The temperature of a 5.00-L container of N2 gas is increased from 20 °C to 250 °C. If the volume is held constant, predict qualitatively how this change affects the following: (a) the average kinetic energy of the molecules.

Verified step by step guidance

1. Identify the relationship between temperature and kinetic energy. According to the kinetic molecular theory, the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.
2. Convert the initial and final temperatures from Celsius to Kelvin for accurate calculations. Recall that the conversion formula is T(K) = T(°C) + 273.15.
3. Understand that since the volume is held constant and the temperature is increased, the pressure will change according to Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature when volume is constant.
4. Analyze how the increase in temperature from 20 °C to 250 °C affects the kinetic energy. Since the temperature increases, the average kinetic energy of the nitrogen molecules will also increase.
5. Conclude that the increase in temperature results in an increase in the average kinetic energy of the nitrogen molecules, leading to faster moving particles and higher collision frequency with the walls of the container.

Key Concepts

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of the motion of their molecules. It states that gas molecules are in constant, random motion and that the temperature of a gas is directly proportional to the average kinetic energy of its molecules. As temperature increases, the average speed and energy of the molecules also increase, leading to greater kinetic energy.

Temperature and Kinetic Energy Relationship

Temperature is a measure of the average kinetic energy of the particles in a substance. In gases, an increase in temperature results in an increase in the average kinetic energy of the molecules. This relationship is crucial for understanding how changes in temperature affect the motion and energy of gas molecules, particularly in a constant volume scenario.

Constant Volume Conditions

In a constant volume scenario, the pressure of a gas will change with temperature according to Gay-Lussac's Law. While the volume remains fixed, increasing the temperature leads to an increase in the average kinetic energy of the gas molecules, which in turn increases the pressure exerted by the gas on the walls of the container. This concept is essential for predicting the behavior of gases under varying thermal conditions.