Potassium nitrate has a lattice energy of -163.8 kcal/mol and a heat of hydration of -155.5 kcal/mol. How much potassium nitrate has to dissolve in water to absorb 1.00⨉102 kJ of heat?
Ch.14 - Solutions

Chapter 14, Problem 47
A KNO3 solution containing 35 g of KNO3 per 100.0 g of water is cooled from 40 °C to 0 °C. What happens during cooling? (Use Figure 14.11.)
Verified step by step guidance1
Identify the solubility of KNO3 at 40 °C using Figure 14.11. This will tell you how much KNO3 can dissolve in 100 g of water at this temperature.
Identify the solubility of KNO3 at 0 °C using Figure 14.11. This will tell you how much KNO3 can dissolve in 100 g of water at this lower temperature.
Compare the initial concentration of KNO3 (35 g per 100 g of water) with the solubility at 40 °C to determine if the solution is saturated, unsaturated, or supersaturated at the starting temperature.
Compare the solubility of KNO3 at 0 °C with the initial concentration to determine if the solution will remain saturated, become unsaturated, or if excess KNO3 will precipitate out as the solution is cooled.
Conclude what happens during cooling: if the solution was initially saturated or supersaturated, and the solubility decreases, KNO3 will precipitate out of the solution as it cools to 0 °C.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Solubility
Solubility refers to the maximum amount of a solute that can dissolve in a solvent at a given temperature and pressure. In the case of KNO3, its solubility decreases as the temperature drops, meaning that less KNO3 can remain dissolved in water at lower temperatures. Understanding solubility is crucial for predicting whether a solution will remain saturated or begin to precipitate solute as it cools.
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Saturation Point
The saturation point is the stage at which a solution can no longer dissolve additional solute at a specific temperature. When a solution is cooled, it may reach a point where the amount of dissolved KNO3 exceeds its solubility limit, leading to the formation of solid KNO3 crystals. Recognizing the saturation point helps in understanding the behavior of solutes in solutions as conditions change.
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Crystallization
Crystallization is the process by which dissolved solute comes out of solution and forms solid crystals. As the KNO3 solution cools, the decrease in temperature can cause the dissolved KNO3 to crystallize out of the solution once it surpasses the saturation point. This process is essential in many chemical applications, including purification and the formation of solid compounds from solutions.
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Scuba divers breathing air at increased pressure can suffer from oxygen toxicity—too much oxygen in their bloodstream— when the partial pressure of oxygen exceeds about 1.4 atm. What happens to the amount of oxygen in a diver's bloodstream when he or she breathes oxygen at elevated pressures? How can this be reversed?
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Textbook Question
A solution contains 35 g of NaCl per 100.0 g of water at 25°C. Is the solution unsaturated, saturated, or supersaturated? (Use Figure 14.11.)
Textbook Question
A KNO3 solution containing 35 g of KNO3 per 100.0 g of water is cooled from 40°C to 0°C. What happens during cooling? (Use Figure 14.11.)
