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Chapter 13: Problem 21

Two nonpolar organic liquids, benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\( and toluene \)\left(\mathrm{C}_{7} \mathrm{H}_{8}\right),\( are mixed. (a) Do you expect \)\Delta H_{\text {soln }}$ to be a large positive number, a large negative number, or close to zero? Explain. (b) Benzene and toluene are miscible with each other in all proportions. In making a solution of them, is the entropy of the system increased, decreased, or close to zero, compared to the separate pure liquids?

Short Answer

Expert verified
(a) The enthalpy of solution, \(\Delta H_{\text {soln }}\), is expected to be close to zero because the interactions between benzene and toluene molecules are similar to their interactions within their respective pure liquids, and the solution process does not require a large transfer of energy. (b) Mixing benzene and toluene increases the entropy of the system, compared to the separate pure liquids, due to the increase in molecular disorder when the two substances are mixed.

Step by step solution

01

Analyze \(\Delta H_{\text {soln }}\)

We need to analyze \(\Delta H_{\text {soln }}\) value when mixing two nonpolar organic liquids, benzene and toluene. In a solution process, two fundamental intermolecular interactions come into play: (1) separating solute and solvent molecules in the initial state (change in positive enthalpy), and (2) mixing solute and solvent molecules to form the solution (change in negative enthalpy). Since benzene and toluene are both nonpolar and have similar London dispersion forces, the energetic interactions between benzene and toluene molecules when mixed should be similar to the interactions between the benzene and benzene molecules in pure benzene or the toluene and toluene molecules in pure toluene.
02

Answer for (a)

Because the interactions between benzene and toluene molecules are similar to their interactions within their respective pure liquids, we can expect the enthalpy of solution, \(\Delta H_{\text {soln }}\), to be close to zero. There is no significant energy difference between the interactions of benzene-benzene and toluene -toluene. Therefore, the solution process does not require a large transfer of energy. So \(\Delta H_{\text {soln }}\approx 0\).
03

Analyze entropy change

When we mix benzene and toluene, we are increasing the number of possible ways the molecules can rearrange and distribute themselves in the solution. The resultant molecular mixture is more disordered than the separate pure liquids. Therefore, mixing benzene and toluene will increase the entropy of the system.
04

Answer for (b)

Benzene and toluene are miscible with each other in all proportions. As a result, making a solution of them will increase the entropy of the system, compared to the separate pure liquids. This increase in entropy of the system stems from the increase in molecular disorder when mixing the two substances.

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Most popular questions from this chapter

Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing \(0.150 \mathrm{~g}\) of this enzyme in \(210 \mathrm{~mL}\) of solution has an osmotic pressure of \(0.127 \mathrm{kPa}\) at \(25^{\circ} \mathrm{C}\). What is the molar mass of lysozyme?

Arrange the following aqueous solutions, each \(10 \%\) by mass in solute, in order of increasing boiling point: glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right),\( sucrose \)\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),$ sodium nitrate \(\left(\mathrm{NaNO}_{3}\right)\).

Ascorbic acid (vitamin C, $\left.\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\( is a water-soluble vitamin. A solution containing \)80.5 \mathrm{~g}\( of ascorbic acid dissolved in \)210 \mathrm{~g}$ of water has a density of \(1.22 \mathrm{~g} / \mathrm{mL}\) at \(55^{\circ} \mathrm{C}\). Calculate (a) the mass percentage, (b) the mole fraction, \((\mathbf{c})\) the molality, \((\mathbf{d})\) the molarity of ascorbic acid in this solution.

An ionic compound has a very negative \(\Delta H_{\text {soln }}\) in water. (a) Would you expect it to be very soluble or nearly insoluble in water? (b) Which term would you expect to be the largest negative number: $\Delta H_{\text {solvent }}, \Delta H_{\text {solute }}\(, or \)\Delta H_{\text {mix }} ?$

An "emulsifying agent" is a compound that helps stabilize a hydrophobic colloid in a hydrophilic solvent (or a hydrophilic colloid in a hydrophobic solvent). Which of the following choices is the best emulsifying agent? (a) \(\mathrm{CH}_{3} \mathrm{COOH},\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH},\) (c) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11}\) COOH, (d) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11} \mathrm{COONa}\).
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