How It Works
Reverse osmosis forces water through a semi-permeable membrane under pressure, leaving dissolved salts and contaminants behind. The applied pressure must exceed the osmotic pressure of the feed solution. The Van't Hoff equation estimates this osmotic pressure from solute concentration, temperature, and ion count, while the rejection equation measures how effectively contaminants are removed. Typical seawater desalination requires 50–70 atm of pressure. Brackish water systems operate at 10–25 atm. Modern RO membranes achieve 95–99.5% salt rejection. A 0.5 gmol/L NaCl solution at 298 K has φ = 0.93, and NaCl dissociates into 2 ions. What is the osmotic pressure? The RO system must apply more than 22.7 atm to produce fresh permeate from this feed. Osmotic pressure is the natural tendency of water to flow from a dilute solution to a concentrated one across a membrane. RO overcomes this by applying higher pressure on the concentrated side, pushing clean water through and leaving salts behind.
Example Problem
A 0.5 gmol/L NaCl solution at 298 K has φ = 0.93, and NaCl dissociates into 2 ions. What is the osmotic pressure?
- π = 0.93 × 2 × 0.5 × 0.082 × 298
- π ≈ 22.7 atm
Osmotic pressure is the natural tendency of water to flow from a dilute solution to a concentrated one across a membrane. RO overcomes this by applying higher pressure on the concentrated side, pushing clean water through and leaving salts behind.
When to Use Each Variable
- Solve for Osmotic Pressure — when you know the solute concentration, temperature, and ion count, e.g., determining the minimum pressure needed to desalinate brackish water.
- Solve for Concentration — when you know the osmotic pressure and want to find the feed salinity, e.g., characterizing an unknown brine stream.
- Solve for Temperature — when you need the temperature at which a given solution reaches a target osmotic pressure, e.g., optimizing system operating conditions.
- Solve for Rejection — when you know feed and permeate concentrations, e.g., evaluating membrane performance after a fouling cycle.
- Solve for Permeate Concentration — when you know the feed concentration and membrane rejection rate, e.g., predicting permeate quality for a new membrane.
Key Concepts
Reverse osmosis works by applying pressure greater than the osmotic pressure of a solution, forcing pure water through a semi-permeable membrane while rejecting dissolved solutes. The Van't Hoff equation estimates osmotic pressure from solute concentration, temperature, and the number of ions produced by dissociation. Membrane rejection quantifies the percentage of contaminant blocked, with modern RO membranes achieving 95-99.5% salt rejection.
Applications
- Seawater desalination: producing potable water from ocean sources at 50-70 atm operating pressure
- Brackish water treatment: purifying groundwater with elevated dissolved solids for municipal or industrial use
- Wastewater reuse: treating secondary effluent for indirect potable reuse or irrigation
- Industrial process water: producing ultrapure water for semiconductor fabrication and pharmaceutical manufacturing
- Food and beverage: concentrating juices, dairy, and other liquid products without heat degradation
Common Mistakes
- Applying pressure below the osmotic pressure — no permeate is produced until the applied pressure exceeds the osmotic pressure of the feed
- Ignoring the osmotic coefficient (phi) — real solutions deviate from ideal behavior, and omitting phi can underestimate osmotic pressure by 10-20%
- Confusing rejection with recovery — rejection measures contaminant removal, while recovery is the fraction of feed converted to permeate
- Neglecting temperature effects — osmotic pressure increases linearly with temperature, so seasonal changes affect system performance
Frequently Asked Questions
What is osmotic pressure in reverse osmosis?
Osmotic pressure is the natural tendency of water to flow from a dilute solution to a concentrated one across a membrane. RO overcomes this by applying higher pressure on the concentrated side, pushing clean water through and leaving salts behind.
What does contaminant rejection mean for RO membranes?
Rejection is the percentage of a solute that the membrane blocks. For example, 98% rejection of a 500 mg/L feed means the permeate contains only 10 mg/L. High-performance RO membranes routinely achieve 99%+ rejection for dissolved salts.
How much energy does reverse osmosis use?
Modern seawater RO plants consume 3–5 kWh per cubic meter of permeate with energy recovery devices. Brackish water RO uses significantly less -- typically 0.5–2 kWh/m³.
Related Calculators
- Ultrafiltration Calculator -- design membrane pretreatment upstream of RO.
- Microorganism Disinfection Calculator -- ensure post-RO disinfection meets CT targets.
- Swimming Pool Calculator -- manage water quality in pool applications.
- Electrodialysis Calculator — size membrane stacks for alternative desalination.
- Fluid Pressure Calculator — calculate the transmembrane pressure driving RO separation.
- Pressure Unit Converter — convert between psi, bar, and kPa for membrane pressures.
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