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Chapter 13: Problem 51

What are the partial and total vapor pressures of a solution obtained by mixing 35.8 g benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\) and \(56.7 \mathrm{g}\) toluene, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3},\) at \(25^{\circ} \mathrm{C} ? \mathrm{At} 25^{\circ} \mathrm{C}\) the vapor pressure of \(\mathrm{C}_{6} \mathrm{H}_{6}=95.1 \mathrm{mm} \mathrm{Hg} ;\) the vapor pressure of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}=28.4 \mathrm{mmHg}\).

Short Answer

Expert verified
To get a short answer, find the mole fractions for benzene and toluene, then use these mole fractions to find the partial vapor pressures via Raoult's Law. Finally, add these partial pressures to find the total vapor pressure.

Step by step solution

01

Calculate the Mole Fraction

First, the molar fractions of benzene and toluene in the solution need to be calculated. To find that, divide the mass of each substance by its molar mass to get the number of moles. The molar mass of benzene (C6H6) is approximately 78.11 g/mol while for toluene (C6H5CH3) it is approximately 92.14 g/mol. Now, compute the mole fractions, which are the ratio of the number of moles of a component to the total number of moles. The total number of moles is the sum of the moles of both benzene and toluene.
02

Application of Raoult's Law

Now, apply Raoult's Law. The partial vapor pressure of a component in a solution equals to the product of mole fraction of the component and the vapor pressure of the pure component. Use the mole fractions calculated in the previous step. The vapor pressure of benzene is given as 95.1 mmHg and for toluene it's 28.4 mmHg. This will give you the partial pressures for both benzene and toluene.
03

Calculate Total Vapor Pressure

The total vapor pressure is simply the sum of the partial vapor pressures. In the context of this problem, to find the total vapor pressure of the solution, sum up the partial pressure values calculated in the previous step, those of benzene and toluene respectively, to get the total vapor pressure of the mixture.

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Most popular questions from this chapter

In a saturated solution at \(25^{\circ} \mathrm{C}\) and 1 bar, for the following solutes, which condition will increase solubility? (a) \(\operatorname{Ar}(g),\) decrease temperature; (b) \(\mathrm{NaCl}(\mathrm{s})\) increase pressure; (c) \(\mathrm{N}_{2}\), decrease pressure; (d) \(\mathrm{CO}_{2}\) increase volume.

Which aqueous solution from the column on the right has the property listed on the left? Explain your choices. $$\begin{array}{ll}\hline \text { Property } & \text { Solution } \\\\\hline \text { 1. lowest electrical } & \text { a. } 0.10 \mathrm{m} \mathrm{KCl}(\mathrm{aq}) \\\\\text { conductivity } & \\\\\text { 2. } \text { lowest boiling } & \text { b. } 0.15 \mathrm{m}\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(\mathrm{aq}) \\\\\text { point } & \\\\\text { 3. highest vapor pressure } & \text { c. } 0.10 \mathrm{m} \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq}) \\\\\text { of water at } 25^{\circ} \mathrm{C} & \\\\\text { 4. lowest freezing point } & \text { d. } 0.05 \mathrm{m} \mathrm{NaCl} \\\\\hline\end{array}$$

Styrene, used in the manufacture of polystyrene plastics, is made by the extraction of hydrogen atoms from ethylbenzene. The product obtained contains about \(38 \%\) styrene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}=\mathrm{CH}_{2}\right)\) and \(62 \%\) ethylbenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{CH}_{3}\right),\) by mass. The mixture is separated by fractional distillation at \(90^{\circ} \mathrm{C} .\) Determine the composition of the vapor in equilibrium with this \(38 \%-62 \%\) mixture at \(90^{\circ} \mathrm{C}\). The vapor pressure of ethylbenzene is \(182 \mathrm{mmHg}\) and that of styrene is \(134 \mathrm{mmHg}\).

Adding \(1.00 \mathrm{g}\) of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) to \(80.00 \mathrm{g}\) cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12},\) lowers the freezing point of the cyclohexane from 6.5 to \(3.3^{\circ} \mathrm{C}\). (a) What is the value of \(K_{f}\) for cyclohexane? (b) Which is the better solvent for molar mass determinations by freezing- point depression, benzene or cyclohexane? Explain.

Calculate the mole fraction of the solute in the following aqueous solutions:(a) \(0.112 \mathrm{M} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) \((d=1.006 \mathrm{g} / \mathrm{mL})\) (b) \(3.20 \%\) ethanol,by volume \((d=0.993 \mathrm{g} / \mathrm{mL}\) pure \(\left.\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}, d=0.789 \mathrm{g} / \mathrm{mL}\right)\).
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