The osmotic pressure calculator above evaluates the van 't Hoff relation for osmotic pressure in three directions. Give it a concentration and it returns the pressure. Give it a target pressure and it returns the concentration that would produce it. Give it a weighed mass of solute and a measured pressure and it returns the solute's molar mass, which is the reason osmometry exists as an analytical technique.
Arb Digital builds free calculators that make the assumptions visible. Osmotic pressure is the colligative property with the most counter-intuitive magnitude — concentrations far too dilute to measure by freezing point produce pressures measured in atmospheres — and the most common error is not arithmetic but the van 't Hoff factor, so this page reports the osmolarity separately so you can see exactly how many particles the calculation assumed.
What This Osmotic Pressure Calculator Does
It computes the pressure that would have to be applied to a solution to stop pure solvent flowing into it across a membrane permeable to solvent alone. The inputs are the molar concentration of solute, the van 't Hoff factor giving particles per formula unit, and the absolute temperature. The output is reported in your choice of five pressure units, with kilopascals and millimetres of mercury always shown alongside for cross-checking.
The fourth grid figure is the height of a column of water that would exert the same pressure. It exists to give the number a physical meaning: an osmotic pressure of eight atmospheres corresponds to a water column over eighty metres tall, which is the sort of comparison that makes it clear why plant cells can hold their shape by turgor and why reverse osmosis needs a serious pump.
Boundary worth stating plainly. Our colligative properties calculator handles boiling-point elevation and freezing-point depression, both of which are computed from molality using the solvent's ebullioscopic and cryoscopic constants. This page handles osmotic pressure, which is computed from molarity and needs no solvent-specific constant at all. Same family of phenomena, different input quantity, different formula, and a difference in sensitivity of several orders of magnitude.
How to Use It
- Choose what you are solving for — pressure, concentration or molar mass.
- Enter the concentration in moles per litre of the solute as dispensed, not of the particles. The van 't Hoff factor handles the particle count.
- Set i honestly. Use 1 for a non-electrolyte, and for salts use a measured value where you have one rather than the ideal whole number.
- Set the temperature. The pressure is proportional to absolute temperature, so a 12-degree error moves the answer by about four percent.
- In molar mass mode, enter the mass you dissolved, the volume of solution, and the pressure you measured.
The Formula and How It Is Calculated
The van 't Hoff equation for osmotic pressure is Π = iMRT, where Π is the osmotic pressure, i is the van 't Hoff factor, M is the molar concentration of solute, R is the molar gas constant and T is the absolute temperature. The product iM is the osmolarity: the concentration of osmotically active particles, whatever they are.
The tool works internally in SI, converting your concentration from moles per litre to moles per cubic metre, so that the pressure comes out in pascals and is then converted to the unit you asked for. The constant used is the CODATA molar gas constant, 8.314462618 J mol⁻¹ K⁻¹, which is exact under the current SI definitions.
Work the default through. Physiological saline is about 0.154 mol/L sodium chloride. Treating it as fully dissociated gives i = 2, so the osmolarity is 0.308 osmol/L, or 308 mol/m³. At 37 °C, which is 310.15 K, the pressure is 308 × 8.3145 × 310.15 = 794,200 Pa, which is 794 kPa or 7.84 atmospheres. Sodium chloride is not quite fully dissociated at that concentration, and using a measured factor near 1.86 instead brings the figure down to about 7.3 atmospheres, which is close to the value quoted for blood plasma. The derivation and several worked examples of the same form appear in the Chemistry LibreTexts module on osmotic pressure.
Why the Formula Looks Like the Ideal Gas Law
Rearranged, ΠV = inRT is the ideal gas law with the number of dissolved particles in place of the number of gas molecules. That resemblance is not a coincidence and it is not an accident of algebra: both describe a system whose pressure comes from the entropy of mixing rather than from any interaction between particles. In a dilute solution, solute particles behave much like an ideal gas occupying the volume of the solution.
The similarity has a practical limit. The ideal gas law fails at high pressure where molecules interact, and the van 't Hoff relation fails at high concentration for the same reason: solute-solute and solute-solvent interactions become significant, activity departs from concentration, and the measured pressure drifts away from the prediction. Below about 0.1 mol/L the agreement is usually good; above 1 mol/L it should not be relied on. Our ideal gas law calculator handles the gas-phase version of the same relationship.
The van 't Hoff Factor Is Rarely a Whole Number
The ideal factor is the number of ions a formula unit would release if it dissociated completely: 2 for sodium chloride, 3 for calcium chloride, 1 for glucose or sucrose. Measured values fall short of the ideal because ions in solution associate into transient ion pairs that behave as one particle rather than two, and the effect grows with concentration and with ionic charge.
Sodium chloride at 0.1 mol/L measures about 1.87 rather than 2. Magnesium sulfate, where both ions carry two charges and pair much more strongly, can measure close to 1.3 rather than 2. As concentration approaches zero the measured factor approaches the ideal one, which is the limit the theory describes. A calculation that assumes the ideal factor at a working concentration therefore overestimates the pressure, and the size of the overestimate depends on the salt.
