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Ch.13 - Solutions & Their Properties
McMurry - Chemistry 8th Edition
McMurry8th EditionChemistryISBN: 9781292336145당신이 사용하는 게 아니라요?교과서 변경
모든 교과서McMurry 8th EditionCh.13 - Solutions & Their Properties문제 128
13장, 문제 128

When a 2.850 g mixture of the sugars sucrose (C12H22O11) and fructose (C6H12O6) was dissolved in water to a volume of 1.50 L, the resultant solution gave an osmotic pressure of 0.1843 atm at 298.0 K. What is Xsucrose of the mixture?

검증된 단계별 안내
1
Step 1: Use the formula for osmotic pressure, \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor (which is 1 for non-electrolytes like sucrose and fructose), \( M \) is the molarity, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.
Step 2: Rearrange the formula to solve for molarity \( M \): \( M = \frac{\Pi}{iRT} \). Substitute the given values: \( \Pi = 0.1843 \) atm, \( i = 1 \), \( R = 0.0821 \) L·atm/mol·K, and \( T = 298.0 \) K.
Step 3: Calculate the total moles of solute in the solution using the molarity \( M \) and the volume of the solution (1.50 L): \( \text{moles of solute} = M \times 1.50 \) L.
Step 4: Let \( x \) be the moles of sucrose and \( y \) be the moles of fructose. The total moles of solute is \( x + y \). Use the molar masses of sucrose (342.30 g/mol) and fructose (180.16 g/mol) to set up the equation: \( 342.30x + 180.16y = 2.850 \) g.
Step 5: Solve the system of equations: \( x + y = \text{total moles of solute} \) and \( 342.30x + 180.16y = 2.850 \) g, to find the mole fraction of sucrose, \( X_{\text{sucrose}} = \frac{x}{x+y} \).

주요 개념

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

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.
추천 영상:
가이드 코스
01:13
Osmotic Pressure Formula

Molar Mass and Moles

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the number of moles of a substance in a mixture, the mass of the substance is divided by its molar mass. This concept is essential for calculating concentrations and relating mass to osmotic pressure in solutions.
추천 영상:
가이드 코스
02:11
Molar Mass Concept

Mass Fraction

Mass fraction is a way of expressing the concentration of a component in a mixture, defined as the mass of the component divided by the total mass of the mixture. In this problem, determining the mass fraction of sucrose (Xsucrose) involves calculating the proportion of sucrose's mass relative to the total mass of the sugar mixture, which is crucial for solving for its contribution to the osmotic pressure.
추천 영상:
가이드 코스
03:07
Mole Fraction Example
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