# Can steam be called the ideal gas

## The general gas equation¶

The equation of state for ideal gases in a closed system can also be written in the following form:

If you look at of a gas, the constant factor on the right-hand side of the above equation is equal to the general gas constant ; if you look at at particles, the constant is accordingly - times as big. The following applies to any amount of gas within a closed system:

This equation is referred to as the “general gas equation” and applies to a very good approximation for real gases even if the pressures are not too high.

Normal volume of a gas:

Equation (1) can be used, for example, to determine which volume the amount of substance of an ideal gas under normal conditions, i.e. at a pressure of and a temperature of occupies:

In the above calculation, the unit Joule was written as Newton times meter and the unit Pascal as Newton per square meter. The result is that one mole of an ideal gas (and to a good approximation also one mole of a real gas) has a volume of around occupies.

Particle number and molar mass

The general gas equation not only establishes a relationship between the three state variables pressure, volume and temperature, but also indicates a relationship to the number of particles. Since a substance amount of a number of corresponds to (“Avogadro constant”), follows as a further relationship between the amount of substance and particle number :

In a substance amount of of a gas are Contain particles. The amount of substance can in turn be determined by looking at the mass of a gas and its molar mass knows:

The molar mass of a gas can be based on the relative atomic mass of an element can be read from a periodic table of the elements. In the case of noble gases, the particles of which consist of individual atoms, the molar mass is identical to the relative atomic mass. With gases like oxygen or nitrogen whose particles consist of two-atom molecules, the molar mass corresponds to twice the relative atomic mass of the element.

*Examples:*

On the basis of the molar mass of a gas, the general gas equation can be used to determine, for example, its density at a certain pressure and a certain temperature:

For air, for example, applies under normal conditions, i.e. at and :

The unit Pascal was replaced by Newton per square meter and the unit Joule by Newton times meter. The density value of air calculated in this way agrees very well with experimental measurements.

### The Van der Waals equation¶

The general gas equation (1) only applies to a good approximation for gases with a low density. With high gas densities, for example with saturated steam, real gases can no longer be regarded as "ideal" gases. In this case, on the one hand, the interaction between the gas molecules and, on the other hand, the inherent volume of the gas particles must be considered. The so-called Van der Waals equation results from the general gas equation with the corresponding correction terms, which is used for Mole of a gas is as follows:

Here referred to the intrinsic volume of the gas particles; through the correction term the internal pressure caused by the interactions of the gas particles is taken into account.

In one -Diagram, the isotherms run above a certain temperature called "critical" just like the isotherms of ideal gases. Below the isotherms are bent in an S-shape.

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