Problem 33
The solubility of \(\mathrm{KNO}_{3}\) is \(155 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water at \(75^{\circ} \mathrm{C}\) and \(38.0 \mathrm{~g}\) at \(25^{\circ} \mathrm{C}\). What mass (in grams) of \(\mathrm{KNO}_{3}\) will crystallize out of solution if exactly \(100 \mathrm{~g}\) of its saturated solution at \(75^{\circ} \mathrm{C}\) is cooled to \(25^{\circ} \mathrm{C} ?\)
Problem 34
A 50-g sample of impure \(\mathrm{KClO}_{3}\) (solubility \(=7.1 \mathrm{~g}\) per \(100 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\) at \(\left.20^{\circ} \mathrm{C}\right)\) is contaminated with 10 percent of \(\mathrm{KCl}\) (solubility \(=25.5 \mathrm{~g}\) per \(100 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) at \(\left.20^{\circ} \mathrm{C}\right)\) Calculate the minimum quantity of \(20^{\circ} \mathrm{C}\) water needed to dissolve all the \(\mathrm{KCl}\) from the sample. How much \(\mathrm{KClO}_{3}\) will be left after this treatment? (Assume that the solubilities are unaffected by the presence of the other compound.)
Problem 35
The solubility of \(\mathrm{CO}_{2}\) in water at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) is \(0.034 \mathrm{~mol} / \mathrm{L}\). What is its solubility under atmospheric conditions? (The partial pressure of \(\mathrm{CO}_{2}\) in air is 0.0003 atm.) Assume that \(\mathrm{CO}_{2}\) obeys Henry's law.
Problem 36
The solubility of \(\mathrm{N}_{2}\) in blood at \(37^{\circ} \mathrm{C}\) and at a partial pressure of 0.80 atm is \(5.6 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\). A deep-sea diver breathes compressed air with the partial pressure of \(\mathrm{N}_{2}\) equal to \(4.0 \mathrm{~atm}\). Assume that the total volume of blood in the body is \(5.0 \mathrm{~L}\). Calculate the amount of \(\mathrm{N}_{2}\) gas released (in liters at \(37^{\circ} \mathrm{C}\) and \(\left.1 \mathrm{~atm}\right)\) when the diver returns to the surface of the water, where the partial pressure of \(\mathrm{N}_{2}\) is \(0.80 \mathrm{~atm}\).
Problem 37
A miner working \(260 \mathrm{~m}\) below sea level opened a carbonated soft drink during a lunch break. To his surprise, the soft drink tasted rather "flat." Shortly afterward, the miner took an elevator to the surface. During the trip up, he could not stop belching. Why?
Problem 38
A beaker of water is initially saturated with dissolved air. Explain what happens when He gas at 1 atm is bubbled through the solution for a long time.
Problem 39
A student carried out the following experiment to measure the pressure of carbon dioxide in the space above the carbonated soft drink in a bottle. First, she weighed the bottle \((853.5 \mathrm{~g})\). Next, she carefully removed the cap to let the \(\mathrm{CO}_{2}\) gas escape. She then reweighed the bottle with the cap \((851.3 \mathrm{~g})\). Finally, she measured the volume of the soft drink (452.4 mL). Given that the Henry's law constant for \(\mathrm{CO}_{2}\) in water at \(25^{\circ} \mathrm{C}\) is \(3.4 \times 10^{-2} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{atm},\) calculate the pressure of \(\mathrm{CO}_{2}\) over the soft drink in the bottle before it was opened. Explain why this pressure is only an estimate of the true value.
Problem 42
What are colligative properties? What is the meaning of the word colligative in this context?
Problem 43
Give two examples of (a) a volatile liquid and (b) a nonvolatile liquid.
Problem 44
Write the equation representing Raoult's law, and express it in words.
