Problem 52 - Chemistry and Chemical Reactivity

Question

Under which set of conditions will \(\mathrm{Cl}_{2}\) deviate least from ideal gas behavior? (a) \(1 \mathrm{atm}, 0^{\circ} \mathrm{C}\) (b) 0.1 atm, \(100^{\circ} \mathrm{C}\) (c) \(10 \mathrm{atm}, 0^{\circ} \mathrm{C}\) (d) \(1 \mathrm{atm}, 100^{\circ} \mathrm{C}\)

Step-by-Step Solution

Answer

Option (b) 0.1 atm, 100°C.

Step 1: Understand Ideal Gas Behavior

An ideal gas perfectly follows the ideal gas law, \(PV = nRT\), without any intermolecular interactions or volume effect. Real gases like \(\mathrm{Cl}_{2}\) deviate from this behavior under low temperatures and high pressures because intermolecular forces and molecular volume become significant.

Step 2: Evaluate Conditions for Least Deviation

For the least deviation from ideal behavior, gases should be under conditions of high temperature and low pressure. High temperatures provide enough kinetic energy to overcome intermolecular forces, and low pressures minimize interactions due to a larger volume.

Step 3: Analyze Each Option

(a) 1 atm, \(0^{\circ} \mathrm{C}\): At this standard temperature and pressure, there will be some deviation as temperature is low.(b) 0.1 atm, \(100^{\circ} \mathrm{C}\): This option offers both a low pressure and a high temperature, which are ideal for minimizing deviations.(c) 10 atm, \(0^{\circ} \mathrm{C}\): High pressure and low temperature result in significant deviation due to increased interactions and limited volume.(d) 1 atm, \(100^{\circ} \mathrm{C}\): Moderate temperature and moderate pressure means moderate deviation.

Step 4: Determine the Best Option

The conditions in option (b) \((0.1 \text{ atm}, 100^{\circ} \mathrm{C})\) represent the least deviation from ideal behavior because they involve low pressure and high temperature. This minimizes both intermolecular interactions and the impact of molecular volume.

Key Concepts

Intermolecular Forces

Intermolecular forces are the attractions that occur between molecules. These forces can influence the physical properties of gases, such as boiling points and solubility.
Understanding these forces is key when discussing gases derailing from ideal gas behavior.
Ideal gases are assumed to have no interactions between particles, but real gases like chlorine (\(\mathrm{Cl}_{2}\)) do experience these interactions. Types of intermolecular forces include:

• Dispersion Forces: These are the weakest and are present in all molecules. They are caused by the temporary shifts in electron density.


• Dipole-Dipole Interactions: Seen in polar molecules, these forces are due to the electrostatic interactions between positive and negative dipoles.


• Hydrogen Bonds: Stronger than dipole-dipole, these occur when hydrogen is bound to electronegative atoms like oxygen or nitrogen.

For gases to follow ideal behavior, these forces must be negligible. However, under strong intermolecular force conditions such as low temperatures and high pressures, gases deviate from ideal gas laws.

Deviation from Ideal Gas Law

The ideal gas law is expressed as \(PV = nRT\), and assumes no volume or interaction between particles.
However, real gases can deviate from this behavior due to intermolecular forces and molecular sizes.
Deviations are most evident under extreme conditions:

• High Pressure: Molecules are forced closer together, increasing the effect of intermolecular forces and causing volume to play a more significant role. This leads to deviation.


• Low Temperature: Molecules move more slowly and spend more time in close proximity, which enhances the effects of intermolecular forces.

To minimize deviations, conditions of high temperature and low pressure are preferred, as the molecules have enough kinetic energy to overcome attraction forces, aligning behavior more closely to the ideal gas assumptions.

Kinetic Molecular Theory

The Kinetic Molecular Theory is central to understanding gas behavior. It provides a model to explain why gases behave the way they do. This theory is built on several assumptions:

• Gas particles are in constant, random motion: They move in straight lines until they collide with something.


• Collisions are elastic: No kinetic energy is lost when gas particles collide with each other or the walls of their container.


• Negligible Interactions: Gas particles do not have attractions or repulsions toward each other.


• Volume of individual gas particles is negligible: Compared to the volume of the container, the volume occupied by gas particles themselves is very small.

Under ideal conditions, these assumptions are valid; however, in real gases, deviations can occur when these assumptions no longer hold due to the conditions affecting intermolecular forces and actual particle volume.

Real Gases Conditions

Real gases often deviate from ideal gas behavior, especially under certain conditions. Understanding these conditions helps predict when a gas is likely to behave less ideally.

• Low Temperature: Gas particles move slower, allowing intermolecular forces to have noticeable influences.


• High Pressure: Particles are compressed into a smaller volume, amplifying the significance of particle volume and interaction forces.

For chlorine gas (\(\mathrm{Cl}_{2}\)), real behavior becomes noticeable under these conditions, as it deviates from the ideal gas assumptions. To approach the ideal gas behavior, gases should instead be at high temperatures and low pressures, reducing the effects of these influences. In summary, the ideal conditions for minimal deviation are high temperatures and low pressures, thereby minimizing intermolecular forces and volume impacts.