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Chapter 13: Problem 71

List the following aqueous solutions in order of increasing boiling point: \(0.080 \mathrm{~m} \mathrm{KBr}, 0.130 \mathrm{~m}\) urea \(\left(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\right)\), $0.080 \mathrm{~m} \mathrm{Mg}\left(\mathrm{NO}_{2}\right)_{2}\( \)0.030 \mathrm{~m}$ phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\)

Short Answer

Expert verified
The aqueous solutions listed in order of increasing boiling point are: Phenol, Urea, KBr, and Mg(NO_2)_2.

Step by step solution

01

Identify the van't Hoff factors for all solutes

Determine the number of ions or particles that each solute dissociates into when dissolved in water: 1. KBr: This is an ionic compound that dissociates into K+ and Br- ions. The van't Hoff factor, i, for KBr is 2. 2. Urea (CO(NH_2)_2): This is a covalent compound that does not dissociate in water. The van't Hoff factor, i, for urea is 1. 3. Mg(NO_2)_2: This ionic compound dissociates into one Mg2+ ion and two NO_2- ions. The van't Hoff factor, i, for this compound is 3. 4. Phenol (C_6H_5OH): This is a covalent compound that does not dissociate in water. The van't Hoff factor, i, for phenol is 1.
02

Calculate the change in boiling point for each solution

Using the boiling point elevation formula, we can determine the change in boiling points for each solution: \[\Delta T_b = iK_bm\] Since we only need to arrange the solutions in order of boiling points and the boiling-point elevation constant, \(K_b\), is the same for all solutes in water, we can compare the product of \(i\) and \(m\) for each solution to determine their order. 1. KBr solution: \((i \times m) = 2 \times 0.080 = 0.16\) 2. Urea solution: \((i \times m) = 1 \times 0.130 = 0.13\) 3. Mg(NO_2)_2 solution: \((i \times m) = 3 \times 0.080 = 0.24\) 4. Phenol solution: \((i \times m) = 1 \times 0.030 = 0.03\)
03

Arrange the solutions in order of increasing boiling point

Now that we have the product of van't Hoff factor and molality for each solution, we can list them in order of increasing boiling points: 1. Phenol solution (\(i \times m = 0.03\)) 2. Urea solution (\(i \times m = 0.13\)) 3. KBr solution (\(i \times m = 0.16\)) 4. Mg(NO_2)_2 solution (\(i \times m = 0.24\)) In conclusion, the aqueous solutions can be listed in order of increasing boiling points as follows: Phenol, Urea, KBr, and Mg(NO_2)_2.

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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 \(\left(\mathrm{NaNO}_{3}\right)\).

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A sulfuric acid solution containing \(697.6 \mathrm{~g}\) of $\mathrm{H}_{2} \mathrm{SO}_{4}\( per liter of solution has a density of \)1.395 \mathrm{~g} / \mathrm{cm}^{3} .$ Calculate (a) the mass percentage, \((\mathbf{b})\) the mole fraction, (c) the molality, \((\mathbf{d})\) the molarity of $\mathrm{H}_{2} \mathrm{SO}_{4}$ in this solution.

You take a sample of water that is at room temperature and in contact with air and put it under a vacuum. Right away, you see bubbles leave the water, but after a little while, the bubbles stop. As you keep applying the vacuum, more bubbles appear. A friend tells you that the first bubbles were water vapor, and the low pressure had reduced the boiling point of water, causing the water to boil. Another friend tells you that the first bubbles were gas molecules from the air (oxygen, nitrogen, and so forth) that were dissolved in the water. Which friend is mostly likely to be correct? What, then, is responsible for the second batch of bubbles? [Section 13.4]
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