Question

Cite two pieces of evidence to show that gases do not behave ideally under all conditions. 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

Gases do not behave ideally due to intermolecular forces and finite particle volume. Gases behave most ideally at high temperature and low pressure.

Step-by-step solution

Identify Non-Ideal Gas Behavior Evidence

Gases deviate from ideal behavior primarily due to intermolecular forces and the volume occupied by gas particles. Two pieces of evidence are: (1) Real gases liquefy at high pressures and low temperatures, indicating strong intermolecular forces. (2) The van der Waals equation modifies the ideal gas law to account for these forces and the finite volume of gas particles, differing from the ideal gas equation.

Determine Conditions for Most Ideal Behavior

Gases will behave more ideally when the conditions minimize intermolecular forces and the volume occupied by gas particles is negligible compared to the container. High temperatures cause particles to have higher kinetic energy, reducing the influence of intermolecular forces. Low pressures ensure the volume of gas particles is much smaller than the volume of the container.

Match Ideal Conditions to Options

Examine the given options to find those matching the ideal behavior conditions described in Step 2. The conditions high temperature and low pressure (option (a)) best correspond to gases behaving ideally, as they minimize intermolecular interactions and particle volume effects.

Key concepts

Intermolecular Forces in Gases

In a perfect world, gases would move freely without any attractive or repulsive forces between their particles. However, in reality, gases do experience forces that influence their behavior. These forces are known as intermolecular forces. There are three main types of intermolecular forces: dispersion forces, dipole-dipole interactions, and hydrogen bonds.

Dispersion forces are the weakest and occur in all molecules, primarily gases. They arise due to temporary fluctuations in the electron density within atoms or molecules, leading to temporary dipoles. Dipole-dipole interactions occur in polar molecules where partial positive and negative charges attract each other. Lastly, hydrogen bonds, which are stronger than the other types, occur in molecules where hydrogen is directly bonded to electronegative atoms like oxygen or nitrogen.

• Gases show non-ideal behavior when intermolecular forces become significant, particularly under conditions of low temperature and high pressure.
• Intermolecular forces can lead to the liquefaction of gases when they are compressed and cooled.

Recognizing these forces helps us understand why gases deviate from ideal behavior, especially when they are compressed into smaller volumes or cooled down.

Van der Waals Equation

The Van der Waals equation is a modified version of the ideal gas law that corrects for non-ideal behavior in real gases. The ideal gas law is represented by \[ PV = nRT \] where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the gas constant, and \(T\) is temperature. However, this model doesn't account for the volume occupied by gas particles or the intermolecular forces between them.

To better approximate real gas behavior, the Van der Waals equation incorporates two specific correction factors. These are included as additional terms in the equation:\[ \left( P + \frac{an^2}{V^2} \right)(V - nb) = nRT \]

• The term \(\frac{an^2}{V^2}\) adds a correction for the attractive forces between molecules, with \(a\) being a constant specific to each gas.
• The term \(nb\) accounts for the finite volume occupied by gas molecules themselves, with \(b\) indicating the volume exclusion per mole of gas.

By using this equation, scientists are able to understand and predict the behaviors of gases under non-ideal conditions, such as high pressures and low temperatures.

Conditions for Ideal Gas Behavior

The ideal gas behavior assumption works best under conditions where the particles in the gas are less likely to interact with one another. For a gas to behave most like an ideal gas, two specific conditions are preferred: high temperature and low pressure.

High temperature ensures that the kinetic energy of gas particles is high, helping them to overcome any attraction or repulsion due to intermolecular forces. When particles move fast, they have little time to interact meaningfully with each other. This minimizes the impact of intermolecular forces on the behavior of the gas.

Low pressure is equally essential because it implies that the gas particles are spread out more within a larger volume, reducing the frequency and significance of particle collisions. With less crowding, the individual volume of gas particles becomes negligible relative to the total volume of the gas. This is in line with the assumptions made in the ideal gas law.

• At high temperatures, particle velocity increases, reducing intermolecular engagement.
• At low pressures, gas molecules occupy a large volume, so their volume is insignificant.

These conditions ensure the behavior of gases aligns more closely with the predictions made by the ideal gas law, as outlined by choice (a) of high temperature and low pressure.