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 osmotic pressure, which can be quantified using the formula:

\(\Pi = i \cdot C \cdot R \cdot T\)

In this equation, \(\Pi\) represents the osmotic pressure measured in atmospheres. The variable \(i\) is known as the van't Hoff factor, which accounts for the number of particles the solute dissociates into in solution. The term \(C\) denotes the molarity (or concentration) of the solution, expressed in moles per liter (mol/L). The gas constant \(R\) is a constant value of \(0.08206 \, \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K})\), and \(T\) is the absolute temperature measured in Kelvin.

It is essential to recognize that both the concentration of the solute and the temperature of the solution significantly influence the osmotic pressure. Higher concentrations of solute or increased temperatures will lead to greater osmotic pressure, thereby affecting the rate and direction of water movement across membranes.

To calculate the osmotic pressure of a solution containing 18.30 milligrams of zinc oxide in 15.1 mL of solution at 26 degrees Celsius, we use the formula for osmotic pressure:

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

In this equation, \(\Pi\) represents the osmotic pressure, \(I\) is the van 't Hoff factor, \(M\) is the molarity, \(R\) 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-), giving us a van 't Hoff factor \(I = 2\).

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

\(15.1 \, \text{mL} = 0.0151 \, \text{L}\)

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

\(18.30 \, \text{mg} = 0.01830 \, \text{g}\)

Next, we calculate the number of moles of zinc oxide using its molar mass. The molar mass of zinc oxide (ZnO) is approximately 81.38 g/mol. The number of moles can be calculated as follows:

\(n = \frac{0.01830 \, \text{g}}{81.38 \, \text{g/mol}} \approx 2.2487 \times 10^{-4} \, \text{moles}\)

Now, we can find the molarity \(M\):

\(M = \frac{n}{V} = \frac{2.2487 \times 10^{-4} \, \text{moles}}{0.0151 \, \text{L}} \approx 0.0149 \, \text{mol/L}\)

Next, we convert the temperature from 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. The ideal gas constant \(R\) is typically \(0.0821 \, \text{L} \cdot \text{atm} / (\text{K} \cdot \text{mol})\):

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

After performing the calculations, we find:

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

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