/*! 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 136 You may have seen the statement ... [FREE SOLUTION] | 91Ó°ÊÓ

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You may have seen the statement made that the liquid state is the stable state of water below \(100^{\circ} \mathrm{C}\) (but above \(0^{\circ} \mathrm{C}\) ), whereas the vapor state is the stable state above \(100^{\circ} \mathrm{C}\). Yet you also know that a pan of water set out on a table at \(20^{\circ} \mathrm{C}\) will probably evaporate completely in a few days, in which case, liquid water has changed to the vapor state. Explain what is happening here. What is wrong with the simple statement given at the beginning of this problem? Give a better statement.

Short Answer

Expert verified
Water can evaporate at temperatures below its boiling point due to surface molecules escaping, despite it being thermodynamically stable in liquid form. A better statement acknowledges this dynamic equilibrium.

Step by step solution

01

Understanding Evaporation below Boiling Point

Even though water vapor is energetically the more stable phase above 100°C, evaporation happens even below the boiling point due to molecules on the surface gaining enough energy to escape into the vapor phase. This shows that a liquid can evaporate at temperatures significantly lower than its boiling point.
02

Recognizing Dynamic Equilibrium

At any temperature within the liquid range (0°C to 100°C), there is a dynamic equilibrium between evaporation and condensation. In an open system, like an open pan, water molecules that evaporate can leave the system, disturbing this equilibrium and leading to complete evaporation over time.
03

Revising the Stability Statement

The initial statement ignores that evaporation from the liquid phase can occur below 100°C. An accurate statement would be that while liquid water is generally the thermodynamically stable phase below 100°C, water molecules can still transition to the vapor phase due to evaporation.

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Key Concepts

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

Evaporation
Evaporation is the process where molecules escape from a liquid into the vapor phase. This process doesn't require the liquid to reach its boiling point. Water, for example, can evaporate well below its boiling temperature of 100°C. The ability of molecules to evaporate depends on their energy.
Molecules at the surface tend to have more energy because they interact less with other molecules. When these high-energy molecules gain enough kinetic energy, they break free from the liquid to become vapor. This means:
  • Evaporation can happen at any temperature.
  • It's a surface phenomenon.
  • It involves energy transfer, influencing cooling.
Even at room temperature, you'll notice water in a pan will slowly disappear over several days. This is because even at 20°C, there are always some molecules with enough energy to evaporate.
Dynamic Equilibrium
Dynamic equilibrium in the context of liquids and gases is where the rate of evaporation of a liquid equals the rate of condensation of its vapor. This is only possible in a closed container where vapor can't escape.
If you have water in a sealed bottle, eventually, you'll see no overall change in the amount of liquid or vapor. Though at any moment, molecules continue to move between the liquid and gas phases, balancing out over time.
In open systems, like the pan of water mentioned earlier, evaporated molecules escape into the atmosphere. This breaks the equilibrium because:
  • Evaporated molecules don't return to the liquid.
  • Condensation can't balance out the lost molecules.
  • The liquid eventually evaporates completely.
This explains why liquids can vanish even in environments where they aren't heated to their boiling point.
Thermodynamic Stability
Thermodynamic stability refers to the state of a system where the free energy is at a minimum for the given conditions. For water, this means the state with the least energy between 0°C and 100°C is liquid.
Above 100°C, vapor has less free energy and is more stable. However, even below this temperature, individual molecules can still have enough energy to transition into vapor. So, although water is thermodynamically stable as a liquid under these conditions, it doesn't prevent localized evaporation.
A better way to understand this is:
  • At temperatures below boiling, although the liquid phase is stable, evaporation can still occur.
  • Stability doesn't mean no phase change. It means the larger portion remains as the lower-energy phase.
  • Evaporation involves localized energy states, which allow molecules to escape even when the container isn't at boiling point.
Thus, while most water stays liquid, evaporation happens continually, explaining the gradual disappearance of water from an open container.

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Most popular questions from this chapter

Nanotechnology, or technology utilizing \(1-100 \mathrm{nm}\) sized particles, has rapidly expanded in the past few decades, with potential applications ranging across far-reaching fields such as electronics, medicine, biomaterials, and consumer products, to name a few. One of the primary advantages of nanoparticles is the presence of large surface/mass ratios, resulting in enhanced surface activities compared to bulk materials. Use the density of silver \(\left(10.49 \mathrm{~g} / \mathrm{cm}^{3}\right)\) to determine the number of Ag atoms in a spherical 20.-nm silver particle. In the crystalline metallic environment, the measured radii of silver atoms has been measured to be \(144 \mathrm{pm}\). Use this to calculate the atomic packing fraction of a 20.-nm silver particle. In other words, calculate the ratio of the volume taken up by \(\mathrm{Ag}\) atoms to the volume of the entire nanoparticle. Based on the result of part (b), silver conforms to which type of cubic crystal lattice? A simple cubic \(\quad\) B body-centered cubic C face-centered cubic d. A cubic Ag ingot having a mass of 5.0 -g is processed to form a batch of 20.-nm Ag nanoparticles. Calculate the ratio of the surface area provided by the batch of nanoparticles to the surface area of the initial cube of \(\mathrm{Ag}\).

Arrange the following substances in order of increasing magnitude of the London forces: \(\mathrm{SiCl}_{4}, \mathrm{CCl}_{4}, \mathrm{GeCl}_{4}\).

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An element crystallizes with a simple cubic lattice with atoms at all the lattice points. If the radius of the atom is \(200 . \mathrm{pm}\), what is the volume of the unit cell? \(8.00 \times 10^{6} \mathrm{pm}^{3}\) \(6.40 \times 10^{7} \mathrm{pm}^{3}\) \(4.00 \times 10^{4} \mathrm{pm}^{3}\) \(1.60 \times 10^{5} \mathrm{pm}^{3}\) \(6.60 \times 10^{7} \mathrm{pm}^{3}\)

How many atoms are there in a body-centered cubic unit cell of an atomic crystal in which all atoms are at lattice points?

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