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Ch.13 - Properties of Solutions
All textbooksBrown 14th EditionCh.13 - Properties of SolutionsProblem 92
Chapter 13, Problem 92

A supersaturated solution of sucrose (C12H22O11) is made by dissolving sucrose in hot water and slowly letting the solution cool to room temperature. After a long time, the excess sucrose crystallizes out of the solution. Indicate whether each of the following statements is true or false: (a) After the excess sucrose has crystallized out, the remaining solution is saturated. (c) After the excess sucrose has crystallized out, the rate of sucrose molecules leaving the surface of the crystals to be hydrated by water is equal to the rate of sucrose molecules in water attaching to the surface of the crystals.

Verified step by step guidance
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Step 1: Understand the concept of a supersaturated solution. A supersaturated solution contains more solute than can be dissolved at the current temperature. It is achieved by dissolving the solute at a higher temperature and then cooling the solution slowly.
Step 2: Consider statement (a). After the excess sucrose has crystallized out, the remaining solution is saturated. A saturated solution is one where the maximum amount of solute has been dissolved at a given temperature. When excess solute crystallizes out, the solution reaches saturation.
Step 3: Evaluate statement (c). After the excess sucrose has crystallized out, the rate of sucrose molecules leaving the surface of the crystals to be hydrated by water is equal to the rate of sucrose molecules in water attaching to the surface of the crystals. This describes a dynamic equilibrium where the processes of dissolution and crystallization occur at equal rates.
Step 4: Relate the concept of dynamic equilibrium to the crystallization process. In a saturated solution at equilibrium, the rate of dissolution of solute is equal to the rate of crystallization, meaning the concentration of dissolved solute remains constant.
Step 5: Conclude the analysis by confirming that both statements (a) and (c) are true based on the principles of saturation and dynamic equilibrium in solutions.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Supersaturation

A supersaturated solution contains more solute than can typically be dissolved at a given temperature. This occurs when a solute is dissolved in hot solvent and then allowed to cool slowly, preventing immediate crystallization. When the solution is disturbed or allowed to sit, excess solute may crystallize out, leading to a saturated solution where the solute concentration is at its maximum for that temperature.
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Saturation Point

The saturation point is the maximum concentration of solute that can dissolve in a solvent at a specific temperature and pressure. When a solution reaches this point, any additional solute will not dissolve and will instead precipitate out. In the context of the question, once excess sucrose crystallizes out, the remaining solution reaches this saturation point.
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Dynamic Equilibrium

Dynamic equilibrium in a solution occurs when the rate of solute molecules leaving the solid phase (crystals) equals the rate of solute molecules entering the solid phase from the solution. This balance means that the concentration of solute remains constant over time. In the case of the sucrose solution, once crystallization has occurred, the system may reach dynamic equilibrium where the rates of hydration and attachment of sucrose molecules are equal.
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Related Practice
Textbook Question

The 'free-base' form of cocaine (C17H21NO4) and its protonated hydrochloride form (C17H22ClNO4) are shown below; the free-base form can be converted to the hydrochloride form with one equivalent of HCl. For clarity, not all the carbon and hydrogen atoms are shown; each vertex represents a carbon atom with the appropriate number of hydrogen atoms so that each carbon makes four bonds to other atoms

(a) One of these forms of cocaine is relatively water-soluble: which form, the free base or the hydrochloride?

Textbook Question

The 'free-base' form of cocaine (C17H21NO4) and its protonated hydrochloride form (C17H21NO4) are shown below; the free-base form can be converted to the hydrochloride form with one equivalent of HCl. For clarity, not all the carbon and hydrogen atoms are shown; each vertex represents a carbon atom with the appropriate number of hydrogen atoms so that each carbon makes four bonds to other atoms (e) How many mL of a concentrated 18.0 M HCl aqueous solution would it take to convert 1.00 kilograms (a 'kilo') of the free-base form of cocaine into its hydrochloride form?

Textbook Question

A supersaturated solution of sucrose (C12H22O11) is made by dissolving sucrose in hot water and slowly letting the solution cool to room temperature. After a long time, the excess sucrose crystallizes out of the solution. Indicate whether each of the following statements is true or false: (b) After the excess sucrose has crystallized out, the system is now unstable and is not in equilibrium.

Textbook Question

Most fish need at least 4 ppm dissolved O2 in water for survival. (a) What is this concentration in mol/L?

Textbook Question

Most fish need at least 4 ppm dissolved O2 in water for survival. (b) What partial pressure of O2 above water is needed to obtain 4 ppm O2 in water at 10 °C? (The Henry's law constant for O2 at this temperature is 1.71⨉10-3 mol/L-atm.)