The equilibrium constant for the dimerization of acetic acid in benzene solution is 1.51 * 102 at 25 °C.2 CH3CO2H ∆ 1CH3CO2H22 Kc = 1.51 * 102 at 25 °C(b) What is the osmotic pressure of the solution at 25 °C?

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Identify the relevant formula for osmotic pressure: \( \Pi = iMRT \), 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.

Determine the van't Hoff factor \( i \). For the dimerization reaction \( 2 \text{CH}_3\text{CO}_2\text{H} \rightleftharpoons (\text{CH}_3\text{CO}_2\text{H})_2 \), the equilibrium constant \( K_c = 1.51 \times 10^2 \) suggests that the reaction favors the dimer formation. Calculate \( i \) based on the extent of dimerization.

Convert the temperature from Celsius to Kelvin: \( T = 25 + 273.15 = 298.15 \text{ K} \).

Assume an initial concentration of acetic acid and use the equilibrium constant \( K_c \) to find the equilibrium concentrations of monomer and dimer. This will help determine the effective molarity \( M \) of particles in solution.

Substitute the values of \( i \), \( M \), \( R \) (0.0821 L atm K⁻¹ mol⁻¹), and \( T \) into the osmotic pressure formula to find \( \Pi \).

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Key Concepts

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

Equilibrium Constant (Kc)

The equilibrium constant (Kc) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. In the case of dimerization, Kc indicates how much acetic acid exists as dimers versus monomers in solution. A higher Kc value suggests a greater tendency for the formation of dimers.

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly related to the concentration of solute particles in the solution, as described by the formula π = iCRT, where π is osmotic pressure, i is the van 't Hoff factor, C is molarity, R is the ideal gas constant, and T is temperature in Kelvin.

Dimerization

Dimerization is a chemical process where two molecules combine to form a larger, more complex molecule called a dimer. In the context of acetic acid, this process affects the concentration of acetic acid in solution, which in turn influences the osmotic pressure. Understanding the extent of dimerization is crucial for calculating the effective concentration of solute particles in the solution.

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