11.4 Colligative properties  (Page 4/30)

The extent to which the vapor pressure of a solvent is lowered and the boiling point is elevated depends on the total number of solute particles present in a given amount of solvent, not on the mass or size or chemical identities of the particles. A 1 m aqueous solution of sucrose (342 g/mol) and a 1 m aqueous solution of ethylene glycol (62 g/mol) will exhibit the same boiling point because each solution has one mole of solute particles (molecules) per kilogram of solvent.

Calculating the boiling point of a solution

What is the boiling point of a 0.33 m solution of a nonvolatile solute in benzene?

Solution

Use the equation relating boiling point elevation to solute molality to solve this problem in two steps.

1. Calculate the change in boiling point.
   
   $\text{Δ}{T}_{\text{b}}=K_{\text{b}}m=2.53\text{°}\text{C}{m}^{\mathrm{-1}}\times 0.33m=0.83\text{°}\text{C}$
2. Add the boiling point elevation to the pure solvent’s boiling point.
   
   $\text{Boiling temperature}=80.1\text{°}\text{C}+0.83\text{°}\text{C}=80.9\text{°}\text{C}$

Check your learning

What is the boiling point of the antifreeze described in [link] ?

Answer:

109.2 °C

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The boiling point of an iodine solution

Find the boiling point of a solution of 92.1 g of iodine, I ₂ , in 800.0 g of chloroform, CHCl ₃ , assuming that the iodine is nonvolatile and that the solution is ideal.

Solution

We can solve this problem using four steps.

1. Convert from grams to moles of I ₂ using the molar mass of I ₂ in the unit conversion factor.
   Result: 0.363 mol
2. Determine the molality of the solution from the number of moles of solute and the mass of solvent, in kilograms.
   Result: 0.454 m
3. Use the direct proportionality between the change in boiling point and molal concentration to determine how much the boiling point changes.
   Result: 1.65 °C
4. Determine the new boiling point from the boiling point of the pure solvent and the change.
   Result: 62.91 °C
   Check each result as a self-assessment.

Check your learning

What is the boiling point of a solution of 1.0 g of glycerin, C ₃ H ₅ (OH) ₃ , in 47.8 g of water? Assume an ideal solution.

Answer:

100.12 °C

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Distillation of solutions

Distillation is a technique for separating the components of mixtures that is widely applied in both in the laboratory and in industrial settings. It is used to refine petroleum, to isolate fermentation products, and to purify water. This separation technique involves the controlled heating of a sample mixture to selectively vaporize, condense, and collect one or more components of interest. A typical apparatus for laboratory-scale distillations is shown in [link] .

Oil refineries use large-scale fractional distillation to separate the components of crude oil. The crude oil is heated to high temperatures at the base of a tall fractionating column , vaporizing many of the components that rise within the column. As vaporized components reach adequately cool zones during their ascent, they condense and are collected. The collected liquids are simpler mixtures of hydrocarbons and other petroleum compounds that are of appropriate composition for various applications (e.g., diesel fuel, kerosene, gasoline), as depicted in [link] .