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Osmotic pressure , represented by the Greek letter pi ( π ), is a colligative property of solutions that corresponds to the pressure that must be applied to a solution to stop osmosis . The latter consists of the passage of solvent through a semipermeable membrane from a more dilute solution (or from a reservoir of pure solvent) to a more concentrated one.
Being a colligative property, that is, it comes from the collective effect of the particles that make up a solution and not from their nature, the osmotic pressure can be calculated from knowledge of the composition of said solution. In other words, if we know what a solution is made of and in what quantities all the components are found, then we can calculate the osmotic pressure.
In the following section, three examples of calculating osmotic pressure in different situations are presented:
- In solutions with a molecular solute or no electrolyte.
- In electrolyte solutions.
- In solutions with several solutes.
In any of these cases, the calculation of the osmotic pressure is based on the use of the following equation:
where π is the osmotic pressure, R is the universal gas constant, T is the absolute temperature in Kelvin, and M is the molar concentration of all free solute particles present in the solution. This last concentration depends on the type of solute or solutes that are present, and basically consists of the sum of the concentrations of all osmotically active particles, that is, those that cannot cross a semipermeable membrane.
In the case of neutral molecular solutes, that is, those that are not electrolytes, M is simply the molarity. However, in the case of electrolytes, M represents the sum of the concentrations of the ions that are formed through dissociation and of the molecules that remain undissociated.
Since the concentration of the ions and of the undissociated molecules depend on the degree of dissociation, and this is determined by the dissociation constant and by the initial or analytical concentration of the solute, then the total concentration of osmotically active particles can be related to the initial concentration by multiplying by a factor known as the van’t Hoff factor, i, which is given by:
This factor can be determined in different ways depending on the type of solute in question:
- For strong electrolytes, those that dissociate completely, the van’t Hoff factor is equal to the total number of ions that dissociate into, regardless of their electrical charges.
- For weak electrolytes, this factor can be determined from the dissociation constant, but it is also tabulated for different solutes at different temperatures, which is more practical.
- In the case of non-electrolyte solutes or molecular solutes, the factor is simply 1.
Multiplying the molarity or analytical concentration of the electrolyte by this factor results in the actual concentration of osmotically active particles present in the solution, so the osmotic pressure remains:
Steps to Calculate Osmotic Pressure
The calculation of the osmotic pressure of any solution can be summarized in the following steps:
- Step 1: Extract the data from the statement and carry out the necessary unit transformations.
- Step 2: Determine the type of solute or solutes and the value of the coefficient or van’t Hoff factor.
- Step 3: Calculate the initial molarity or molar concentration of the solute(s).
- Step 4: Use the formula to calculate the osmotic pressure.
Next, it is shown how to follow these steps to calculate the osmotic pressure in the three situations mentioned above.
Case 1: Calculation of the osmotic pressure of a non-electrolyte solution
statement
Determine the osmotic pressure at 25.0 °C of a solution containing 30.0 g of glucose (C 6 H 12 O 6 ) dissolved in enough water to make 150.0 mL of solution.
Step #1: Extract the data from the statement and carry out the necessary unit transformations.
In this case, the temperature, the mass of the solute, and the volume of the solution are given. The temperature must be transformed to Kelvin and the volume to liters (since the molarity will be calculated).
Also, unless we already have its number of moles, we always need the molar mass of the solute:
Step 2: Determine the type of solute or solutes and the value of the coefficient or van’t Hoff factor.
Glucose is a neutral molecular compound, which means that it is a non-electrolyte (does not dissociate in solution). For this reason, its van’t Hoff factor is equal to 1.
Step 3: Calculate the initial molarity or molar concentration of the solute(s).
Since we have the mass of the solute, the volume of the solution, and the molar mass of the solute, we only need to apply the molarity formula:
Step #4: Use the formula to calculate the osmotic pressure.
We now have everything we need to calculate the osmotic pressure. Depending on the units in which we want to calculate the pressure, we can use different values of the ideal gas constant. For the purposes of most of the calculations carried out in chemistry and biology, this pressure is calculated in atmospheres, so the ideal gas constant is used in these units, that is, 0.08206 atm.L/ mol.K:
Case 2: Calculation of the osmotic pressure of an electrolyte solution
statement
Determine the osmotic pressure at 37.0 °C of a solution that contains 0.900 g of sodium chloride (NaCl) per 100.0 mL of solution.
