Reverse Osmosis Calculator
Calculate osmotic pressure using the Van't Hoff equation and membrane rejection rate for RO system design. Free online reverse osmosis calculator.
Our free online Reverse Osmosis Calculator helps engineers and water treatment professionals calculate osmotic pressure using the Van't Hoff equation and determine membrane contaminant rejection rates. Whether you are designing a seawater desalination plant, sizing a brackish water RO system, or evaluating membrane performance, this tool provides quick and accurate results.
How to Use the Reverse Osmosis Calculator
Select a calculation mode: Osmotic Pressure or Contaminant Rejection. For osmotic pressure, enter the osmotic coefficient, ions per molecule, solute concentration, and temperature. The calculator applies the Van't Hoff equation and also shows the recommended applied pressure (typically 2 times the osmotic pressure). For rejection, enter the feed and permeate concentrations to see the membrane rejection percentage.
Van't Hoff Osmotic Pressure Formula
The Van't Hoff equation estimates the osmotic pressure of a solution: π = φ × N × C × R × T
Where π is the osmotic pressure (atm), φ is the osmotic coefficient (typically 0.85-0.95 for NaCl), N is the number of dissociated ions per formula unit, C is the molar concentration (mol/L), R is the ideal gas constant (0.082057 L·atm/(mol·K)), and T is the absolute temperature (K).
Membrane Rejection Formula
The rejection rate quantifies how effectively the membrane removes contaminants: R = (Cin − Cout) / Cin × 100%
Where Cin is the feed concentration and Cout is the permeate concentration. Modern thin-film composite RO membranes achieve 95-99.7% salt rejection.
Applications
- Seawater Desalination: Calculate the osmotic pressure of seawater (~27 atm) to determine the required pump pressure
- Brackish Water Treatment: Evaluate membrane performance for groundwater with elevated dissolved solids
- Membrane Sizing: Determine rejection rates to ensure permeate quality meets drinking water standards
- Process Optimization: Analyze how temperature and concentration changes affect system performance
Also check: Water Intake Calculator, Rainwater Collection Calculator, Tank Volume Calculator, Pressure Calculator, Density Calculator, and Unit Converter.
Frequently Asked Questions
What is osmotic pressure in reverse osmosis?
Osmotic pressure is the natural pressure that would drive water from the dilute side to the concentrated side of a membrane. RO reverses this flow by applying feed-side pressure greater than the osmotic pressure. Only above this threshold does permeate begin to flow.
What is a good salt rejection percentage?
Modern thin-film composite RO membranes typically achieve 95-99.7% salt rejection for monovalent salts. A rejection rate below 95% may indicate membrane fouling, damage, or the need for replacement. For drinking water treatment, NSF/ANSI 58 certified membranes must meet minimum rejection requirements.
How does temperature affect RO operation?
Higher feed temperature lowers water viscosity and raises permeate flux at the same pressure. However, warmer feed also increases osmotic pressure linearly with temperature. Most RO plants operate at 20-25°C for optimal performance and membrane longevity.
What is the difference between rejection and recovery?
Rejection measures the fraction of solute blocked by the membrane (a quality metric). Recovery is the fraction of feed water converted to permeate (a process metric). A system can have high rejection (99%) but low recovery (40%), meaning it discharges 60% as concentrated brine.
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