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Chapter 12: Problem 28

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 \(25^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified
117 grams of \( \mathrm{KNO}_{3} \) will crystallize out when the solution is cooled from \( 75^\circ \mathrm{C} \) to \( 25^\circ \mathrm{C} \).

Step by step solution

01

Determine Solubility at Both Temperatures

Firstly, identify the solubility of \( \mathrm{KNO}_{3} \) at both temperatures. From the problem, the solubility at \( 75^\circ \mathrm{C} \) is \( 155 \mathrm{g} \) of \( \mathrm{KNO}_{3} \) in \( 100 \mathrm{g} \) of water, and at \( 25^\circ \mathrm{C} \), it's \( 38.0 \mathrm{g} \) of \( \mathrm{KNO}_{3} \) in \( 100 \mathrm{g} \) of water. This represents how much \( \mathrm{KNO}_{3} \) can be dissolved in \( 100 \mathrm{g} \) of water at these temperatures.
02

Calculate the Mass of \( \mathrm{KNO}_{3} \) in the Initial Solution

Next, determine the original amount of \( \mathrm{KNO}_{3} \) in the given \( 100 \mathrm{g} \) solution at \( 75^\circ \mathrm{C} \). This is simply \( 155 \mathrm{g} \), representing the total mass of \( \mathrm{KNO}_{3} \) that the \( 100 \mathrm{g} \) of water can hold at \( 75^\circ \mathrm{C} \).
03

Calculate the Mass of \( \mathrm{KNO}_{3} \) that Remains Dissolved

Then, calculate how much \( \mathrm{KNO}_{3} \) will remain in solution when it's cooled to \( 25^\circ \mathrm{C} \). Given that \( 38.0 \mathrm{g} \) of \( \mathrm{KNO}_{3} \) can dissolve in \( 100 \mathrm{g} \) of water at \( 25^\circ \mathrm{C} \), this will be the amount of \( \mathrm{KNO}_{3} \) that stays dissolved when the solution is cooled to \( 25^\circ \mathrm{C} \).
04

Determine the Mass of \( \mathrm{KNO}_{3} \) that Crystallizes Out

Finally, determine the amount of \( \mathrm{KNO}_{3} \) that will crystallize out of the solution when it's cooled to \( 25^\circ \mathrm{C} \). This is the difference between the initial mass of \( \mathrm{KNO}_{3} \) at \( 75^\circ \mathrm{C} \) and the mass that remains dissolved at \( 25^\circ \mathrm{C} \). So the mass that crystallizes out is \( 155 \mathrm{g} - 38.0 \mathrm{g} = 117 \mathrm{g} \).

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Most popular questions from this chapter

Iodine \(\left(\mathrm{I}_{2}\right)\) is only sparingly soluble in water (left photo). Yet upon the addition of iodide ions (for example, from KI), iodine is converted to the triiodide ion, which readily dissolves (right photo): $$\mathrm{I}_{2}(s)+\mathrm{I}^{-}(a q) \rightleftharpoons \mathrm{I}_{3}^{-}(a q) $$ Describe the change in solubility of \(\mathrm{I}_{2}\) in terms of the change in intermolecular forces.

Concentrated hydrochloric acid is usually available at a concentration of 37.7 percent by mass. What is its molar concentration? (The density of the solution is \(1.19 \mathrm{~g} / \mathrm{mL} . ?\)

The vapor pressure of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) at \(20^{\circ} \mathrm{C}\) is \(44 \mathrm{mmHg},\) and the vapor pressure of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) at the same temperature is \(94 \mathrm{mmHg} . \mathrm{A}\) mixture of \(30.0 \mathrm{~g}\) of methanol and \(45.0 \mathrm{~g}\) of ethanol is prepared (and can be assumed to behave as an ideal solution). (a) Calculate the vapor pressure of methanol and ethanol above this solution at \(20^{\circ} \mathrm{C}\). (b) Calculate the mole fraction of methanol and ethanol in the vapor above this solution at \(20^{\circ} \mathrm{C}\). (c) Suggest a method for separating the two components of the solution.

Describe the fractional crystallization process and its application.

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