent heat of condensation of chlorine at $-15^\circ\text{C}$ is $\Delta H_{\text{cond}} = 275\text{ kJ/kg}$.
- Specific heat of gaseous chlorine is $c_p = 0.49\text{ kJ/(kg}\cdot\text{K)}$.
- Calculate the molar flow rates of entering $\text{Cl}_2$ and non-condensable inerts.
- Determine the molar composition of the tail gas ("sniff gas") exiting the condenser and the moles of $\text{Cl}_2$ remaining in the sniff gas.
- Calculate the percentage of chlorine liquefied.
- Calculate the refrigeration cooling duty required ($\text{kW}$).
Step 1: Input Molar Flow Rates
Average molar mass of feed gas:
Total molar feed rate:
- Entering $\text{Cl}_2$: $\dot{n}_{\text{Cl}_2, \text{in}} = 0.970 \times 71.764 = 69.611\text{ kmol/h} = 4,935.4\text{ kg/h}$
- Entering inerts: $\dot{n}_{\text{inerts}} = 0.030 \times 71.764 = 2.153\text{ kmol/h}$
Step 2: Sniff Gas Equilibrium & Chlorine Loss
In the sniff gas at $-15^\circ\text{C}$ and $P = 8.0\text{ bar}$:
The inert fraction is $y_{\text{inerts}} = 1 - 0.16875 = 0.83125$. Since inerts do not condense, all $2.153\text{ kmol/h}$ of inerts leave in the sniff gas:
Chlorine lost in sniff gas:
Mass of $\text{Cl}_2$ lost:
Step 3: Chlorine Liquefaction Yield
Liquefied chlorine:
Liquefaction recovery:
Step 4: Refrigeration Cooling Duty
- Sensible cooling of gas from $30^\circ\text{C}$ to $-15^\circ\text{C}$ ($\Delta T = 45\text{ K}$):
- Latent heat of condensation:
Total thermal duty:
In thermal kilowatts ($\text{kW}$):
The refrigeration unit delivers $405.3\text{ kW}$ of cooling, liquefying $99.37\%$ of the chlorine.
An $\text{HCl}$ synthesis unit reacts pure chlorine and hydrogen:
- Chlorine feed rate is $\dot{m}_{\text{Cl}_2} = 1,418\text{ kg/h}$ ($20.0\text{ kmol/h}$, $M = 70.90\text{ g/mol}$).
- Hydrogen is supplied at a $6.0\%$ stoichiometric excess.
- The generated anhydrous $\text{HCl}$ gas ($36.46\text{ g/mol}$) is completely absorbed into demineralized water in an isothermal falling-film graphite absorber to produce commercial $33.0\text{ wt}\%\text{ aqueous hydrochloric acid}$.
- Calculate the required mass feed rate of hydrogen gas in $\text{kg/h}$ ($M = 2.016\text{ g/mol}$).
- Determine the production rate of anhydrous $\text{HCl}$ gas in $\text{kg/h}$.
- Calculate the required demineralized water flow rate and the total production rate of $33.0\text{ wt}\%\text{ HCl}$ in metric tons per hour.
Step 1: Hydrogen Feed Rate
Moles of $\text{Cl}_2$ fed per hour:
With $6.0\%$ stoichiometric excess:
Mass feed rate of $\text{H}_2$:
Step 2: Anhydrous $\text{HCl}$ Gas Production
From stoichiometry, $1\text{ mol Cl}_2 \to 2\text{ mol HCl}$:
Mass of anhydrous $\text{HCl}$:
Step 3: Demineralized Water Flow & Product Acid Rate
Target concentration is $33.0\text{ wt}\%\text{ HCl}$:
Demineralized water absorption rate:
The plant feeds $42.7\text{ kg/h}$ H2 and $2.96\text{ t/h}$ water to produce $4.42\text{ metric tons/h}$ of $33\%\text{ HCl}$ acid.
A sulfuric acid plant produces $1,000\text{ metric tons/day}$ ($41.67\text{ t/h}$) of $100\%\text{ H}_2\text{SO}_4$ equivalent ($98.08\text{ g/mol}$) utilizing a $3+1$ bed Double Contact Double Absorption (DCDA) layout.
- The sulfur burner produces process gas containing $11.0\text{ vol}\%\text{ SO}_2$ and $10.0\text{ vol}\%\text{ O}_2$.
- In the primary contact loop (Beds 1, 2, 3), fractional conversion of $\text{SO}_2$ to $\text{SO}_3$ reaches $\alpha_1 = 94.0\%$.
- The intermediate absorption tower (IPAT) absorbs $99.8\%$ of the generated $\text{SO}_3$.
- In the secondary contact loop (Bed 4), the remaining unreacted $\text{SO}_2$ achieves a fractional conversion of $\alpha_2 = 98.0\%$.
- Calculate the overall cumulative $\text{SO}_2 \to \text{SO}_3$ conversion efficiency ($\alpha_{\text{total}}$) of the DCDA plant.
- Determine the mass of unreacted $\text{SO}_2$ ($64.06\text{ g/mol}$) discharged to the stack per hour in $\text{kg/h}$.
- Calculate the specific $\text{SO}_2$ emission per metric ton of $100\%\text{ H}_2\text{SO}_4$ produced and verify if it meets the World Bank/EPA standard ($\le 2.0\text{ kg SO}_2\text{/t acid}$).
Step 1: Overall Cumulative Conversion ($\alpha_{\text{total}}$)
Let initial moles of $\text{SO}_2$ entering Bed 1 be $n_0 = 1.000$.
