Osmotic Pressure of Seawater Calculator
Find the osmotic pressure of seawater from salinity and temperature, or the brine pressure and minimum energy a desalination plant must overcome at a chosen recovery.
🌊 What is the Osmotic Pressure of Seawater?
The osmotic pressure of seawater is the pressure that would have to be applied to seawater to stop pure water flowing into it through a semipermeable membrane. Dissolved salts lower the chemical potential of the water, so fresh water tends to move toward the saltier side. For open ocean water with a salinity of 35 g/kg at 25 °C the effect is equal to about 2.6 MPa (roughly 26 bar or 374 psi), which is the same as the pressure at the bottom of a freshwater column more than 250 m tall. Reverse osmosis desalination works by pushing the seawater harder than this so that water crosses the membrane the wrong way and the salt is left behind.
The number matters in several places. Desalination engineers use it to size high pressure pumps and to decide how much of the feed can be recovered as fresh water before the brine becomes too salty. Marine biologists use it to understand why fish, algae and bacteria must regulate their internal salts, and why a freshwater organism swells and bursts in the ocean. Oceanographers meet it through the water activity of seawater, which sets its vapour pressure and the rate of evaporation. Chemists use the same ideas to relate salinity, molality and freezing point.
Seawater is not an ideal solution, and this is the most common misunderstanding. The simple van 't Hoff equation treats every dissolved particle as independent, but sea salt is a concentrated mixture of charged ions (mainly sodium, chloride, magnesium, sulfate, calcium and potassium) that attract each other. The osmotic coefficient φ corrects for this. For sea salt it is about 0.90 at salinity 35 and 25 °C, so the real pressure is roughly 10 percent below the ideal value. Also note that the pressure to drive reverse osmosis in practice is much larger than the osmotic pressure of the feed, because the brine is concentrated as water is removed and a driving force is needed for flux.
This calculator has two modes. The Seawater mode converts salinity and temperature into osmotic pressure in MPa, bar, atm and psi, together with the equivalent head of water, the total ion molality and the water activity. The Desalination mode takes the feed salinity, recovery and temperature, computes the brine salinity for a fully rejecting membrane, and reports the minimum applied pressure and an approximate lower bound for the specific energy. For the general van 't Hoff equation with arbitrary solutes see the osmotic pressure calculator, and for cells and membranes see the biological membranes version.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Open Ocean Seawater
S = 35 g/kg at 25 °C
Example 2 — Red Sea Surface Water
S = 38 g/kg at 28 °C
Example 3 — Brackish Estuary Water
S = 10 g/kg at 10 °C
Example 4 — SWRO Plant at 50 Percent Recovery
Feed 35 g/kg, recovery 50 percent, 25 °C
Example 5 — Warm Gulf Water at 45 Percent Recovery
Feed 38 g/kg, recovery 45 percent, 28 °C
❓ Frequently Asked Questions
🔗 Related Calculators
What is the osmotic pressure of seawater?
About 2.6 MPa (26 bar, 374 psi) for open ocean water at salinity 35 g/kg and 25 degrees C with this calculator's model. Commonly quoted rounded figures are around 27 bar. It is the pressure that must be exceeded to push pure water out of seawater through a membrane.
How do you calculate the osmotic pressure of seawater?
Use Pi = phi x m x rho_w x R x T. Here m is the total molality of dissolved ions (about 1.155 mol/kg at S = 35), phi is the osmotic coefficient (about 0.90), rho_w is the density of water, R is 8.3145 J/(mol K) and T is absolute temperature.
Why is the osmotic coefficient of seawater less than 1?
Dissolved ions attract each other, so the water is less free to leave than ideal van 't Hoff theory predicts. The osmotic coefficient measures that departure from ideal behaviour, and for sea salt at 25 degrees C it is about 0.90.
How much pressure does seawater reverse osmosis need?
Typical SWRO plants operate at about 55 to 70 bar, well above the 26 bar osmotic pressure of the feed, because the brine becomes about twice as salty at 50 percent recovery and extra pressure is needed to drive a useful flux.
What is the minimum energy to desalinate seawater?
The thermodynamic minimum for 35 g/kg seawater at 50 percent recovery is about 1.0 to 1.1 kWh per cubic metre of fresh water. This calculator gives 1.008 kWh/m3 at 25 degrees C. Practical SWRO uses roughly 2.5 to 4 kWh/m3.
How does recovery affect the pressure needed?
Recovery sets the brine salinity: S_brine = S_feed / (1 - recovery). At 50 percent recovery the brine is twice as salty as the feed, so its osmotic pressure and the minimum applied pressure roughly double to about 53 bar.
Does temperature change the osmotic pressure of seawater?
Yes, slightly. Osmotic pressure is proportional to absolute temperature, so 35 g/kg seawater has about 2.37 MPa at 0 degrees C and about 2.58 MPa at 25 degrees C, an increase of roughly 9 percent.
What is osmotic pressure in metres of water?
Dividing by rho_w x g converts pressure to a water column. At 2.575 MPa the head is about 263 m of water, which is why a membrane must be held back against a pressure equal to a column of freshwater more than 250 m tall.
What is the difference between this and the van 't Hoff osmotic pressure calculator?
The generic van 't Hoff equation assumes ideal behaviour. Seawater is a concentrated mixed electrolyte, so this calculator adds a measured osmotic coefficient and uses the total sea salt molality derived from salinity.
What happens to the osmotic pressure in the brine?
The brine from a desalination plant has higher salinity, so a higher osmotic pressure. At 70 g/kg it is about 5.3 MPa (53 bar), twice the feed value. This is the pressure the membrane must overcome at the end of the module.
Is the 83 bar limit a hard limit?
It is a typical rating for seawater RO elements and vessels (about 1200 psi), though some sources quote 82 bar. Check the manufacturer datasheet, since the actual limit depends on the element.