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Chapter 13: Problem 57

A benzene-toluene solution with \(x_{\text {benz }}=0.300\) has a normal boiling point of \(98.6^{\circ} \mathrm{C}\). The vapor pressure of pure toluene at \(98.6^{\circ} \mathrm{C}\) is \(533 \mathrm{mm} \mathrm{Hg}\). What must be the vapor pressure of pure benzene at \(98.6^{\circ} \mathrm{C} ?\) (Assume ideal solution behavior.)

Short Answer

Expert verified
The vapor pressure of pure benzene at \(98.6^{\circ} \mathrm{C}\) can be calculated using Raoult's law and the given information about the benzene-toluene solution. This involves four steps: understanding Raoult's law, applying Raoult's law to the benzene-toluene solution, calculating the mole fraction of toluene, and substituting the known variables into the equation to solve for \(P_{\text{benzene}}^{0}\).

Step by step solution

01

Understand Raoult's Law

Raoults's law states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture. It can be represented as:\(P_i = x_i*P_{i}^{0}\) where \(P_i\) is the partial pressure of component i in the solution, \(x_i\) is the mole fraction of component i in the solution and \(P_{i}^{0}\) is the vapor pressure of pure component i.
02

Apply Raoult's Law for Benzene and Toluene

In the case of a benzene-toluene solution, the total pressure is equal to the sum of the partial pressures of benzene and toluene, i.e.\(P_{\text{total}} = P_{\text{benzene}} + P_{\text{toluene}}\) which translates to \(P_{\text{total}} = x_{\text{benzene}}*P_{\text{benzene}}^{0} + x_{\text{toluene}}*P_{\text{toluene}}^{0}\)
03

Calculate the Mole Fraction of Toluene

The mole fraction of toluene can be calculated by subtracting the mole fraction of benzene from 1. In this case, \(x_{\text{toluene}} = 1 - x_{\text{benzene}}= 1 - 0.300 = 0.700\).
04

Substitute Known Variables and Solve for \(P_{\text{benzene}}^{0}\)

The next step is to substitute the known variables into the equation obtained in step 2 and solve for \(P_{\text{benzene}}^{0}\):\n\(P_{\text{total}} - x_{\text{toluene}}*P_{\text{toluene}}^{0} = x_{\text{benzene}}*P_{\text{benzene}}^{0}\)\nAfter rearranging, the equation becomes\n\(P_{\text{benzene}}^{0} = \frac{P_{\text{total}} - x_{\text{toluene}}*P_{\text{toluene}}^{0}}{x_{\text{benzene}}}\)\nOn substituting the known values, \(P_{\text{benzene}}^{0}\) can be calculated.

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Most popular questions from this chapter

At \(25^{\circ} \mathrm{C}\) and under an \(\mathrm{O}_{2}(\mathrm{g})\) pressure of \(1 \mathrm{atm},\) the solubility of \(\mathrm{O}_{2}(\mathrm{g})\) in water is \(28.31 \mathrm{mL} / 1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) At \(25^{\circ} \mathrm{C}\) and under an \(\mathrm{N}_{2}(\mathrm{g})\) pressure of \(1 \mathrm{atm},\) the solubility of \(\mathrm{N}_{2}(\mathrm{g})\) in water is \(14.34 \mathrm{mL} / 1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) The composition of the atmosphere is \(78.08 \% \mathrm{N}_{2}\) and \(20.95 \% \mathrm{O}_{2},\) by volume. What is the composition of air dissolved in water expressed as volume percents of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2} ?\)

Which of the following ions has the greater charge density? (a) \(\mathrm{Na}^{+} ;\) (b) \(\mathrm{F}^{-} ;\) (c) \(\mathrm{K}^{+} ;\) (d) \(\mathrm{Cl}^{-}\).

Explain the important distinctions between each pair of terms: (a) molality and molarity; (b) ideal and nonideal solution; (c) unsaturated and supersaturated solution; (d) fractional crystallization and fractional distillation; (e) osmosis and reverse osmosis.

What is the molarity of \(\mathrm{CO}_{2}\) in a liter of ocean water at \(25^{\circ} \mathrm{C}\) that contains approximately \(280 \mathrm{ppm}\) of \(\mathrm{CO}_{2} ?\) The density of ocean water is \(1027 \mathrm{kg} / \mathrm{m}^{3}\).

Every year, oral rehydration therapy (ORT)-the feeding of an electrolyte solution-saves the lives of countless children worldwide who become severely dehydrated as a result of diarrhea. One requirement of the solution used is that it be isotonic with human blood.(a) One definition of an isotonic solution given in the text is that it have the same osmotic pressure as \(0.92 \% \mathrm{NaCl}(\mathrm{aq})\) (mass/volume). Another definition is that the solution have a freezing point of \(-0.52^{\circ} \mathrm{C}\) Show that these two definitions are in reasonably close agreement given that we are using solution concentrations rather than activities.(b) Use the freezing-point definition from part (a) to show that an ORT solution containing \(3.5 \mathrm{g} \mathrm{NaCl}\) \(1.5 \mathrm{g} \mathrm{KCl}, 2.9 \mathrm{g} \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\) (sodium citrate), and \(20.0 \mathrm{g} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (glucose) per liter meets the requirement of being isotonic. [Hint: Which of the solutes are nonelectrolytes, and which are strong electrolytes?]
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