# When Z>1 are repulsive forces dominant or are attractive forces dominant?

According to PVreal = ZRT

If z >1 repulsive forces are dominant or are attractive forces? Different teachers are telling contradictory answers and after referring a few books, I have become more confused.

Points for ATTRACTIVE FORCES are dominant:

• At high pressure the molecules do not strike the walls with full impact as they are dragged back by attractive forces.
• When molecules are farther away from each other(as Vreal > Videal) the attractive forces are dominant.
• Repulsive force are dominant when he molecules are almost in contact .

Points for REPULSIVE FORCES are dominant:

• At high pressure the molecules are close each other that attractive forces are negligible but molecular size is significant.Thus repulsive forces are significant
• As volume of real gas is more than volume of ideal gas , the real gas is more difficult to compress.Thus repulsive forces are dominating.

There was a question where P = 12atm T = 350K and Z = 1.2(after calculation). It was given that repulsive force are dominant.But my teacher said it was wrong and it should be attractive forces.

Your arguments for attractive forces are not quite correct, particularly the first one, the other two are partly correct. The points for repulsive forces are more accurate but not completely correct.

The intermolecular potential energy is fixed by the type of molecule and varies with separation between molecules (e.g. a Lennard-Jones potential). The potential well formed by the interaction is short-range. It is effectively zero at about four to six molecular diameters decreases to negative values as the molecules approach one another (negative energy is attractive) but rapidly becomes positive ( repulsive) when the molecules are effectively in contact.The potential is unaffected by temperature and pressure.

The ratio $p\overline{V}/RT$ is called the compressibility ratio Z and is unity for an ideal gas. ($\overline V$ is the molar volume $V/n$). Ideal gases have no intermolecular potential, or size. Real gases differ primarily in their size and magnitude of their intermolecular potential energy and so deviations from $Z=1$ are to be expected. At all temperatures and pressures the molecules have an attractive potential that tries to pair up molecules, and repulsion on collision when the charge on the electrons in each molecule force them to repel one another.

It is the competition between attraction, repulsion and kinetic energy at a give temperature that determines the shape of the $Z ~ vs. p$ plot.

For molecules at low temperature the line of the graph $Z= p\overline{V}/RT$ vs. p dips down further below $Z=1$ than it does for the same molecules at higher temperatures. This is because at low temperatures the molecules have less kinetic energy ( so move more slowly) and are more influenced by attractive forces than at higher temperatures. This makes the actual volume of gas smaller than the ideal (as a larger fraction of molecules are paired up), which in turn makes Z smaller.

Similarly, at a given temperature, a larger negative Z is seen in gases with a larger attractive interaction, say $\ce{CO2, CH4 or ethene}$ compared to those with smaller attraction, e.g. $\ce{He or H2}$ .

At high temperature the molecules have more kinetic energy and so attractive interactions are relatively less important, and repulsion more so as the kinetic energy is larger. This makes the actual volume greater than the ideal and $Z>1$.