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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

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.

The planet Jupiter has a surface temperature of \(140 \mathrm{~K}\) and a mass 318 times that of Earth. Mercury has a surface temperature between \(600 \mathrm{~K}\) and \(700 \mathrm{~K}\) and a mass \(0.05\) times that of Earth. On which planet is the atmosphere more likely to obey the ideal-gas law? Explain.

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?

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is \(65.0 \mathrm{~L}\) and which contains \(\mathrm{O}_{2}\) gas at a pressure of \(16,500 \mathrm{kPa}\) at \(23{ }^{\circ} \mathrm{C}\). (a) What mass of \(\mathrm{O}_{2}\) does the tank contain? (b) What volume would the gas occupy at STP? (c) At what temperature would the pressure in the tank equal \(150.0 \mathrm{~atm} ?\) (d) What would be the pressure of the gas, in \(\mathrm{kPa}\), if it were transferred to a container at \(24^{\circ} \mathrm{C}\) whose volume is \(55.0 \mathrm{~L} ?\)

Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose \(120.00 \mathrm{~kg}\) of \(\mathrm{N}_{2}(g)\) is stored in a 1100.0-L metal cylinder at \(280^{\circ} \mathrm{C}\). (a) Calculate the pressure of the gas, assuming ideal-gas behavior. (b) By using data in Table 10.3, calculate the pressure of the gas according to the van der Waals equation. (c) Under the conditions of this problem, which correction dominates, the one for finite volume of gas molecules or the one for attractive interactions?
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