Question

Compare the average kinetic energy at room temperature of a nitrogen molecule to that of a nitrogen atom. Which has the larger kinetic energy? a) nitrogen atom b) nitrogen molecule c) They have the same energy. d) It depends upon the pressure.

Short answer

Answer: c) They have the same energy.

Step-by-step solution

Calculate average kinetic energy at room temperature

Average kinetic energy (K.E.) of gas particles can be calculated using the formula: K.E. = (3/2)kT where k is the Boltzmann constant (1.38 x 10^{-23} J/K) and T is the temperature in kelvins. At room temperature (approximately 25°C), the temperature in kelvins is T = 25 + 273.15 = 298.15 K.

Compare the average kinetic energy of nitrogen atom and nitrogen molecule

We know that at the same temperature, all gas particles have the same average kinetic energy. Therefore, we don't need to calculate the average kinetic energy of nitrogen atom and nitrogen molecule separately, as they will have the same kinetic energy at the same temperature.

Determine which has the larger kinetic energy

Since the average kinetic energy of nitrogen atom and nitrogen molecule is the same at room temperature, the correct answer is: c) They have the same energy.

Key concepts

Nitrogen Molecule

A nitrogen molecule is composed of two nitrogen atoms bound together. It is denoted as \( N_2 \). At room temperature, the kinetic energy of a nitrogen molecule is determined by how fast the entire molecule is moving. The molecule, being more massive than a single atom, moves more slowly on average, making its motion different from individual nitrogen atoms.

• Nitrogen molecules are the primary form of nitrogen in the atmosphere.
• They have more mass than individual atoms, which influences their speed for a given kinetic energy.

The average kinetic energy doesn't depend on mass when temperature is constant. So, both a single nitrogen atom and an \( N_2 \) molecule will have the same kinetic energy at the same temperature.

Nitrogen Atom

A nitrogen atom is a single particle of nitrogen, represented by \( N \). It is lighter than a nitrogen molecule. Despite its lighter weight, its kinetic energy is equal to that of a nitrogen molecule at a given temperature.

• Single atoms move faster than combined molecular forms at the same kinetic energy.
• They have applications in various scientific fields, particularly in understanding atomic behaviors.

Kinetic energy, defined by the formula \( K.E. = \frac{3}{2} kT \), remains constant for atoms and molecules at the same temperature, illustrating the relationships dictated by fundamental thermodynamic principles.

Boltzmann Constant

The Boltzmann constant is a crucial factor in thermodynamic calculations, denoted by \( k \) with a value of \( 1.38 \times 10^{-23} \) J/K. This constant connects temperature with energy, enabling the calculation of kinetic energy for gas particles like nitrogen.

• Essential in calculating average kinetic energies for gas particles.
• Relates macroscopic and microscopic physical quantities.

By using the formula \( K.E. = \frac{3}{2} kT \), where \( T \) is the temperature in kelvins, the Boltzmann constant helps determine that kinetic energy is independent of particle mass at constant temperature. It's at the heart of many fundamental principles in physical chemistry and statistical mechanics.