Problem 149 - Chemistry

Question

Which of the noble gases would not behave ideally under any circumstance? Why?

Step-by-Step Solution

Answer

The noble gas radon would not behave ideally under any circumstance, as its large atomic size leads to significant volume and interactions that violate the assumptions of the ideal gas law.

Step 1: List the sizes of the Noble Gases

The first thing to understand is the atomic sizes of the noble gases. The atomic size increases down the group from helium to radon, meaning helium is the smallest and radon is the largest. Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), Radon (Rn).

Step 2: Understand why size matters

According to the ideal gas law, the size of the individual particles does not matter. However, as the atomic size increases, the volume occupied by the individual particles becomes significant. This violates the ideal gas law.

Step 3: Identify the least ideal gas

Therefore, as Radon (Rn) is the largest of the noble gases, it would be the least likely to behave as an ideal gas under any circumstance. The larger the atom, the less likely it is to satisfy the conditions of the ideal gas law.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry and physics that relates the pressure, volume, and temperature of an ideal gas with its amount. It is expressed as \( PV = nRT \), where:

• \( P \) is the pressure of the gas.
• \( V \) is the volume the gas occupies.
• \( n \) is the amount of substance of gas, measured in moles.
• \( R \) is the ideal gas constant.
• \( T \) is the temperature of the gas, measured in Kelvin.

The concept assumes gases have extremely small particles in terms of size compared to the distance between particles. Thus, particles themselves take up no volume and have no interaction or attraction with one another. Under this assumption, gases behave ideally, which is often not the case with real gases. As real gases increase in atomic size, individual gas volumes and intermolecular forces become significant, deviating from ideal behavior.

Atomic Size

Atomic size, often referred to as atomic radius, is a measure of the size of an atom. It denotes the typical distance from the nucleus to the boundary of the surrounding cloud of electrons. Atomic size increases down a group in the periodic table because additional electron shells are added. Thus, radon has a larger atomic radius than helium.
In the context of the Ideal Gas Law, larger atomic sizes make it difficult for gases like radon to act ideally. Because their volumes become significant compared to the total volume of the gas, they cannot be considered negligible in calculations. Large atoms may also experience more van der Waals forces, deviating from the assumption that there are no attractions between particles in an ideal gas scenario. This is crucial when considering noble gases and their deviation from ideality.

Radon

Radon is a noble gas, the heaviest and largest in its group. Because it has the largest atomic size among the noble gases, it is less likely to behave as an ideal gas than its smaller counterparts like helium or neon. The substantial volume that radon atoms occupy is non-negligible, contradicting the assumptions made in the Ideal Gas Law.

• Radon tends to exhibit significant van der Waals forces, given its large size and number of electrons.
• These forces result in greater attractions between radon atoms, leading to a failure to match ideal gas predictions.

Hence, radon's behavior under the conditions described in the step-by-step solution shows it's predicted to deviate from ideality, especially at high pressures and low temperatures where real gas behavior becomes more pronounced. Understanding this helps in predicting and explaining why it does not conform to the ideal gas model.