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Osmotic pressure (Π) refers to the pressure that must be applied to a solution to slow osmosis of solvent across a semipermeable membrane from a reservoir of pure solvent. This is a colligative property of solutions that is of great importance in different fields.
Osmotic pressure is particularly relevant in the fields of biology and medicine, since it regulates the water balance of the cells that make up all living beings. On the other hand, osmotic pressure is also important in the field of engineering because it represents the minimum pressure that must be applied to a solution in order to carry out reverse osmosis, a procedure that forms the basis of seawater desalination.
In any of these cases it is essential to be able to calculate the osmotic pressure of different solutions. For this reason, a problem for calculating the osmotic pressure of a complex aqueous solution is presented below , that is, one that contains several solutes, some ionic and others not.
On the other hand, it is also important to be able to determine the concentration required to reach a certain osmotic pressure in order to be able to prepare hypertonic, hypotonic or isotonic solutions as needed. The solution of a problem dealing with this point is also presented.
How is osmotic pressure calculated?
The calculation of the osmotic pressure of a solution is carried out using the following formula:
Where Π is the osmotic pressure in atmospheres, i is the van’t Hoff coefficient, M is the molar concentration of the solute, R is the ideal gas constant whose value is 0.08206 atm.L/mol.K and T is the absolute temperature in kelvin.
In the case of several solutes, the total osmotic pressure is calculated as the sum of the contributions of each solute, that is:
The values of the van’t Hoff coefficients can be determined theoretically (approximately) from the number of particles into which the solute dissociates if it is a strong electrolyte, or from the resolution of ionic equilibrium in the case of weak electrolytes.
However, the most suitable value is the one that is determined by means of experiments such as the cryoscopic descent or the ebulloscopic ascent of a solution.
Problem 1: Calculation of the osmotic pressure of a complex solution
statement
You want to calculate the osmotic pressure, in millimeters of mercury, of a solution prepared by dissolving 5.00 g of glucose, 0.500 g of sodium chloride, and 0.200 g of calcium chloride in enough water to make 250 mL of solution at 25°C. .
Solution
The solution of this type of problems is carried out through the following steps:
Step 1: Extract the data from the statement, transform the units, and calculate the relevant molar masses.
The first step, as in all problems, is to obtain the data of the statement. In this case we are given the masses of three solutes, the total volume of the solution, and the temperature. In addition, the solutes are indicated to be glucose (formula C 6 H 12 O 6 ), sodium chloride (NaCl), and calcium chloride (CaCl 2 ).
The following table summarizes the data provided. Since molar concentrations will be calculated, the volume in liters is required. The molar masses were calculated by adding the molar masses of each atom present in the formula, as is normal.
| m glucose = | 5.00g | MM glucose = | 180.16 g/mol |
| m NaCl = | 0.500g | MM NaCl = | 58.44 g/mol |
| mCaCl2 = _ | 0.200g | MM CaCl2 = | 110.98 g/mol |
| V solvent = | 250 mL x (1L/1000mL) = 0.250L | T = | 25°C + 273.15 = 298.15K |
Step 2: Calculate the molar concentration of all the solutes.
This solution contains 3 solutes, so 3 molarities must be calculated. These are:
Step 3: Determine the van’t Hoff factor for each solute.
As mentioned at the beginning, these factors can be determined experimentally or theoretically. In this case, we will do it theoretically.
Glucose
Because it is a molecular solute that does not dissociate, the van’t Hoff factor for glucose is i=1 .
Sodium chloride
NaCl is an ionic solute and is also a strong electrolyte. In this case, the van’t Hoff factor is determined by the total number of ions or particles into which the solute dissociates in solution. The following is the dissolution reaction of this solute:
As we can see, each formula of NaCl that dissociates produces a total of two ions, so for this solute i=2 .
Calcium chloride
As in the previous case, calcium chloride consists of an ionic solute that completely dissociates in aqueous solution. The dissociation reaction is:
Unlike sodium chloride, calcium chloride produces three ions on dissociation, so it has a theoretical van’t Hoff factor of i=3 .
Step 4: Use the formula to determine the osmotic pressure.
The last step is to determine the osmotic pressure itself. The initial result will be expressed in atmospheres, so we will then have to transform it to mmHg, as specified in the statement.
Answer
The solution will have an osmotic pressure of 3,740 mmHg.
Problem 2: Calculation of concentration from osmotic pressure
statement
Determine the mass of calcium chloride needed to prepare 100 mL of solution with an osmotic pressure of 380 Torr at 37°C.
Solution
This type of problem is attacked in a similar way to the previous one. The only thing that changes is the use of the osmotic pressure equation, which must be solved to obtain the desired unknown, in this case the solute concentration, instead of being used directly.
Step 1: Extract the data from the statement, transform the units, and calculate the relevant molar masses.
The first step is the same as in the previous case.
| V solvent = | 100 mL x (1L/1000mL) = 0.100L | T = | 37°C + 273.15 = 310.15K |
| Π = | 380 Torr. (1atm/760 Torr) = 0.500 atm | MM CaCl2 = | 110.98 g/mol |
| mCaCl2 = _ | ? |
Step 2: Determine the van’t Hoff factor
As we saw in the previous problem, since it is a strong electrolyte that produces three ions when it dissociates, the van’t Hoff factor of calcium chloride is i=3 .
Step 3: Clear and calculate the molar concentration of the solute.
Since it is a single solute, the osmotic pressure is given by:
We already know the values of all the variables except the molar concentration, so we can solve this equation for that variable:
Step 4: Using the molarity formula, isolate the mass of solute.
The formula for molarity or molar concentration is:
Solving this equation for the mass of the solute, msto , gives:
Answer
0.0727 g of calcium chloride must be weighed to prepare 100 mL of a solution that has an osmotic pressure of 380 Torr at a temperature of 37 °C.
References
- Castro, S. (2019). Osmotic pressure Formula and solved exercises . teacher10math. https://www.profesor10demates.com/2018/12/presion-osmotica-formula-y-ejercicios-resueltos.html
- Chang, R. (2021). Chemistry (Ninth ed.). McGraw-Hill.
- Osmotic pressure. What is it, Formula and Examples. (2020). Visual Core. https://nucleovisual.com/presion-osmotica-que-es-y-como-calcular/
- Zapata, M. (2020). Colligative Properties : Osmotic Pressure . Chemistry at home.com. https://quimicaencasa.com/propiedades-coligativas-presion-osmotica/
