The observed osmotic pressure for a 0.125 M solution of MgCl2 at 310 K is 8.57 atm. Calculate the value of the van’t Hoff factor for MgCl2 under these conditions.

Verified step by step guidance

Step 1: Recall the formula for osmotic pressure, which is \( \Pi = iMRT \), where \( \Pi \) is 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.

Step 2: Identify the given values from the problem: \( \Pi = 8.57 \text{ atm} \), \( M = 0.125 \text{ M} \), \( T = 310 \text{ K} \), and \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \).

Step 3: Rearrange the osmotic pressure formula to solve for the van’t Hoff factor \( i \): \( i = \frac{\Pi}{MRT} \).

Step 4: Substitute the known values into the rearranged formula: \( i = \frac{8.57}{0.125 \times 0.0821 \times 310} \).

Step 5: Calculate the expression to find the value of \( i \), which represents the van’t Hoff factor for MgCl_2 under the given conditions.

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, R is the ideal gas constant, and T is the temperature in Kelvin.

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 like MgCl2, which dissociates into one magnesium ion (Mg²⁺) and two chloride ions (Cl⁻), the van’t Hoff factor is 3. This factor is crucial for calculating colligative properties, including osmotic pressure, as it accounts for the total number of solute particles affecting the solution's behavior.

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. Understanding colligative properties is essential for predicting how solute concentration affects the physical properties of a solution, which is key in calculating osmotic pressure and the van’t Hoff factor.

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When 9.12 g of HCl was dissolved in 190 g of water, the freezing point of the solution was - 4.65 °C. What is the value of the van't Hoff factor for HCl?

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A solution concentration must be expressed in molality when considering boiling-point elevation or freezing-point depression but can be expressed in molarity when consider- ing osmotic pressure. Why?

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Textbook Question

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