Step 1: Extract the data from the statement and carry out the necessary unit transformations.
In this case, the temperature, the mass of the solute, and the volume of the solution are again given. Again, the temperature must be transformed to Kelvin and the volume to liters and the molar mass of the solute must be calculated:
Step 2: Determine the type of solute or solutes and the value of the coefficient or van’t Hoff factor.
Sodium chloride is a strong electrolyte that completely dissociates in aqueous solution. The dissociation reaction is:
As can be seen, each formula unit of NaCl gives rise to two ions, a sodium cation and a choride anion, and no undissociated NaCl unit remains. Therefore, for this solute, the van’t Hoff coefficient or factor has a value of 2.
Step #3: Calculate the initial molarity or molar concentration of the solute(s).
As in the previous case, we have the mass of the solute, the volume of the solution and the molar mass of the solute, so the molarity is given by:
Step #4: Use the formula to calculate the osmotic pressure.
This step is carried out in the same way as before. Again, we will calculate the osmotic pressure in atmospheres:
Case 3: Calculation of the osmotic pressure of a solution with several solutes
statement
Determine the osmotic pressure at the average body temperature of 37°C of a lactated Ringer’s solution having the following composition:
102.7 mM sodium chloride
27.8 mM sodium lactate (NaC 3 H 5 O 3 )
5.4 mM potassium chloride
1.8 mM calcium chloride dihydrate.
This is an important example of calculating osmotic pressure, since sera such as the lactated Ringer’s solution cited above must be prepared with a specific osmotic pressure. Some are set to have the same osmotic pressure as the blood serum, while others are set to have a higher or lower osmotic pressure, depending on the patient’s conditions.
Step 1: Extract the data from the statement and carry out the necessary unit transformations.
In this case, we have a solution with four different solutes. The concentrations of the solutes are provided directly, but in units of mM (millimolar) so they must be transformed to molarity. The temperature is also provided, which must be transformed to Kelvin. The first transformation is carried out by dividing by 1000.
Step 2: Determine the type of solute or solutes and the value of the coefficient or van’t Hoff factor.
Sodium chloride, sodium lactate, and potassium chloride are strong electrolytes that dissociate to form 2 ions each, so their van’t Hoff coefficients are equal to 2.
In the case of calcium chloride, the dissociation reaction is:
If it dissociates completely, 3 ions in total would be produced, giving a van’t Hoff factor of 3. However, it has been determined experimentally that this solute does not completely dissociate, and that it has a factor of slightly less than 2, 7.
Step 3: Calculate the initial molarity or molar concentration of the solute(s).
This step is not necessary for this problem since the statement provided all the necessary concentrations.
Step 4: Use the formula to calculate the osmotic pressure.
When there are several solutes, the total osmotic pressure simply corresponds to the sum of the contributions of each of them. This can be summarized as follows:
where the sum is over all solutes present, whether electrolyte or non-electrolyte. The result of this summation is what is commonly known as the osmolarity of the solution, that is, the total concentration of all osmotically active particles.
Since we already have all the necessary data, everything is a matter of applying this formula to calculate the osmotic pressure:
References
Brown, T. (2021). Chemistry: The Central Science (11th ed.). London, England: Pearson Education.
Castro, S. (2019, February 22). Osmotic pressure Formula and solved exercises. Retrieved from https://www.profesor10demates.com/2018/12/presion-osmotica-formula-y-ejercicios-resueltos.html
Chang, R., Manzo, Á. R., Lopez, PS, & Herranz, ZR (2020). Chemistry (10th ed.). New York City, NY: MCGRAW-HILL.
Foundation for Health Training and Research of the Region of Murcia. (nd). 2.-Basic principles of osmosis and osmotic pressure. Calculation of plasma osmolality (OSMP). Retrieved from http://www.ffis.es/volviendoalobasico/2principios_bsicos_de_la_smosis_y_la_presin_onctica_clculo_de_la_osmolalidad_plasmtica_osmp.html
Young. (nd). Electrolytes: van’t Hoff Factor | Protocol (Translated to Spanish). Retrieved from https://www.jove.com/science-education/11371/electrolitos-factor-de-van-t-hoff?language=Spanish
Tabazz, U. (2012, September 20). Electrochemistry. Retrieved from https://www.slideshare.net/utabazz/electroquimica-14366482
