Question

What is the effect on the pressure of a gas if its temperature is increased at constant volume? (a) The pressure of the gas increases. (b) The pressure of the gas decreases. (c) The pressure of the gas remains same. (d) The pressure of the gas becomes double.

Short answer

The pressure of the gas increases at constant volume when its temperature is increased (option a).

Step-by-step solution

Understanding Gay-Lussac's Law

To determine the effect of temperature on the pressure of a gas at constant volume, refer to Gay-Lussac's Law. This law states that the pressure of a fixed mass of gas is directly proportional to its temperature (measured in Kelvin) when the volume is kept constant.

Exploring the Relationship Between Pressure and Temperature

According to the law, if the temperature of a gas increases, its pressure must also increase if the volume of the gas does not change. This is because an increase in temperature results in an increase in the kinetic energy of the gas particles, thus increasing the frequency and force of collisions with the container walls.

Choosing the Correct Option

Based on the direct relationship between temperature and pressure at constant volume, the pressure of the gas will increase if its temperature is raised. This aligns with option (a).

Key concepts

Understanding the Relationship Between Pressure and Temperature

The behavior of gases under various conditions is a fundamental topic in chemistry and physics. To grasp the effects of temperature changes on gas pressure, we look at Gay-Lussac's Law, a principle central to gas behavior. This law outlines that for a given mass of gas at a constant volume, its pressure is directly proportional to its temperature, provided the temperature is measured in Kelvin.

What does this proportional relationship mean? Simply put, if we heat a gas while keeping its volume fixed, its pressure will rise. The increase in temperature imparts more kinetic energy to the gas particles. Greater kinetic energy means the particles move faster and collide more often, and with greater force, against the container’s walls. These intensified collisions manifest as increased pressure. Conversely, if the temperature drops, the gas particles slow down, resulting in fewer and weaker collisions, hence lower pressure.

It's essential to understand that this law applies only when the volume remains unchanged. When volume does vary, different gas laws come into play. Remember, for real-world applications and safety—like when inflating a tire or cooking with a pressure cooker—it’s crucial to consider this relationship to avoid accidents caused by overpressure.

Unraveling Gas Laws

The behavior of gases is not governed by only one law, but a series. These fundamental principles are collectively known as Gas Laws, which describe how gases respond to changes in temperature, pressure, and volume. Gay-Lussac's Law is just one member of this family, alongside others such as Boyle's Law (pressure vs. volume) and Charles's Law (volume vs. temperature).

When combined, these individual laws underpin the Combined Gas Law, which allows us to calculate the pressure, volume, and temperature of a gas under different conditions. Moreover, when if we include the factor of the amount of gas (in moles), we arrive at the Ideal Gas Law, represented by the equation \( PV = nRT \). This equation is a cornerstone in the study of thermodynamics, providing a comprehensive model for predicting the behavior of gases under a multitude of conditions, except when gases are at very high pressure or low temperature, where they deviate from ideal behavior and we may need to consider real gas laws, like Van der Waals Equation.

Kinetic Energy of Gas Particles

The kinetic energy of gas particles is the energy they possess due to their motion. Kinetic energy is crucial in understanding the nature of gases. According to Kinetic Molecular Theory, gas particles are always in random, constant, straight-line motion, and the temperature of the gas reflects the average kinetic energy of these particles.

When the temperature increases, particles move faster because they gain kinetic energy. Faster movement results in more vigorous and frequent collisions against container walls, which is directly observable as increased pressure. In contrast, a decrease in temperature would result in lower kinetic energy, leading to less frequent and forceful collisions, and therefore, a reduction in pressure.

Kinetic energy also explains why, at the same temperature, lighter gas particles (such as hydrogen) will move faster than heavier ones (like oxygen), because kinetic energy for gases at a given temperature is more significant in lighter particles which leads to the concept of effusion and diffusion where lighter gases spread out faster than heavier ones.