Question

Why do we define percentage by volume for an ideal gas in a closed container in spite of that we know the ideal gas will occupy the volume of the whole container?

I have seen many people who prove that % by volume is equal to the percentage by mol for an ideal gas (at constant temperature and pressure conditions). They follow the following procedure...

PV = nRT

V = nRT/P

(let RT/P = K as a constant as pressure and temperature are constants)

V=Kn

as volume is directly proportional to the number of moles and hence % by volume is equal to the percentage by mole...

But the doubt is here, when we write PV=nRT for a gas in a closed container then we write volume as the volume of the container then where do we define % volume for gas?

Answer 1

Percentage by volume for ideal gases is used because, for an ideal gas mixture, the volume occupied by a gas is directly proportional to its moles, and thus its percentage by volume is equal to its percentage by moles.

Step-by-step explanation:

The question regarding why percentage by volume is used for ideal gases even though an ideal gas occupies the entire volume of the container concerns the application of the ideal gas law, PV = nRT.

When discussing gas mixtures, percentage by volume is often a useful concept because, according to Avogadro's Law, equal volumes of gases at the same temperature and pressure contain equal numbers of moles.

Consequently, for an ideal gas mixture, the percentage by volume of a particular gas is equal to its percentage by moles.

This is because the volume each gas occupies (assuming ideal behavior) is directly proportional to the number of moles of that gas in the mixture given constant temperature and pressure.

When we refer to the volume in the ideal gas equation, we are indeed discussing the volume of the entire container. The percentage by volume is defined with respect to the total volume occupied by the gas mixture.

Since each gas in a mixture will expand to occupy the full volume of the container, the percentage by volume can be seen as a way of expressing the contribution of each gas to the total pressure (partial pressure) according to Dalton's Law of Partial Pressures.