/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 38 A solution is made containing \(... [FREE SOLUTION] | 91影视

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A solution is made containing \(25.5 \mathrm{~g}\) phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) in \(425 \mathrm{~g}\) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\). Calculate (a) the mole fraction of phenol, (b) the mass percent of phenol, (c) the molality of phenol.

Short Answer

Expert verified
(a) Mole fraction of phenol (蠂鈧氠担鈧戔倣鈧氣倳鈧戔倷鈧掆倵鈧) = 0.263 (b) Mass percent of phenol = 5.66% (c) Molality of phenol (m) = 5.53 mol/kg

Step by step solution

01

Determine the moles of phenol and ethanol

To calculate molality and mole fraction, we will need to determine the number of moles of each component in the solution. The molecular mass of phenol (C鈧咹鈧匫H) is: C: 6 atoms 脳 12.01 g/mol = 72.06 g/mol H: 6 atoms 脳 1.008 g/mol = 6.048 g/mol O: 1 atom 脳 16.00 g/mol = 16.00 g/mol Total molecular mass = 94.108 g/mol The number of moles of phenol is given by: Phenol moles = \(\frac{\text{mass}}{\text{molar mass}} = \frac{25.5 \text{ g}}{94.108 \text{ g/mol}}\) The molecular mass of ethanol (C鈧侶鈧匫H) is: C: 2 atoms 脳 12.01 g/mol = 24.02 g/mol H: 6 atoms 脳 1.008 g/mol = 6.048 g/mol O: 1 atom 脳 16.00 g/mol = 16.00 g/mol Total molecular mass = 46.068 g/mol The number of moles of ethanol is given by: Ethanol moles = \(\frac{\text{mass}}{\text{molar mass}} = \frac{425 \text{ g}}{46.068 \text{ g/mol}}\) Calculate the number of moles of phenol and ethanol.
02

Calculate the mole fraction of phenol

To calculate the mole fraction of phenol (蠂鈧氠担鈧戔倣鈧氣倳鈧戔倷鈧掆倵鈧), we will use the formula: Mole fraction of phenol = \(\frac{\text{moles of phenol}}{\text{total moles in the solution}}\) 蠂鈧氠担鈧戔倣鈧氣倳鈧戔倷鈧掆倵鈧 = \(\frac{\text{moles of phenol}}{\text{moles of phenol} + \text{moles of ethanol}}\) Calculate the mole fraction of phenol using the previously calculated values of moles of phenol and ethanol.
03

Calculate the mass percent of phenol

To calculate the mass percentage of phenol, we will use the following formula: Mass percent of phenol = \(\frac{\text{mass of phenol}}{\text{total mass of the solution}} 脳 100\%\) Total mass of the solution = 25.5 g (phenol) + 425 g (ethanol) Calculate the mass percent of phenol using the given masses and the total mass of the solution.
04

Calculate the molality of phenol

To calculate the molality (m) of phenol, we will use the following formula: Molality = \(\frac{\text{moles of phenol}}{\text{mass of ethanol (solvent) in kilograms}}\) Convert the mass of ethanol to kilograms: 425 g 脳 \(\frac{1 \text{ kg}}{1000 \text{ g}}\) Calculate the molality of phenol using the previously calculated moles of phenol and the mass of ethanol in kilograms.

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