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Chapter 10: Problem 85

Based on their respective van der Waals constants (Table 10.3), is Ar or \(\mathrm{CO}_{2}\) expected to behave more nearly like an ideal gas at high pressures? Explain.

Short Answer

Expert verified
Argon (Ar) is expected to behave more nearly like an ideal gas at high pressures compared to Carbon Dioxide \(\mathrm{CO}_2\), as Ar has weaker intermolecular interactions (\(a_{Ar} = 1.34 \ L^2\cdot atm\cdot mol^{-2}\) vs \(a_{CO2} = 3.59 \ L^2\cdot atm\cdot mol^{-2}\)) and smaller molecular size (\(b_{Ar} = 0.0322 \ L\cdot mol^{-1}\) vs \(b_{CO2} = 0.0427 \ L\cdot mol^{-1}\)).

Step by step solution

01

Review constants for Ar and CO2

Refer to Table 10.3 to find the van der Waals constants for Argon (Ar) and Carbon Dioxide (\(\mathrm{CO}_2\)): Argon (Ar): - \(a_Ar = 1.34 \ L^2\cdot atm\cdot mol^{-2}\) - \(b_Ar = 0.0322 \ L\cdot mol^{-1}\) Carbon Dioxide (\(\mathrm{CO}_2\)): - \(a_{CO2} = 3.59 \ L^2\cdot atm\cdot mol^{-2}\) - \(b_{CO2} = 0.0427 \ L\cdot mol^{-1}\)
02

Compare intermolecular interaction constants

Compare the van der Waals constant for intermolecular interactions (\(a\)) for both gases: - For Argon: \(a_Ar = 1.34 \ L^2\cdot atm\cdot mol^{-2}\) - For Carbon Dioxide: \(a_{CO2} = 3.59 \ L^2\cdot atm\cdot mol^{-2}\) Since \(a_Ar < a_{CO2}\), this indicates that Argon has weaker intermolecular interactions compared to Carbon Dioxide.
03

Compare molecular size constants

Compare the van der Waals constant for molecular size (\(b\)) for both gases: - For Argon: \(b_Ar = 0.0322 \ L\cdot mol^{-1}\) - For Carbon Dioxide: \(b_{CO2} = 0.0427 \ L\cdot mol^{-1}\) Since \(b_Ar < b_{CO2}\), this indicates that Argon molecules are smaller in size compared to Carbon Dioxide molecules.
04

Determine gas behavior at high pressures

We have learned that Argon has weaker intermolecular interactions and smaller molecular size than Carbon Dioxide. Based on these factors, Argon should behave more like an ideal gas at high pressures compared to Carbon Dioxide.

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Most popular questions from this chapter

Assume that you have a cylinder with a movable piston. What would happen to the gas pressure inside the cylinder if you do the following? (a) Decrease the volume to one-fourth the original volume while holding the temperature constant. (b) Reduce the Kelvin temperature to half its original value while holding the volume constant. (c) Reduce the amount of gas to half while keeping the volume and temperature constant.

In the United States, barometric pressures are generally reported in inches of mercury (in. \(\mathrm{Hg}\) ). On a beautiful summer day in Chicago the barometric pressure is \(30.45\) in. Hg. (a) Convert this pressure to torr. (b) A meteorologist explains the nice weather by referring to a "high-pressure area." In light of your answer to part (a), explain why this term makes sense.

A sample of \(1.42 \mathrm{~g}\) of helium and an unweighed quantity of \(\mathrm{O}_{2}\) are mixed in a flask at room temperature. The partial pressure of helium in the flask is \(42.5\) torr, and the partial pressure of oxygen is 158 torr. What is the mass of the oxygen in the container?

In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below \(100^{\circ} \mathrm{C}\) in a boiling-water bath and determine the mass of vapor required to fill the bulb (see drawing). From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor, \(1.012 \mathrm{~g}\); volume of bulb, \(354 \mathrm{~cm}^{3}\); pressure, 742 torr; temperature, \(99^{\circ} \mathrm{C}\).

Consider the following reaction: $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) $$ Imagine that this reaction occurs in a container that has a piston that moves to allow a constant pressure to be maintained when the reaction occurs at constant temperature. (a) What happens to the volume of the container as a result of the reaction? Explain. (b) If the piston is not allowed to move, what happens to the pressure as a result of the reaction? [Sections \(10.3\) and \(10.5]\)
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