Question

What do we assume about the volume of the actual molecules themselves in a sample of gas, compared to the bulk volume of the gas overall? Why?

Short answer

In the ideal gas model, we assume that the volume of the actual gas molecules themselves is negligible compared to the bulk volume of the gas overall in order to simplify calculations and gas behaviors using the Ideal Gas Law (\[PV = nRT\]). However, this assumption becomes inaccurate when dealing with real gases under conditions like low temperatures and high pressures, where the finite size of gas molecules and intermolecular forces become significant. In such cases, advanced models like the van der Waals equation are required for more accurate predictions.

Step-by-step solution

Assumptions about the volume of gas molecules

In the ideal gas model, we assume that the volume of the actual gas molecules is negligible compared to the bulk volume of the gas overall. This means that we consider gas molecules as point-sized particles and do not take into account the actual space they occupy.

Reason for this assumption

This assumption is made to simplify the calculations and behaviors of gases. By considering their volume negligible compared to the overall volume, we can analyze gas behavior using mathematical equations, specifically the Ideal Gas Law, which states: \[PV = nRT\] Here, P represents pressure, V represents volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin. The ideal gas law is a simple, but powerful model that can predict the behavior of a gas under various conditions, such as changes in pressure, volume, and temperature. However, it is important to note that this assumption renders the ideal gas law inaccurate when dealing with real gases under certain conditions, including low temperatures and high pressures.

Ideal Gas vs. Real Gas

In real-world scenarios, gas molecules have a finite volume, and attractive and repulsive forces between them exist. These factors become significant under conditions of high pressure (where the volume of the gas is reduced) and low temperature (where the kinetic energy of the gas molecules decreases). In these situations, the ideal gas law will not accurately predict the behavior of real gases. We must then use more advanced models, such as the van der Waals equation, that take into account the finite size and intermolecular forces of gas molecules. In summary, we assume that the volume of gas molecules is negligible compared to the bulk volume of the gas to simplify the analysis of gas behavior, using models like the Ideal Gas Law. However, under specific conditions, we need to take the finite size of gas molecules and the forces between them into account for more accurate predictions.

Key concepts

Real Gases

In the real world, gases aren't just a collection of invisible, point-sized particles. Real gases consist of molecules that have definite volumes and exert forces upon each other. Unlike ideal gases, the behavior of real gases often varies from the predictions of the ideal gas law, especially under conditions of high pressure and low temperature. Under these conditions, the effects of the molecular volume and intermolecular forces become significant.
Real gases tend to compress less than ideal gases at high pressures because the volume of their molecules starts to play a crucial role. At lower temperatures, real gases may condense into liquids, demonstrating that their interactions are more complex than what the ideal gas law accounts for. These factors complicate the study of gases, necessitating more sophisticated models beyond the ideal gas law.

• Real gases have a finite volume.
• Intermolecular forces affect gas behavior.
• Deviations from ideal behavior become evident at high pressures and low temperatures.

Van der Waals Equation

To bridge the gap between ideal and real gases, the van der Waals equation introduces corrections to account for molecular volume and intermolecular forces. This equation modifies the ideal gas law to better predict the behavior of real gases:
\[\left( P + \frac{a}{V^2} \right) (V - b) = nRT\]
In this modified equation:

• a and b are constants specific to each gas, representing the strength of intermolecular attractions and the volume occupied by the molecules, respectively.
• P stands for pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

The van der Waals equation helps us understand real gas behaviors more accurately than the ideal gas law by including factors that account for non-ideal interactions and finite volumes.

Gas Behavior Assumptions

When we study gases, one fundamental assumption in the ideal gas law is that the molecules themselves occupy no space, acting as if they are point-sized and not exerting forces on each other. This simplifies calculations but can lead to inaccuracies with real gases, which have non-negligible volumes and exhibit forces between molecules.
This assumption works well under certain conditions where gases behave almost ideally, for instance, at high temperatures and low pressures. In these scenarios, molecules are far apart, and their negligible volume and interactions don't significantly impact the calculations. However, under different conditions, real gas behavior deviates from this model due to:

• Finite molecular sizes contributing to the overall volume.
• Intermolecular forces impacting gas interactions.

Volume of Gas Molecules

In the context of gas laws, especially when contrasting real with ideal gases, understanding the volume of gas molecules is crucial. In the ideal gas model, this volume is considered negligible compared to the gas's bulk volume, treating molecules as if they don't occupy space. This simplification facilitates calculations in an idealized context, making mathematical models like the ideal gas law neat and straightforward.
However, every gas molecule occupies some space. In reality, these volumes become significant under high pressure, where the overall space reduces, and need to be factored in for accurate predictions. The concept of the volume of gas molecules plays a vital role when employing advanced equations, like the van der Waals equation, where the parameter b is introduced to account for this occupied volume.

• Ideal gases assume molecules have no volume.
• Real gases occupy finite volumes.
• At high pressures, molecular volume significantly affects gas behavior.