A 0.100 M ionic solution has an osmotic pressure of 8.3 atm at 25 °C. Calculate the van't Hoff factor (i) for this solution.

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Identify the formula for osmotic pressure, which is given by \(\Pi = iMRT\), where \(\Pi\) is the osmotic pressure, \(i\) is the van't Hoff factor, \(M\) is the molarity of the solution, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin.

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. For this problem, convert 25 °C to Kelvin.

Use the value of the ideal gas constant \(R\) that is appropriate for the units of pressure in atmospheres, which is approximately 0.0821 L·atm/mol·K.

Rearrange the osmotic pressure formula to solve for the van't Hoff factor \(i\). The rearranged formula is \(i = \frac{\Pi}{MRT}\).

Substitute the values of \(\Pi\), \(M\), \(R\), and \(T\) into the rearranged formula to calculate the van't Hoff factor \(i\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van't Hoff factor, C is the molarity of the solution, and R is the ideal gas constant.

van't Hoff Factor (i)

The van't Hoff factor (i) represents the number of particles into which a solute dissociates in solution. For ionic compounds, this factor can be greater than one, as they separate into multiple ions. For example, NaCl dissociates into Na⁺ and Cl⁻, giving it a van't Hoff factor of 2. Understanding this concept is crucial for calculating colligative properties like osmotic pressure.

Colligative Properties

Colligative properties are properties of solutions that depend on the number of solute particles rather than their identity. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. The van't Hoff factor plays a significant role in these properties, as it affects the effective concentration of solute particles in the solution.