The diagram to the right shows plots of vapor pressure versus temperature for a solvent and a solution.
c. What is the approximate concentration of the solution in mol/kg, if 1 mol of solute particles raises the boiling point of 1 kg of solvent by 3.63 °C?
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검증된 단계별 안내

Step 1: Analyze the graph provided. The blue curve represents the vapor pressure of the pure solvent, while the orange curve represents the vapor pressure of the solution. The boiling point is determined by the temperature at which the vapor pressure equals 760 mmHg (the dashed horizontal line). Identify the boiling points for both the solvent and the solution from the graph.

Step 2: Calculate the boiling point elevation (ΔT_b) by subtracting the boiling point of the pure solvent from the boiling point of the solution. This value represents the increase in boiling point due to the presence of solute particles.

Step 3: Use the boiling point elevation formula: ΔT_b = i × K_b × m, where ΔT_b is the boiling point elevation, i is the van't Hoff factor (number of particles the solute dissociates into), K_b is the boiling point elevation constant (given as 3.63 °C·kg/mol), and m is the molality (mol/kg). Rearrange the formula to solve for molality (m): m = ΔT_b / (i × K_b).

Step 4: Assume the solute does not dissociate (i = 1) unless otherwise specified. Substitute the values for ΔT_b (calculated in Step 2) and K_b (3.63 °C·kg/mol) into the formula to calculate the molality of the solution.

Step 5: Interpret the calculated molality (m) as the concentration of the solution in mol/kg. This value represents the approximate concentration of solute particles in the solution.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It indicates how readily a substance will evaporate; higher vapor pressure means a higher tendency to vaporize. In the context of the diagram, the vapor pressure of the solvent and solution changes with temperature, affecting boiling point elevation.

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a solute is added. This phenomenon occurs because the presence of solute particles disrupts the solvent's ability to vaporize, requiring a higher temperature to reach the boiling point. The relationship can be quantified using the formula ΔT_b = i * K_b * m, where ΔT_b is the boiling point elevation, i is the van 't Hoff factor, K_b is the ebullioscopic constant, and m is the molality of the solution.

Molality

Molality is a measure of concentration defined as the number of moles of solute per kilogram of solvent. It is expressed in mol/kg and is particularly useful in colligative property calculations, such as boiling point elevation. In this question, determining the molality of the solution is essential to find out how much the boiling point has increased due to the addition of solute particles.

The diagram to the right shows plots of vapor pressure versus temperature for a solvent and a solution.c. What is the approximate concentration of the solution in mol/kg, if 1 mol of solute particles raises the boiling point of 1 kg of solvent by 3.63 °C?<IMAGE>