Osmotic Pressure: Videos & Practice Problems

Osmotic pressure is a crucial concept in understanding how water moves across semipermeable membranes, specifically from areas of lower solute concentration to areas of higher solute concentration. This movement is driven by the need to equalize solute concentrations on either side of the membrane. The osmotic pressure of a solution is influenced by both its concentration and temperature, making these factors essential in various biological and chemical processes.

The formula for calculating osmotic pressure (\( \Pi \)) is given by:

\[\Pi = i \cdot C \cdot R \cdot T\]

In this equation, \( \Pi \) represents the osmotic pressure measured in atmospheres. The variables involved are:

• i: the van't Hoff factor, which accounts for the number of particles the solute dissociates into in solution.
• C: the molarity (or concentration) of the solution, expressed in moles per liter (mol/L).
• R: the ideal gas constant, valued at 0.08206 L·atm/(mol·K).
• T: the absolute temperature in Kelvin (K).

Understanding how concentration and temperature affect osmotic pressure is vital for applications in fields such as biology, chemistry, and medicine, where the movement of water and solutes is fundamental to many processes.

To calculate the osmotic pressure of a solution containing zinc oxide, we use the formula for osmotic pressure, which is given by:

\(\Pi = I \times C \times R \times T\)

In this equation, \(\Pi\) represents the osmotic pressure, \(I\) is the van 't Hoff factor, \(C\) is the molarity of the solution, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin.

Zinc oxide (ZnO) is an ionic compound that dissociates into two ions: zinc ions (Zn²⁺) and oxide ions (O^2-). Therefore, the van 't Hoff factor \(I\) for zinc oxide is 2.

Next, we need to calculate the molarity \(C\) of the solution. Molarity is defined as the number of moles of solute per liter of solution. First, we convert the volume of the solution from milliliters to liters:

15.1 mL = 0.0151 L

Now, we convert the mass of zinc oxide from milligrams to grams:

18.30 mg = 0.01830 g

To find the number of moles of zinc oxide, we use its molar mass. The molar mass of zinc oxide is approximately 81.38 g/mol. The number of moles \(n\) can be calculated as follows:

\(n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{0.01830 \, \text{g}}{81.38 \, \text{g/mol}} \approx 2.25 \times 10^{-4} \, \text{moles}\)

Now, we can calculate the molarity \(C\):

\(C = \frac{n}{\text{volume (L)}} = \frac{2.25 \times 10^{-4} \, \text{moles}}{0.0151 \, \text{L}} \approx 0.0149 \, \text{M}\)

Next, we convert the temperature from degrees Celsius to Kelvin:

\(T = 26 \, \text{°C} + 273.15 = 299.15 \, \text{K}\)

Now we can substitute all the values into the osmotic pressure formula:

\(\Pi = 2 \times 0.0149 \, \text{M} \times 0.0821 \, \text{L·atm/(K·mol)} \times 299.15 \, \text{K}\)

Calculating this gives:

\(\Pi \approx 0.731 \, \text{atm}\)

Thus, the osmotic pressure of the solution is approximately 0.731 atmospheres.