Chemistry · Ch 10 — States of Matter

Deviation from Ideal behaviour

10.7

Deviation from Ideal behaviour

An ideal gas is one that exactly obeys the ideal gas equation at every temperature and pressure; rearranging $PV = nRT$ to $n = PV/RT$ , one mole of a perfectly ideal gas should give $PV/RT = 1$ at any pressure. A gas whose measured $PV/RT$ ratio departs from $1$ -- either above or below it -- is called a real gas, and every gas that actually exists shows this kind of deviation to some degree, especially at high pressure and low temperature. Two competing effects cause the deviation. First, real gas molecules DO attract each other (unlike the zero-attraction assumption of kinetic theory), and this attraction pulls molecules back slightly before they strike the container wall with their full, unimpeded force, so the measured pressure is somewhat LOWER than the ideal prediction. Second, at high pressure molecules are pushed so close together that short-range repulsive forces kick in and the molecules start behaving like small, hard, incompressible spheres -- here the molecules' own volume is no longer negligible next to the (now much smaller) space available for them to move in, so the measured volume tends to be HIGHER than the ideal prediction. At very low temperature, particle motion also slows enough for attractive forces to dominate and again pull the gas away from ideal behaviour. This deviation is quantified by the compressibility factor $Z = \frac{PV}{nRT} = \frac{V_{real}}{V_{ideal}}$ -- the ratio of a real gas's actual molar volume to the molar volume it would have if it behaved ideally at the same $T$ and $P$ . For a truly ideal gas $Z = 1$ at every pressure (a horizontal line on a $Z$ vs $P$ plot); $Z > 1$ (a positive deviation) means …

Table Table 10.6Table 10.6: Difference between ideal gas and real gas

Ideal gas | Real Gas

Strictly obeys Boyle's and Charles's law; PV/nRT = 1 | 1. Deviates from Boyle's and Charles's law at high pressure and low temperature; obeys them reasonably well only at low pressure and high temperature; PV/nRT not equal to 1
Molecules are perfectly elastic | 2. Molecules are not perfectly elastic
No attraction or repulsion between molecules; collisions lose no kinetic energy | 3. Intermolecular attraction is present, so collisions occur with some loss of kinetic energy
Actual volume of gas molecules is negligible compared to total gas volume | 4. Actual molecular volume becomes significant at high pressure and low temperature …

Figure Fig 10.14Fig. 10.14: Pressure vs volume plot for real and ideal gas

What this figure shows. A single P-V graph at a given temperature showing two curves: a smooth 'Ideal gas' curve following the expected Boyle's-law hyperbola shape all the way down, and a 'Real gas' curve that follows the ideal curve reasonably closely at low pressure/high volume but visibly departs from it (showing a noticeably larger measured volume than the ideal prediction) as pressure increases and volume decreases, illustrating the real-gas deviation described i …

Figure Fig 10.15Fig. 10.15: Compressibility factor Z vs pressure for several gases

What this figure shows. A graph with the compressibility factor Z = PV/nRT on the y-axis (ranging roughly 0.4 to 1.8) and pressure P (in bar, up to about 1000) on the x-axis. A horizontal dashed line at Z = 1 represents an ideal gas at every pressure. Curves for real gases N2, H2, O2, CH4 and CO2 are plotted around it: some (like H2) rise above Z = 1 fairly quickly as pressure increases (molecular-volume effects dominate), while others (like CH4 and CO2) first dip below Z = 1 at moderate pressure (attractive forces dominate there) before eventually curving back up above Z = 1 at very high pressure, illustrating that the size and even the direction of a real gas's deviation from ideal behaviour depends on …

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