Weak electrolytes are a separate case. An acid that is ten percent ionised gives 1.1 particles per formula unit, not 2, and the degree of ionisation itself changes with dilution. If your solute is a weak acid or base, the factor must come from the ionisation equilibrium rather than from the formula — our pH calculator and pKa and Ka calculator deal with that side. The calculator here reports osmolarity explicitly so that whatever assumption you made is visible in the output rather than buried in it.
Why Osmometry Measures Molar Mass and Cryoscopy Cannot
Compare two colligative properties for the same solution. A 0.001 mol/L aqueous solution of a non-electrolyte depresses the freezing point by 0.00186 °C, which no ordinary thermometer can resolve. The same solution has an osmotic pressure of about 2.5 kPa, or 19 mmHg, which an ordinary pressure transducer measures comfortably. The difference in practical sensitivity is roughly three orders of magnitude.
That is why osmometry is the classical method for determining the molar mass of a protein or a synthetic polymer. A large molecule contributes very few moles per gram, so any concentration you can reasonably prepare is extremely dilute in molar terms — and dilute is exactly where every other colligative measurement runs out of resolution and where the van 't Hoff relation is at its most accurate. Rearranged, the molar mass is M = imRT / (ΠV), which is the third mode of this calculator.
Two cautions come with it. Membrane osmometry measures the number-average molar mass, which for a polydisperse polymer is not the same as the weight-average value a light-scattering measurement returns, and the two can differ by a large factor for a broad distribution. And any small molecule that passes through the membrane is invisible to the measurement, so a protein preparation contaminated with salt gives a pressure that reflects only the protein — usually helpful, occasionally misleading. Our protein concentration calculator and molar mass calculator cover the neighbouring steps.
Where the Number Shows Up in the Real World
Reverse osmosis is osmosis run backwards under pressure, so the applied pressure must exceed the feed's osmotic pressure before any water crosses at all. Seawater, with roughly 1.1 moles of dissolved ions per litre, has an osmotic pressure near 27 atmospheres, which sets the floor for a desalination plant's pump — and explains why practical systems operate well above it, since the pressure difference remaining above the osmotic threshold is what drives the flow.
In plants, turgor pressure is the osmotic pressure of the cell contents pressing the membrane against the cell wall, and it is what holds a non-woody stem upright. In food preservation, the very high osmolarity of a brine or a sugar syrup draws water out of microbial cells, which is why salting and candying work without any antimicrobial agent. In soil science, saline soil raises the osmotic pressure of the water around a root and reduces what the plant can take up even when the soil is visibly wet. Our concentration converter and molarity calculator help with getting from a mass-per-volume figure to the molar concentration this page needs.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Using molality instead of molarity — this relation takes moles per litre of solution, unlike freezing-point and boiling-point calculations, which take moles per kilogram of solvent.
- Leaving the van 't Hoff factor at 1 for a salt — that halves the answer for sodium chloride and cuts it by two thirds for calcium chloride.
- Assuming the ideal factor at working concentrations — ion pairing means measured values fall short, badly so for salts with doubly charged ions.
- Using Celsius in the formula — the pressure is proportional to absolute temperature, so the value must be in kelvin.
- Applying the relation to a concentrated solution — above roughly 1 mol/L the ideal-dilute assumption fails and the prediction runs high.
Related Free Tools From Arb Digital
Work out freezing and boiling shifts with the colligative properties calculator, prepare the solution with the molarity calculator, switch units with the concentration converter, and count particles with the mole fraction calculator. For the gas-phase analogue use the ideal gas law calculator, and for molar masses the molar mass calculator. If your data arrives in Fahrenheit, the temperature converter will sort it out. The full free online tools hub lists everything else.
Frequently Asked Questions
It is the pressure that must be applied to a solution to stop pure solvent flowing into it through a membrane permeable to the solvent alone. It rises with the concentration of dissolved particles and with absolute temperature.
Molarity, in moles per litre of solution. That distinguishes it from freezing-point depression and boiling-point elevation, which use molality in moles per kilogram of solvent and need a solvent-specific constant.
It is the number of osmotically active particles one formula unit of solute releases. It is 1 for non-electrolytes such as glucose, close to 2 for sodium chloride and close to 3 for calcium chloride, and falls below the ideal value as concentration rises.
Because ions in solution associate into transient ion pairs that behave as a single particle. The effect strengthens with concentration and with ionic charge, so magnesium sulfate departs from its ideal factor far more than sodium chloride does.
Because the relation has the same form as the ideal gas law, and a tenth of a mole of particles per litre generates a pressure comparable to that of a gas at the same particle density. A 0.1 molar non-electrolyte solution already exerts about 2.4 atmospheres at room temperature.
Rearranging the relation gives molar mass as the mass dissolved times the factor, the gas constant and the temperature, divided by the pressure and the volume. Because it works well at very low molar concentrations, it suits large molecules that other colligative methods cannot resolve.
As concentration rises. Below about 0.1 moles per litre agreement is generally good; above about 1 mole per litre solute interactions become significant, activity departs from concentration, and the predicted pressure runs higher than the measured one.
This calculator is provided for education and general reference. It describes how osmotic pressure is computed and is not medical, laboratory or safety guidance; follow the procedures and risk assessments issued by your own institution.
