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Chapter 5: Problem 88

Does \(\mathrm{SF}_{6}\) (boiling point \(=16^{\circ} \mathrm{C}\) at 1 atm) behave more ideally at \(150^{\circ} \mathrm{C}\) or at \(20^{\circ} \mathrm{C}\) ? Explain.

Short Answer

Expert verified
\(\mathrm{SF}_{6}\) behaves more ideally at \(150^{\circ} \mathrm{C}\) than at \(20^{\circ} \mathrm{C}\).

Step by step solution

01

Understand Ideal Gas Behavior

Under ideal gas behavior, a gas follows the ideal gas law: \[ PV = nRT \]Here, P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Gases behave more ideally at higher temperatures and lower pressures because interactions between molecules are minimized.
02

Compare Given Temperatures to Boiling Point

Compare the given temperatures to the boiling point of \(\mathrm{SF}_{6}\), which is \(16^{\circ} \mathrm{C}\). The two temperatures given are \(150^{\circ} \mathrm{C}\) and \(20^{\circ} \mathrm{C}\). Both are above the boiling point, meaning \(\mathrm{SF}_{6}\) will be in a gaseous state at both temperatures.
03

Determine Influence of Temperature on Ideal Gas Behavior

Gases behave more ideally at higher temperatures due to increased kinetic energy, which reduces intermolecular interactions. Therefore, compare the given temperatures: \(150^{\circ} \mathrm{C}\) is significantly higher than \(20^{\circ} \mathrm{C}\). This means molecular interactions are minimized more at \(150^{\circ} \mathrm{C}\).
04

Conclusion Based on Temperature

Since gases behave more ideally at higher temperatures, \(\mathrm{SF}_{6}\) will behave more ideally at \(150^{\circ} \mathrm{C}\) than at \(20^{\circ} \mathrm{C}\).

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Key Concepts

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

Ideal Gas Law
The Ideal Gas Law is a foundational principle in chemistry and physics. It is represented by the equation \[ PV = nRT \]. Here:
  • P stands for pressure
  • V represents volume
  • n indicates the number of moles
  • R is the gas constant
  • T is temperature
This law describes how these variables interact and relate to one another. According to the Ideal Gas Law, gases perform ideally under specific conditions: high temperatures and low pressures. These conditions reduce the chance of molecules interacting closely. When molecules are heated, they gain kinetic energy, moving more rapidly and behaving in a more 'ideal' manner.
Temperature Influence on Gases
Temperature plays a crucial role in the behavior of gases. Higher temperatures increase the kinetic energy of gas molecules. This means gas particles move faster and are less likely to experience significant intermolecular forces. For instance, consider the provided temperatures: 150掳C is significantly higher than 20掳C. At 150掳C, the kinetic energy of the sulfur hexafluoride (SF6) molecules would be much higher than at 20掳C.
This is why gases tend to behave more ideally at elevated temperatures; their enhanced motion makes intermolecular interactions even less significant.
Intermolecular Interactions
Intermolecular interactions refer to the forces between individual molecules in a substance. These forces can include:
  • Van der Waals forces
  • Dipole-dipole interactions
  • Hydrogen bonds (unlikely in nonpolar SF6)
In the realm of ideal gases, these forces are considered negligible. However, in real gases, they can influence behavior. When temperature increases, intermolecular interactions decrease. This is due to the fact that molecules have increased kinetic energy, making it easier for them to overcome any attracting or repelling forces between them.
Sulfur Hexafluoride (SF6)
Sulfur hexafluoride (SF6) is a gas frequently used in electrical insulation and in medical imaging. Its boiling point is 16掳C at 1 atm, meaning it becomes a gas above this temperature. Both 20掳C and 150掳C are above this threshold. Therefore, SF6 will be in its gaseous form at both temperatures. However, at 150掳C, SF6 will exhibit more ideal behavior compared to 20掳C due to its high kinetic energy and reduced molecular interaction. This aligns with the Ideal Gas Law, confirming that higher temperatures make gases behave more ideally.

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Most popular questions from this chapter

One way to prevent emission of the pollutant NO from industrial plants is by a catalyzed reaction with \(\mathrm{NH}_{3}\) : $$4 \mathrm{NH}_{3}(g)+4 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \stackrel{\text { catalyst }}{\longrightarrow} 4 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ (a) If the NO has a partial pressure of \(4.5 \times 10^{-5}\) atm in the flue gas, how many liters of \(\mathrm{NH}_{3}\) are needed per liter of flue gas at \(1.00 \mathrm{~atm} ?(\mathrm{~b})\) If the reaction takes place at \(1.00 \mathrm{~atm}\) and \(365^{\circ} \mathrm{C}\) how many grams of \(\mathrm{NH}_{3}\) are needed per kiloliter (kL) of flue gas?

At \(10.0^{\circ} \mathrm{C}\) and \(102.5 \mathrm{kPa},\) the density of dry air is \(1.26 \mathrm{~g} / \mathrm{L}\) What is the average "molar mass" of dry air at these conditions?

In the \(19^{\text {th }}\) century, \(\mathrm{J}\). \(\mathrm{B}\). A. Dumas devised a method for finding the molar mass of a volatile liquid from the volume, temperature, pressure, and mass of its vapor. He placed a sample of such a liquid in a flask that was closed with a stopper fitted with a narrow tube, immersed the flask in a hot water bath to vaporize the liquid, and then cooled the flask. Find the molar mass of a volatile liquid from the following: Mass of empty flask \(=65.347 \mathrm{~g}\) Mass of flask filled with water at \(25^{\circ} \mathrm{C}=327.4 \mathrm{~g}\) Density of water at \(25^{\circ} \mathrm{C}=\) \(0.997 \mathrm{~g} / \mathrm{mL}\) Mass of flask plus condensed unknown liquid \(=65.739 \mathrm{~g}\) Barometric pressure \(=101.2 \mathrm{kPa}\) Temperature of water bath \(=99.8^{\circ} \mathrm{C}\)

The Hawaian volcano Kilauea emits an average of \(1.5 \times 10^{3} \mathrm{~m}^{3}\) of gas each day, when corrected to \(298 \mathrm{~K}\) and \(1.00 \mathrm{~atm} .\) The mixture contains gases that contribute to global warming and acid rain, and some are toxic. An atmospheric chemist analyzes a sample and finds the following mole fractions: \(0.4896 \mathrm{CO}_{2}, 0.0146 \mathrm{CO}, 0.3710 \mathrm{H}_{2} \mathrm{O}\) \(0.1185 \mathrm{SO}_{2}, 0.0003 \mathrm{~S}_{2}, 0.0047 \mathrm{H}_{2}, 0.0008 \mathrm{HCl},\) and \(0.0003 \mathrm{H}_{2} \mathrm{~S} .\) How many metric tons (t) of each gas are emitted per year ( \(1 \mathrm{t}=1000 \mathrm{~kg}\) )?

White phosphorus melts and then vaporizes at high temperatures. The gas effuses at a rate that is 0.404 times that of neon in the same apparatus under the same conditions. How many atoms are in a molecule of gaseous white phosphorus?
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