Question

At constant volume the pressure of a monoatomic gas depends upon (1) Thickness of the walls of the container (2) The absolute temperature (3) The atomic number of the element (4) The number of valence electrons

Short answer

(2) The absolute temperature

Step-by-step solution

Understand the Problem

The given problem asks to determine the factor upon which the pressure of a monoatomic gas depends when the volume is constant.

Identify Relevant Gas Law

Use the Ideal Gas Law: \[ PV = nRT \] where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature. Under constant volume, the formula simplifies to \[ P \propto T \].

Analyze Each Option

Examine each option to see if it affects pressure:1. Thickness of the walls of the container: This does not affect the gas molecules inside.2. The absolute temperature: From the simplified Ideal Gas Law, pressure is directly proportional to temperature at constant volume.3. The atomic number of the element: This is unrelated to pressure directly since monoatomic gases are considered ideal and their atomic structure doesn't change this basic relationship.4. The number of valence electrons: This also does not directly affect pressure as it relates to chemical reactivity, not physical state or gas laws.

Choose the Correct Option

Based on the Ideal Gas Law and the analysis, the pressure at constant volume depends on the absolute temperature.

Key concepts

monoatomic gas

A monoatomic gas is a gas composed of individual atoms, rather than molecules. Common examples of monoatomic gases are the noble gases such as Helium (He), Neon (Ne), and Argon (Ar). These gases are chemically inert because they have complete valence electron shells, meaning they don't easily form bonds with other atoms.
Monoatomic gases are often assumed to be 'ideal gases' in many physics problems. This idealization means that the gas particles are considered to have no volume and no intermolecular forces. This simplification helps in focusing on the basic principles of the gas laws, such as the Ideal Gas Law.

pressure-temperature relationship

The relationship between pressure and temperature in gases is a crucial concept in thermodynamics. For an ideal gas kept at a constant volume, this relationship can be derived from the Ideal Gas Law, which states: \[ PV = nRT \] If the volume (V) is kept constant, then the relationship simplifies to: \[ P \proptoT \] This equation shows that the pressure (P) of a gas is directly proportional to its absolute temperature (T). As temperature increases, the pressure of the gas increases and vice versa. This is because increasing the temperature adds kinetic energy to the gas molecules, causing them to move more vigorously and collide with the walls of the container more frequently, which increases the pressure.

constant volume

When we say a gas is held at constant volume, it means the container holding the gas does not change in size. This assumption simplifies many calculations and deductions related to gas behavior. In practical scenarios, this could be a rigid container where the walls do not expand or contract.
At constant volume, any changes to the system's pressure must come from changes in temperature or quantity of gas. This principle is extremely useful in understanding how gases behave under different thermodynamic conditions. For example, if a gas in a fixed volume container is heated, its pressure will rise in direct proportion to the increase in temperature, according to the Ideal Gas Law. Likewise, if the gas is cooled, the pressure will decrease.