According to the principle of corresponding states, what can be said about real gases at the same reduced volume and reduced temperature?

The principle of corresponding states posits that all gases, when expressed in terms of their reduced properties—such as reduced volume, reduced temperature, and reduced pressure—exhibit similar behavior. Reduced properties are defined as the ratio of the actual property of the gas to its critical property (e.g., reduced volume (v_r) = V/V_c, where V is the molar volume and V_c is the critical volume).

When real gases are at the same reduced volume and reduced temperature, they can be said to exert the same reduced pressure. This is a consequence of the fact that real gases, when scaled by their critical properties, should show comparable behavior under these conditions due to their similar intermolecular forces and characteristics.

In essence, by studying gases at these corresponding states, one can predict and model the behaviors of different gas types without requiring specific knowledge about their unique characteristics. This correlation is particularly useful because it allows chemists to apply results from one type of gas to another under similar thermodynamic conditions. Thus, when real gases share the same reduced volume and reduced temperature, they will have the same reduced pressure, confirming the fundamental concept behind the principle of corresponding states.