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Chapter 13: Problem 42

A solution is made containing \(20.8 \mathrm{~g}\) phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) in \(425 \mathrm{~g}\) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O} \mathrm{H}\right) .\) 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 = 0.017 (b) Mass percent of phenol = 4.67 % (c) Molality of phenol = 0.479 \(mol/kg\)

Step by step solution

01

(Step 1: Calculate the number of moles for each substance)

Given masses of phenol and ethanol are \(20.8 \mathrm{~g}\) and \(425 \mathrm{~g}\), respectively. To get the number of moles for each substance, we need to divide the given mass by the molar mass of each substance. The molar masses of phenol \(\left(\mathrm{C}_{6}\mathrm{H}_{5}\mathrm{OH}\right)\) and ethanol \(\left(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\right)\) are \(94.11 \mathrm{~g/mol}\) and \(46.07 \mathrm{~g/mol}\), respectively. Thus, Moles of phenol = \(\frac{20.8}{94.11}\) Moles of ethanol = \(\frac{425}{46.07}\)
02

(Step 2: Calculate the mole fraction of phenol)

Mole fraction is the ratio of the moles of a particular component to the total moles of the system. Mole fraction of phenol = \(\frac{\text{Moles of phenol}}{\text{Total moles}}\) Total moles = Moles of phenol + Moles of ethanol Calculate the mole fraction of phenol from the above formula.
03

(Step 3: Calculate the mass percent of phenol)

Mass percent is the ratio of the mass of a particular component to the total mass of the system multiplied by 100 to get the percentage. Mass percent of phenol = \(\frac{\text{Mass of phenol}}{\text{Total mass}} \times 100\) Total mass = Mass of phenol + Mass of ethanol = \(20.8 \mathrm{~g}\) + \(425 \mathrm{~g}\) Calculate the mass percent of phenol using the formula above.
04

(Step 4: Calculate the molality of phenol)

Molality is defined as the number of moles of solute per kilogram of solvent. Molality of phenol = \(\frac{\text{Moles of phenol}}{\text{Mass of ethanol in kg}}\) The mass of ethanol should be converted to kilograms by dividing it by 1000. Calculate the molality of phenol using the formula above. Now, we have calculated all the required parameters: mole fraction, mass percent, and molality of phenol in the given solution.

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Most popular questions from this chapter

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