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Chapter 13: Problem 4

Which two statements about gas mixtures are true? (a) Gases always mix with other gases because the gas particles are too far apart to feel significant intermolecular attractions or repulsions. (b) Just like water and oil don't mix in the liquid phase, two gases can be immiscible and not mix in the gas phase. (c) If you cool a gaseous mixture, you will liquefy all the gases at the same temperature. (d) Gases mix in all proportions in part because the entropy of the system increases upon doing so.

Short Answer

Expert verified
Statements (a) and (d) are true.

Step by step solution

01

Evaluate Statement (a)

Statement (a) claims that gases always mix because gas particles are far apart, minimizing intermolecular attractions or repulsions. Since gases are indeed typically very far apart, making intermolecular forces negligible, this encourages mixing. Thus, statement (a) is true.
02

Evaluate Statement (b)

Statement (b) suggests that like water and oil, two gases can be immiscible and not mix. In reality, gases generally mix in any proportion due to their nature and the lack of significant intermolecular forces. Therefore, statement (b) is false.
03

Evaluate Statement (c)

Statement (c) claims that cooling a gas mixture results in all gases liquefying at the same temperature. This is not true since different gases have unique boiling points and thus liquefy at different temperatures. Hence, statement (c) is false.
04

Evaluate Statement (d)

Statement (d) asserts that gases mix in all proportions because the entropy of the system increases. This aligns with basic thermodynamic principles, whereby mixing gases increases disorder or entropy. Therefore, statement (d) is true.

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Key Concepts

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

Intermolecular Forces in Gas Mixtures
Intermolecular forces are the attractions or repulsions between particles, and in the context of gas mixtures, these forces are rather minimal. Since gases have particles that are typically spread far apart, they don't interact with each other significantly. This minimal interaction allows gases to mix freely with other gases, unlike liquids or solids, which may have more pronounced intermolecular forces affecting their miscibility.

The lack of significant intermolecular forces means that gases do not "choose" which other gases to mix with. Unlike liquids such as oil and water, gases do not become "layered" or remain separate because their particles do not have strong attractions or repulsions. Gas mixtures form easily and tend to be uniform because the particles just don't exert enough force on each other to stay apart.
Understanding Entropy in Gas Mixtures
Entropy is a measure of disorder or randomness in a system. In the case of gas mixtures, entropy plays a major role. When two gases are mixed, there is an increase in the overall disorder of the system, effectively increasing the entropy.

This increase in entropy is a driving factor for the mixing of gases. As gases mix, the particles become distributed more randomly, and nature tends to favor states with higher entropy or disorder. This is one reason why, at a fundamental level, gases tend to mix in all proportions rather than remaining separate.
  • Higher entropy makes a system more stable.
  • Mixing increases randomness, benefiting the natural path of physical transformations.
The Role of Thermodynamics in Gas Mixing
Thermodynamics is the study of energy transformations, and it closely ties into how gases behave and mix. A key principle in thermodynamics relevant to gas mixtures is the tendency of systems to move toward increased entropy and potential energy minimization.

Thermodynamics helps explain why gases mix. When gases are mixed, the entropy of the system increases, as discussed before. Thermodynamically, this is a favorable change because systems naturally progress toward higher entropy states. Additionally, mixing gases does not require energy input since the process is spontaneous and driven by entropy.
  • Gas mixtures tend to follow thermodynamic stability.
  • Increased entropy upon mixing aligns with thermodynamic principles.
  • Energy calculations in thermodynamics show that gas mixing is energetically favorable.

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Most popular questions from this chapter

The following table presents the solubilities of several gases in water at \(25^{\circ} \mathrm{C}\) under a total pressure of gas and water vapor of \(101.3 \mathrm{kPa}\). (a) What volume of \(\mathrm{CH}_{4}(g)\) under standard conditions of temperature and pressure is contained in \(4.0 \mathrm{~L}\) of a saturated solution at \(25^{\circ} \mathrm{C} ?\) (b) The solubilities (in water) of the hydrocarbons are as follows: methane \(<\) ethane \(<\) ethylene. Is this because ethylene is the most polar molecule? (c) What intermolecular interactions can these hydrocarbons have with water? (d) Draw the Lewis dot structures for the three hydrocarbons. Which of these hydrocarbons possess \(\pi\) bonds? Based on their solubilities, would you say \(\pi\) bonds are more or less polarizable than \(\sigma\) bonds? (e) Explain why \(\mathrm{NO}\) is more soluble in water than either \(\mathrm{N}_{2}\) or \(\mathrm{O}_{2}\). (f) \(\mathrm{H}_{2} \mathrm{~S}\) is more water-soluble than almost all the other gases in table. What intermolecular forces is \(\mathrm{H}_{2} \mathrm{~S}\) likely to have with water? \((\mathbf{g}) \mathrm{SO}_{2}\) is by far the most water-soluble gas in table. What intermolecular forces is \(\mathrm{SO}_{2}\) likely to have with water? $$ \begin{array}{lc} \hline \text { Gas } & \text { Solubility (mM) } \\ \hline \mathrm{CH}_{4} \text { (methane) } & 1.3 \\ \mathrm{C}_{2} \mathrm{H}_{6} \text { (ethane) } & 1.8 \\ \mathrm{C}_{2} \mathrm{H}_{4} \text { (ethylene) } & 4.7 \\ \mathrm{~N}_{2} & 0.6 \\ \mathrm{O}_{2} & 1.2 \\ \mathrm{NO} & 1.9 \\ \mathrm{H}_{2} \mathrm{~S} & 99 \\ \mathrm{SO}_{2} & 1476 \\ \hline \end{array} $$

Would you expect alanine (an amino acid) to be more soluble in water or in hexane?

If you compare the solubilities of the noble gases in water, you find that solubility increases from smallest atomic weight to largest, \(\mathrm{Ar}<\mathrm{Kr}<\mathrm{Xe}\). Which of the following statements is the best explanation? (a) The heavier the gas, the more it sinks to the bottom of the water and leaves room for more gas molecules at the top of the water. (b) The heavier the gas, the more dispersion forces it has, and therefore the more attractive interactions it has with water molecules. (c) The heavier the gas, the more likely it is to hydrogenbond with water. (d) The heavier the gas, the more likely it is to make a saturated solution in water.

(a) Do colloids made only of gases exist? Why or why not? (b) In the 1850 s, Michael Faraday prepared ruby-red colloids of gold nanoparticles in water that are still stable today. These brightly colored colloids look like solutions. What experiment(s) could you do to determine whether a given colored preparation is a solution or colloid?

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?
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