A solid mixture of KCl, KNO3, and Ba1NO322 is20.92 mass % chlorine, and a 1.000 g sample of the mix- ture in 500.0 mL of aqueous solution at 25 °C has an osmotic pressure of 744.7 mm Hg. What are the mass percents of KCl, KNO3, and Ba1NO322 in the mixture?

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Determine the molar mass of each compound (KCl, KNO3, and Ba(NO3)2) using the atomic masses of each element.

Calculate the moles of chlorine in the 1.000 g sample based on the given mass percent of chlorine. Use the formula: moles of Cl = (mass of Cl in sample / molar mass of Cl).

Use the osmotic pressure formula \\(\\Pi = iMRT\\) to find the molarity (M) of the solution. Here, \\(\\Pi\\) is the osmotic pressure, i is the van't Hoff factor, R is the gas constant, and T is the temperature in Kelvin.

Calculate the total moles of solute in the solution using the molarity obtained from the osmotic pressure calculation and the volume of the solution.

Determine the mass percentages of KCl, KNO3, and Ba(NO3)2 in the original mixture by setting up equations based on the moles of each compound contributing to the total moles of solute and the moles of chlorine from each compound.

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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, as described by the van 't Hoff equation: 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.

Mass Percent Composition

Mass percent composition is a way to express the concentration of a component in a mixture as a percentage of the total mass. It is calculated by dividing the mass of the component by the total mass of the mixture and multiplying by 100. This concept is essential for determining the individual contributions of KCl, KNO3, and Ba(NO3)2 in the given mixture.

Colligative Properties

Colligative properties are properties of solutions that depend on the number of solute particles rather than their identity. These include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Understanding colligative properties is crucial for solving the problem, as the osmotic pressure measured will help determine the total concentration of solute particles in the solution.

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