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Chapter 5: Problem 90

Under what set of conditions would a gas be expected to behave most ideally: (a) high temperature and low pressure, (b) high temperature and high pressure, (c) low temperature and high pressure, or (d) low temperature and low pressure?

Short Answer

Expert verified
Under high temperature and low pressure conditions, a gas would behave most ideally.

Step by step solution

01

Understanding the Ideal Gas Law

The Ideal Gas Law states that the pressure (P) multiplied by the volume (V) is equal to the number of moles (n) of gas times the gas constant (R) times the temperature (T). It is the theoretical model for the behavior of gases. However, real gases can deviate from this ideal behavior.
02

Considering Temperature and Pressure

The kinetic theory of gases assumes that gas particles are always in motion and that they collide with each other and the walls of their container but do not otherwise interact. As the temperature increases, the gas molecules have greater kinetic energy, which overcomes attractive forces. Thus, increased temperature makes a gas behave more ideally. Conversely, high pressure pushes gas molecules closer together, which makes the forces between them more significant and the volume of the individual gas molecules compared to the volume of the container more significant, forcing the gas to deviate from ideal behavior. Therefore lower pressure makes a gas behave more ideally.
03

Evaluating the Options

Taking the temperature and pressure behavior of gases into account, let's evaluate the given options: (a) high temperature and low pressure, (b) high temperature and high pressure, (c) low temperature and high pressure, and (d) low temperature and low pressure. Option (a) has high temperature, which is good for ideal behavior, and low pressure, which is also good for ideal behavior. Thus option (a) provides the conditions under which a gas would behave most ideally.

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Most popular questions from this chapter

The empirical formula of a compound is \(\mathrm{CH}\). At \(200^{\circ} \mathrm{C}, 0.145 \mathrm{~g}\) of this compound occupies \(97.2 \mathrm{~mL}\) at a pressure of 0.74 atm. What is the molecular formula of the compound?

Two vessels are labeled A and B. Vessel A contains \(\mathrm{NH}_{3}\) gas at \(70^{\circ} \mathrm{C},\) and vessel \(\mathrm{B}\) contains \(\mathrm{Ne}\) gas at the same temperature. If the average kinetic energy of \(\mathrm{NH}_{3}\) is \(7.1 \times 10^{-21} \mathrm{~J} / \mathrm{molecule},\) calculate the rootmean- square speed of Ne atoms.

Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are \(250 \mathrm{~K}\) and \(1.0 \times 10^{-3}\) atm, respectively. How many ozone molecules are present in \(1.0 \mathrm{~L}\) of air under these conditions?

A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in \(15.0 \mathrm{~min} .\) Under the same conditions of temperature and pressure, it takes an equal volume of \(\mathrm{N}_{2} 12.0 \mathrm{~min}\) to effuse through the same barrier. Calculate the molar mass of the gas and suggest what the gas might be.

In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at \(43^{\circ} \mathrm{C}\) : $$ \mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g) $$ This reaction separates nickel from other solid impurities. (a) Starting with \(86.4 \mathrm{~g}\) of \(\mathrm{Ni}\), calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume \(4.00 \mathrm{~L}\). (Assume the above reaction goes to completion.) (b) At temperatures above \(43^{\circ} \mathrm{C}\), the pressure of the gas is observed to increase much more rapidly than predicted by the ideal gas equation. Explain.
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