Question

I'm looking at Elements of Physical Chemistry by Atkins and de Paula. In section 1A.3, they state Dalton's law as

The pressure exerted by a mixture of perfect gases is the sum of the pressures that each gas would exert if it were alone in the container at the same temperature:

p=pA+pB+...(1)

In this expression, pJ is the pressure that the gas J would exert if it were alone in the container at the same temperature. Dalton's law is strictly valid only for mixtures of perfect gases [...].

They then go on to define the partial pressure as

pJ=xJp(2)

where xJ is the mole fraction of J and p is the total pressure of the mixture.

So my question is this: Eq. 1 holds for all gases given the definition in Eq. 2. So when they say Dalton's law only holds for perfect gases, do they mean that because pJ in Dalton's law is not the same as Eq. 2, Dalton's law doesn't hold for all gases? Using the same notation for the two different meanings for pJ seems to be widespread and potentially quite confusing.

Answer 1

Dalton's Law of Partial Pressures is valid for ideal gases and states that the total pressure of a mixture of gases is the sum of the individual gases' partial pressures. The law assumes no interaction between gas molecules, which is not strictly true for real gases, potentially leading to deviations and some confusion with the notation used for partial pressures.

Step-by-step explanation:

The concept in question is Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases in the mixture. As per this law, each gas in a mixture contributes to the total pressure independently, reflecting the pressure it would exert if it occupied the entire volume alone. However, Dalton's Law is strictly applicable only to ideal or perfect gases.

This is because ideal gases are assumed not to interact and to have completely elastic collisions, whereas real gases experience intermolecular forces and non-elastic collisions, especially at high pressures and low temperatures, which can cause their behaviour to deviate from ideal.

The equation p=pA+pB+... is applicable to perfect gases where p represents the total pressure of the gas mixture, and pA, pB, etc., represent the partial pressures of the gases if each were alone in the container at the same temperature. The partial pressure itself can be defined as pJ=xJ*p where xJ is the mole fraction of gas J in the mixture and p is the total pressure. For non-ideal gases, these equations might not hold accurately due to deviations from ideal behaviour.

In summary, when Dalton's Law states that it holds for perfect gases, it implies that real gases may not follow the law strictly. The notation for pJ being used for both the pressure exerted by the gas when alone (in ideal conditions) and as the partial pressure in the mixture (expressed through mole fraction) may lead to confusion.

However, it is standard practice in chemistry to use this notation with the understanding that care must be taken when dealing with non-ideal gas behaviours.