/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 92 A supersaturated solution of suc... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A supersaturated solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) 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. (b) After the excess sucrose has crystallized out, the system is now unstable and is not in equilibrium. (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.

Short Answer

Expert verified
(a) True, (b) False, (c) True.

Step by step solution

01

Understand Supersaturation and Crystallization

A supersaturated solution is one that contains more solute than it can theoretically hold at a given temperature. When it cools, the excess solute tends to crystallize out. After crystallization, the solution returns to its saturation limit, meaning it is now saturated but no longer supersaturated.
02

Evaluate Statement (a)

After the excess sucrose crystallizes out, the remaining solution reaches a point where it has an equilibrium amount of sucrose for the given temperature, becoming saturated. Thus, statement (a) is true.
03

Evaluate Statement (b)

Once the excess sucrose has crystallized out and the solution is saturated, the system is in a stable condition and at equilibrium between the dissolved sucrose and the solid form. Therefore, statement (b) is false, as the system is stable and in equilibrium.
04

Evaluate Statement (c)

At equilibrium, the dynamic balance between sucrose molecules moving from the solid to the solution and vice versa is maintained, meaning the rate of molecules dissolving equals the rate of molecules crystallizing. Therefore, statement (c) is true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Crystallization Process
Crystallization is a fascinating process where a solute turns from a liquid solution to a solid form. Imagine a crowded dance floor, which is our supersaturated solution, packed with more dancers (solute particles) than it can reasonably accommodate.
You might have noticed that when you dissolve a lot of sugar in hot water and let it cool, crystals begin to form. This happens because the solution can no longer hold the excess sugar as it gets cooler. Crystallization occurs because the solution was initially over-saturated, like how once the dance floor gets too crowded, some people might have to step off.
Once the crystallization process starts, the solute molecules, such as sucrose, come together to form a solid, and slowly drift out of the solution forming a regular pattern. With time, the excess solute that was dissolved beyond the saturation point precipitates out as crystals.
Saturation and Equilibrium
In chemistry, saturation refers to the maximum amount of solute that a solvent can dissolve at a given temperature. Once this point is reached, the solution is said to be saturated. Think of it like a sponge that has soaked up all the water it can and cannot hold anymore.
At this stage, equilibrium is achieved. Saturation and equilibrium go hand-in-hand. Equilibrium in a saturated solution is a dynamic state. Even though it may seem like nothing is happening, at a microscopic level, there's a constant exchange of solute molecules between the dissolved state and the crystallized state.
  • Solute molecules continuously leave the solvent to join the crystal.
  • At the same time, molecules from the crystal dissolve back into the solvent.
This exchange maintains the equilibrium, with the concentration of dissolved solute remaining constant under steady conditions.
Chemical Equilibrium
Chemical equilibrium is when the rate of the forward reaction equals the rate of the backward reaction. In the context of our crystallization example, it means the rate at which sucrose dissolves back into the solution is equal to the rate at which sucrose crystallizes out.
This balance ensures the system does not change over time. It's a bit like a two-way street where cars (solute molecules) are moving in both directions at the same rate.
Importantly, this doesn't mean that all movement stops. Instead, it is a dynamic process where molecules are continuously moving, yet the overall concentration remains unchanged.
  • Equilibrium ensures the solution remains stable.
  • Even if crystallization initially seems to make things unbalanced, equilibrium is quickly restored.
This dynamic stability is a hallmark of chemical equilibrium in solutions.
Solubility and Temperature
Solubility tells us how much solute can dissolve in a solvent at a specific temperature. Typically, higher temperatures increase solubility because molecules move faster and can hold more solute, similar to how warm air can hold more moisture.
However, when you cool a hot saturated solution, solubility decreases, leading to crystallization as we've seen in our sucrose example. It's like cooling a mug of tea whereby the excess sugar that couldn't dissolve at the cooler temperature drops out of the solution.
  • The solubility of a substance is crucial for determining how much solute can be dissolved.
  • Temperature changes can quickly alter the solubility and thus the state of the solution.
Understanding these concepts helps explain why a supersaturated solution can form crystals when cooled, as the solution can no longer sustain the same concentration of solute.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) Would you expect stearic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{COOH},\) to be more soluble in water or in carbon tetrachloride? (b) Which would you expect to be more soluble in water, cyclohexane or dioxane?

At ordinary body temperature \(\left(37^{\circ} \mathrm{C}\right),\) the solubility of \(\mathrm{N}_{2}\) in water at ordinary atmospheric pressure is \(0.015 \mathrm{~g} / \mathrm{L}\). Air is approximately \(78 \mathrm{~mol} \% \mathrm{~N}_{2} .\) (a) Calculate the number of moles of \(\mathrm{N}_{2}\) dissolved per liter of blood, assuming blood is a simple aqueous solution. (b) At a depth of \(30.5 \mathrm{~m}\) in water, the external pressure is \(405 \mathrm{kPa}\). What is the solubility of \(\mathrm{N}_{2}\) from air in blood at this pressure? (c) If a scuba diver suddenly surfaces from this depth, how many milliliters of \(\mathrm{N}_{2}\) gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood?

The vapor pressure of pure water at \(70^{\circ} \mathrm{C}\) is \(31.2 \mathrm{kPa}\). The vapor pressure of water over a solution at \(70^{\circ} \mathrm{C}\) containing equal numbers of moles of water and glycerol \(\left(\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3}\right.\), a nonvolatile solute) is \(13.3 \mathrm{kPa}\). Is the solution ideal according to Raoult's law?

(a) What is the mass percentage of iodine in a solution containing \(0.035 \mathrm{~mol} \mathrm{I}_{2}\) in \(125 \mathrm{~g}\) of \(\mathrm{CCl}_{4} ?\) (b) Seawater contains \(0.0079 \mathrm{~g}\) of \(\mathrm{Sr}^{2+}\) per kilogram of water. What is the concentration of \(\mathrm{Sr}^{2+}\) in \(\mathrm{ppm}\) ?

Proteins can be precipitated out of aqueous solution by the addition of an electrolyte; this process is called "salting out" the protein. (a) Do you think that all proteins would be precipitated out to the same extent by the same concentration of the same electrolyte? (b) If a protein has been salted out, are the protein-protein interactions stronger or weaker than they were before the electrolyte was added? (c) A friend of yours who is taking a biochemistry class says that salting out works because the waters of hydration that surround the protein prefer to surround the electrolyte as the electrolyte is added; therefore, the protein's hydration shell is stripped away, leading to protein precipitation. Another friend of yours in the same biochemistry class says that salting out works because the incoming ions adsorb tightly to the protein, making ion pairs on the protein surface, which end up giving the protein a zero net charge in water and therefore leading to precipitation. Discuss these two hypotheses. What kind of measurements would you need to make to distinguish between these two hypotheses?

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.