- After primary loop (Beds 1-3):
- Converted to $\text{SO}_3$: $\alpha_1 = 0.940$
- Remaining unreacted $\text{SO}_2$: $1 - \alpha_1 = 0.060$
- In Bed 4, this remaining $0.060$ undergoes conversion $\alpha_2 = 0.980$:
- Additional $\text{SO}_3$ formed: $0.060 \times 0.980 = 0.0588$
- Final unconverted $\text{SO}_2$: $0.060 \times (1 - 0.980) = 0.060 \times 0.020 = 0.0012$
Total $\text{SO}_2$ converted across the plant:
The DCDA plant achieves an overall conversion efficiency of $99.88\%$.
Step 2: Unreacted $\text{SO}_2$ Discharged to Stack
Hourly production of $100\%\text{ H}_2\text{SO}_4$:
Moles of sulfuric acid produced per hour:
Since $1\text{ mole of converted SO}_2$ yields $1\text{ mole of H}_2\text{SO}_4$:
Initial $\text{SO}_2$ burned:
Unreacted $\text{SO}_2$ exiting to stack:
Mass of stack $\text{SO}_2$:
Step 3: Specific Emission Compliance
Specific emission factor:
Since $0.784\text{ kg/t} < 2.0\text{ kg/t}$, the plant easily meets the regulatory limit with a $61\%$ safety margin.
A chlor-alkali plant operates at an electrical current of $I = 100\text{ kA}$ ($100,000\text{ A}$) to produce $100\%\text{ pure NaOH}$ ($40.00\text{ g/mol}$) at $\eta = 96.0\%$ current efficiency ($F = 96,485\text{ C/mol}$).
- In a conventional hydrogen-evolving membrane cell, the operational cell voltage is $U_1 = 3.050\text{ V}$.
- In an advanced Oxygen-Depolarized Cathode (ODC) cell, pure oxygen gas is supplied to the cathode, reducing the operational cell voltage to $U_2 = 2.050\text{ V}$.
Industrial electricity costs $\$0.080\text{ per kWh}$.
- Calculate the hourly direct-current electrical power consumption of a single cell under:
- Conventional cell ($U_1 = 3.050\text{ V}$).
- ODC cell ($U_2 = 2.050\text{ V}$).
- Determine the specific direct-current energy consumption per metric ton of pure $\text{NaOH}$ for both technologies ($\text{kWh/t NaOH}$).
- Calculate the percentage electrical energy savings and the annual electricity cost savings per cell (operating $8,400\text{ hours/year}$).
Step 1: Hourly Electrical Power per Cell
Power is $P = U \times I$:
- Conventional Cell:
- ODC Cell:
Step 2: Specific Energy Consumption per Metric Ton NaOH
Hourly NaOH production per cell ($M = 40.00\text{ g/mol}$):
Specific energy consumption ($w_{\text{spec}} = P / \dot{m}$):
- Conventional:
- ODC Cell:
Step 3: Savings Analysis
Percentage energy savings:
Annual electrical energy saved per cell ($8,400\text{ operating hours}$):
Annual financial savings per cell:
ODC technology slashes power consumption by $32.8\%$, saving $\$67,200\text{ per cell annually}$.
A chemical zero-liquid-discharge facility treats industrial waste sodium sulfate ($\text{Na}_2\text{SO}_4$, $142.04\text{ g/mol}$) using Bipolar Membrane Electrodialysis (BMED) to regenerate sodium hydroxide ($\text{NaOH}$, $40.00\text{ g/mol}$) and sulfuric acid ($\text{H}_2\text{SO}_4$, $98.08\text{ g/mol}$).
- The BMED stack comprises $N = 200\text{ repeating cell triplets}$ (Bipolar Membrane - Anion Exchange Membrane - Cation Exchange Membrane) operating in electrical series at $I = 500\text{ A}$.
- At the bipolar membrane junction, water dissociates into $\text{H}^+$ and $\text{OH}^-$ ions:
- The current efficiency for $\text{NaOH}$ is $\eta = 88.0\%$ ($F = 96,485\text{ C/mol}$).
- The overall cell triplet operating voltage is $U = 1.80\text{ V}$.
- Calculate the daily production rate of pure $100\%\text{ NaOH}$ in metric tons per day.
- Determine the daily production rate of pure $\text{H}_2\text{SO}_4$ generated in metric tons per day.
- Calculate the specific direct-current electrical energy consumption per metric ton of $\text{NaOH}$ produced ($\text{kWh/t NaOH}$).
Step 1: Daily $\text{NaOH}$ Production
Total charge passed across $N = 200$ cells in series per day ($t = 86,400\text{ s}$):
Moles of electrons passed:
At $\eta = 88.0\%$ current efficiency, moles of $\text{NaOH}$ generated:
Mass of pure $\text{NaOH}$:
Step 2: Daily $\text{H}_2\text{SO}_4$ Production
Each mole of $\text{H}_2\text{SO}_4$ requires $2\text{ moles of H}^+$:
Mass of pure $\text{H}_2\text{SO}_4$:
Step 3: Specific Electrical Energy Consumption
Total direct-current electrical power of the stack ($200\text{ triplets}$ at $1.80\text{ V}$, total voltage $= 360\text{ V}$):
Daily energy consumed:
Specific energy consumption per ton of $\text{NaOH}$:
BMED produces $3.15\text{ t/day}$ NaOH and $3.86\text{ t/day}$ H2SO4, consuming $1,371\text{ kWh/t NaOH}$.
Solved Honors Problems & Derivations
Step-by-step rigorous solutions with full physical, thermodynamic, and process engineering validation.