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 summary, we assume that the volume of individual gas molecules is negligible compared to the bulk volume of the gas overall to simplify the mathematical model of an ideal gas and make calculations easier. This assumption works well for many gas samples, particularly at low pressures and high temperatures.

Step-by-step solution

Recall the Ideal Gas Law

The ideal gas law is a mathematical equation that describes the behavior of an ideal gas. It is given by the formula $PV=nRT$, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

Assumptions of the Ideal Gas Law

The ideal gas law is based on a few assumptions about the behavior of gases. These assumptions help to simplify the concepts and make calculations easier. One of these assumptions is that the individual gas molecules have negligible volume compared to the total volume of the gas.

Comparison of Molecular Volume and Bulk Gas Volume

This assumption implies that the volume occupied by the individual gas molecules is considered to be negligible, or insignificant, when compared to the overall volume of the gas sample. In other words, the size of the gas molecules is considered to be very small compared to the space between them.

Reason for the Assumption

The main reason behind this assumption is to simplify the mathematical model and to make calculations easier. An ideal gas is considered to have no interactions between the molecules and each molecule is considered to have no volume. Although in reality, molecules do have a definite volume and there can be interactions between them, the assumption enables the ideal gas law to work well for a wide range of gas samples under various conditions, especially at low pressures and high temperatures. In summary, we assume that the volume of individual gas molecules is negligible compared to the bulk volume of the gas overall to simplify the mathematical model of an ideal gas and make calculations easier. This assumption works well for many gas samples, particularly at low pressures and high temperatures.