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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
Based on the van der Waals constants, Ar has weaker intermolecular forces (a = 1.355 L虏 atm/mol虏) and a smaller particle size (b = 0.0321 L/mol) than CO鈧� (a = 3.640 L虏 atm/mol虏, b = 0.0427 L/mol). Therefore, Ar is expected to behave more nearly like an ideal gas at high pressures compared to CO鈧�.

Step by step solution

01

Identify the van der Waals constants for Ar and CO鈧�

Refer to Table 10.3 and look for the van der Waals constants for Ar and CO鈧�. Note down the values for both gases. For Ar: a = 1.355 L虏 atm/mol虏 b = 0.0321 L/mol For CO鈧�: a = 3.640 L虏 atm/mol虏 b = 0.0427 L/mol
02

Compare the "a" constants

Compare the "a" constants of Ar and CO鈧� to determine which one has weaker intermolecular forces. Ar: a = 1.355 L虏 atm/mol虏 CO鈧�: a = 3.640 L虏 atm/mol虏 Since the van der Waals constant "a" for Ar (1.355 L虏 atm/mol虏) is smaller than the "a" constant for CO鈧� (3.640 L虏 atm/mol虏), Ar has weaker intermolecular forces.
03

Compare the "b" constants

Compare the "b" constants of Ar and CO鈧� to determine which one has smaller particle size. Ar: b = 0.0321 L/mol CO鈧�: b = 0.0427 L/mol Since the van der Waals constant "b" for Ar (0.0321 L/mol) is smaller than the "b" constant for CO鈧� (0.0427 L/mol), Ar has a smaller particle size.
04

Conclusion

Based on the comparison of van der Waals constants "a" and "b", Ar has weaker intermolecular forces and a smaller particle size than CO鈧�. Thus, Ar is expected to behave more nearly like an ideal gas at high pressures compared to CO鈧�.

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Key Concepts

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

Ideal Gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions. The concept helps scientists model gas behavior because ideal gases follow the ideal gas law given by the equation:\[ PV = nRT \]where:
  • \(P\) is the pressure
  • \(V\) is the volume
  • \(n\) is the amount of substance in moles
  • \(R\) is the ideal gas constant
  • \(T\) is the temperature in Kelvin
Ideal gases do not account for intermolecular forces or molecular volume, which means they cannot compress entirely or expand infinitely.
In reality, no gas perfectly behaves as an ideal gas but under certain conditions like high temperatures and low pressures, real gases approximate ideal gas behavior. This is because the particles are moving faster and have more space to do so without interacting with each other.
Intermolecular Forces
Intermolecular forces are the forces of attraction or repulsion between neighboring particles (atoms, molecules, or ions). They are distinct from chemical bonds.
These forces play a significant role in determining the physical properties of substances, including their boiling and melting points.
Several types of intermolecular forces exist:
  • London dispersion forces: These are weak, temporary forces that occur due to the movement of electrons creating temporary dipoles in molecules.
  • Dipole-dipole interactions: These occur when polar molecules align so that the positive end of one molecule is near the negative end of another.
  • Hydrogen bonding: A strong type of dipole-dipole interaction occurring when hydrogen is bonded to highly electronegative atoms like oxygen or nitrogen.
The van der Waals constant "a" accounts for these intermolecular forces in the van der Waals equation, correcting the ideal gas law by considering the attractive forces between particles.
Van der Waals Constants
The van der Waals constants "a" and "b" are used in the van der Waals equation to adjust the ideal gas law for real gas behavior. The equation is presented as:\[ \left( P + \frac{an^2}{V^2} \right) (V - nb) = nRT \]Here:
  • \(a\) corrects for the attractive intermolecular forces between particles, with larger values indicating stronger forces.
  • \(b\) corrects for the volume occupied by the gas particles themselves, with larger values indicating larger particle sizes.
The van der Waals constants vary for different gases and help explain deviations from ideal behavior.
In the exercise example, Argon (Ar) and Carbon Dioxide (CO鈧�) have different values for "a" and "b", indicative of the differences in their intermolecular forces and molecular sizes.
This leads to the conclusion that Argon, having weaker attractions and smaller particle size, behaves more closely to an ideal gas under high pressure conditions compared to CO鈧�.

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Most popular questions from this chapter

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?

A scuba diver's tank contains \(0.29 \mathrm{~kg}\) of \(\mathrm{O}_{2}\) compressed into a volume of \(2.3\) L. (a) Calculate the gas pressure inside the tank at \(9{ }^{\circ} \mathrm{C}\). (b) What volume would this oxygen occupy at \(26^{\circ} \mathrm{C}\) and \(0.95 \mathrm{~atm}\) ?

Chlorine dioxide gas \(\left(\mathrm{ClO}_{2}\right)\) is used as a commercial bleaching agent. It bleaches materials by oxidizing them. In the course of these reactions, the \(\mathrm{ClO}_{2}\) is itself reduced. (a) What is the Lewis structure for \(\mathrm{ClO}_{2}\) ? (b) Why do you think that \(\mathrm{ClO}_{2}\) is reduced so readily? (c) When a \(\mathrm{ClO}_{2}\) molecule gains an electron, the chlorite ion, \(\mathrm{ClO}_{2}^{-}\), forms. Draw the Lewis structure for \(\mathrm{ClO}_{2}^{-}\). (d) Predict the \(\mathrm{O}-\mathrm{Cl}-\mathrm{O}\) bond angle in the \(\mathrm{ClO}_{2}^{-}\) ion. (e) One method of preparing \(\mathrm{ClO}_{2}\) is by the reaction of chlorine and sodium chlorite: $$ \mathrm{Cl}_{2}(g)+2 \mathrm{NaClO}_{2}(s) \longrightarrow 2 \mathrm{ClO}_{2}(g)+2 \mathrm{NaCl}(s) $$ If you allow \(10.0 \mathrm{~g}\) of \(\mathrm{NaClO}_{2}\) to react with \(2.00 \mathrm{~L}\) of chlorine gas at a pressure of \(1.50 \mathrm{~atm}\) at \(21^{\circ} \mathrm{C}\), how many grams of \(\mathrm{ClO}_{2}\) can be prepared?

What property or properties of gases can you point to that support the assumption that most of the volume in a gas is empty space?

(a) List two experimental conditions under which gases deviate from ideal behavior. (b) List two reasons why the gases deviate from ideal behavior. (c) Explain how the function \(P V / R T\) can be used to show how gases behave nonideally.
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